# world.lapla.si — Laplace’s Mini World (拉普拉斯的迷你世界)

> Interactive 3D science models in the browser, each with a short illustrated essay and a laboratory to try things in. Chinese (zh) and English (en). No accounts, no ads. Licence: CC BY-NC 4.0.

Every model can be shown on its own, sized to its frame: https://world.lapla.si/embed/{lang}/{slug}/ (?chapter=<id>, ?lab=1, ?theme=light|dark, lab settings by id). The full catalog, with chapters and lab settings, is https://world.lapla.si/models.json. AI chats can connect to the MCP server at https://world.lapla.si/mcp (tools: search_models, show_model, list_chapters); oEmbed: https://world.lapla.si/oembed?url=<plate URL>.

When citing a plate, link its page (https://world.lapla.si/en/{slug}/ or https://world.lapla.si/zh/{slug}/, not the embed page) and name the site, e.g. Laplace’s Mini World, Plate 10, “How the Moon Moves the Sea”, https://world.lapla.si/en/tides/, CC BY-NC 4.0. Every plate page ends with its own citation line and carries schema.org LearningResource data.

## Catalog

- [API and MCP docs](https://world.lapla.si/en/api/) ([中文](https://world.lapla.si/zh/api/)): connecting the MCP server in ChatGPT, Claude and other clients; the fields of models.json; embed parameters; oEmbed; licence and how to cite
- [models.json](https://world.lapla.si/models.json): every plate with titles, summaries, chapters, embed URLs and lab settings
- [MCP server](https://world.lapla.si/mcp): Streamable HTTP, read-only
- Every plate's words as Markdown: https://world.lapla.si/{lang}/{slug}/index.html.md (the essay, notes, sources, licence and how to cite)
- [llms.txt](https://world.lapla.si/llms.txt): the short version of this file

## Nature / Space

- [Halley’s Comet Is Far Away. Its Dust Is Here. (哈雷彗星还在远方，它的尘埃先到了)](https://world.lapla.si/en/orionids/): plate 40. Every late October the Earth ploughs through dust shed by Halley’s Comet, and the Orionids streak across the night. In 2026 the best night is October 21 to 22. Markdown: [en](https://world.lapla.si/en/orionids/index.html.md), [中文](https://world.lapla.si/zh/orionids/index.html.md).
  - 中文: [哈雷彗星还在远方，它的尘埃先到了](https://world.lapla.si/zh/orionids/) — 每年十月下旬，地球都会穿过哈雷彗星撒下的尘埃，夜空里便下起猎户座流星雨。2026 年最盛的一夜，是 10 月 21 日到 22 日。
  - Halley’s Comet won’t be back until 2061, but every October the Earth runs into the dust it has scattered along its path. In 2026 the shower is strongest on the night of October 21 to 22: wait for the Moon to set, then look up before dawn.
  - Embed: https://world.lapla.si/embed/en/orionids/ · https://world.lapla.si/embed/zh/orionids/
  - Chapters: `cover` Halley’s Comet Is Far Away. Its Dust Is Here.; `sky` Orion Over Mount Fuji; `radiant` Out of One Point; `burn` A Speck of Dust, a Streak of Light; `halley` The Road Halley Travels; `headon` Head-On; `real` Last Year’s Meteors, Measured; `when` How to Watch in 2026; `lab` Your Turn
  - Lab settings: `play` Run time (1/0); `choice` Place (kawaguchiko | beijing | shanghai | hongkong | taipei | tokyo | singapore | london | newyork | sydney); `night` Night (-19–17, step 1); `time` Time (-6–6, step 0.05); `sky` Sky (0–3, step 1); `lines` Constellation lines (1/0); `trails` Long exposure (1/0); `labels` Labels (1/0)
- [The Shadow of the Moon (月亮的影子)](https://world.lapla.si/en/eclipse/): plate 03. The Sun is about 400 times wider than the Moon, and about 400 times farther away. That coincidence lets day turn to night for a few minutes. Markdown: [en](https://world.lapla.si/en/eclipse/index.html.md), [中文](https://world.lapla.si/zh/eclipse/index.html.md).
  - 中文: [月亮的影子](https://world.lapla.si/zh/eclipse/) — 太阳的直径约是月亮的四百倍，离我们也远了约四百倍。这个巧合，让白昼能在几分钟里变成黑夜。
  - The Sun is about 400 times wider than the Moon, and about 400 times farther away. That coincidence lets day turn to night for a few minutes. The Earth and Moon below are drawn to scale, in size and in distance.
  - Embed: https://world.lapla.si/embed/en/eclipse/ · https://world.lapla.si/embed/zh/eclipse/
  - Chapters: `cover` The Shadow of the Moon; `sizes` A Coincidence; `shadow` A Shadow in Two Parts; `tilt` Why Not Every Month; `seasons` Two Chances a Year; `iceland` August 12, 2026; `luxor` August 2, 2027; `annular` A Ring of Fire; `lab` Your Turn
  - Lab settings: `play` Run time (1/0); `rate` Time (2–60, step 1); `tilt` Tilt of the orbit (0–10, step 0.1); `distance` Moon’s distance (356500–406700, step 500); `labels` Labels (1/0)
- [Why Summer Is Warm (夏天为什么热)](https://world.lapla.si/en/seasons/): plate 05. Not because the Earth is closer to the Sun. In early January the Earth is at its closest — in the dead of the northern winter. Markdown: [en](https://world.lapla.si/en/seasons/index.html.md), [中文](https://world.lapla.si/zh/seasons/index.html.md).
  - 中文: [夏天为什么热](https://world.lapla.si/zh/seasons/) — 不是因为地球离太阳更近。一月初，地球离太阳最近，北半球却正是隆冬。
  - Not because the Earth is closer to the Sun. In early January the Earth is at its closest — in the dead of the northern winter. The answer lies in a tilt.
  - Embed: https://world.lapla.si/embed/en/seasons/ · https://world.lapla.si/embed/zh/seasons/
  - Chapters: `cover` Why Summer Is Warm; `tilt` A Tilted Axis; `june` June: The North Leans In; `beam` The Same Beam of Sunlight; `distance` Not Because It Is Closer; `poles` The Sun That Never Sets; `cities` A Year in Four Cities; `lab` Your Turn
  - Lab settings: `play` Let a year pass (1/0); `choice` City (beijing | singapore | sydney | tromso); `date` Date (1–365, step 1); `tilt` Tilt of the axis (0–40, step 0.1); `labels` Labels (1/0)
- [How the Moon Moves the Sea (月亮怎样拉动大海)](https://world.lapla.si/en/tides/): plate 10. Why are there two high tides a day? Because the Moon pulls the near ocean toward it — and leaves the far ocean behind. Markdown: [en](https://world.lapla.si/en/tides/index.html.md), [中文](https://world.lapla.si/zh/tides/index.html.md).
  - 中文: [月亮怎样拉动大海](https://world.lapla.si/zh/tides/) — 为什么一天有两次涨潮？答案是：月亮不只拉近处的海，也把远处的海“留”在了身后。
  - Why are there two high tides a day? Because the Moon pulls the near ocean toward it — and leaves the far ocean behind.
  - Embed: https://world.lapla.si/embed/en/tides/ · https://world.lapla.si/embed/zh/tides/
  - Chapters: `cover` How the Moon Moves the Sea; `pull` Pulled Harder Up Close; `two` Twice a Day; `sun` The Sun Pulls Too; `real` Three Real Coasts; `shape` The Shape of the Coast; `lab` Your Turn
  - Lab settings: `play` Run time (1/0); `sun` Sun’s tide-raising force (0–1, step 0.01); `bulge` Exaggerate bulges (0.3–2, step 0.05); `labels` Labels (1/0)
- [Why the Moon Changes Shape (月亮为什么会变脸)](https://world.lapla.si/en/moon/): plate 12. The Moon never changes shape. What changes is how much of its sunlit half we can see. Markdown: [en](https://world.lapla.si/en/moon/index.html.md), [中文](https://world.lapla.si/zh/moon/index.html.md).
  - 中文: [月亮为什么会变脸](https://world.lapla.si/zh/moon/) — 月亮从不改变形状。变的，是我们看到它被太阳照亮的那一半的多少。
  - The Moon never changes shape, and its phases are not the Earth’s shadow nibbling at it. What changes is how much of its sunlit half we can see from here.
  - Embed: https://world.lapla.si/embed/en/moon/ · https://world.lapla.si/embed/zh/moon/
  - Chapters: `cover` Why the Moon Changes Shape; `half` Always Half Lit; `orbit` Once Around; `sides` Right Side First, Then Left; `shadow` Not the Earth’s Shadow; `face` Always the Same Face; `tonight` Tonight’s Moon; `lab` Your Turn
  - Lab settings: `play` Run the month (1/0); `day` Days since new moon (0–29.530588853, step 0.1); `south` View from the south (1/0); `shadow` Earth’s shadow (1/0); `labels` Labels (1/0)
- [The Space Station Is Falling (一直在下落的空间站)](https://world.lapla.si/en/orbit/): plate 18. Astronauts float not because there is no gravity in space, but because they and their station are always falling. Markdown: [en](https://world.lapla.si/en/orbit/index.html.md), [中文](https://world.lapla.si/zh/orbit/index.html.md).
  - 中文: [一直在下落的空间站](https://world.lapla.si/zh/orbit/) — 宇航员飘浮着，不是因为太空里没有引力，而是因为他们和空间站一起，一直在往下掉。
  - Astronauts drift around the space station, but not because gravity has gone. The station and everyone in it are falling all the time — just moving sideways so fast that they never hit the ground.
  - Embed: https://world.lapla.si/embed/en/orbit/ · https://world.lapla.si/embed/zh/orbit/
  - Chapters: `cover` The Space Station Is Falling; `float` Gravity Is Still There; `cannon` Newton’s Cannon; `around` Falling Around the Earth; `escape` Getting Away; `now` Where the Station Is Now; `lab` Your Turn
  - Lab settings: `speed` Cannonball speed (3–12, step 0.05); `labels` Labels (1/0)
- [Why a Foucault Pendulum Turns (傅科摆为什么会转)](https://world.lapla.si/en/pendulum/): plate 22. A long pendulum swings back and forth, and the line of its swing slowly turns. What turns is the floor beneath it, and the Earth beneath the floor. Markdown: [en](https://world.lapla.si/en/pendulum/index.html.md), [中文](https://world.lapla.si/zh/pendulum/index.html.md).
  - 中文: [傅科摆为什么会转](https://world.lapla.si/zh/pendulum/) — 一个长摆来回摆动，摆动的方向慢慢转开。转的是摆下面的地板，和地板下面的地球。
  - A heavy bob hangs on a long wire and swings. After a few minutes the line of the swing has shifted; after a few hours, by tens of degrees. The pendulum keeps swinging the same way. The floor, with everyone on it, turns underneath.
  - Embed: https://world.lapla.si/embed/en/pendulum/ · https://world.lapla.si/embed/zh/pendulum/
  - Chapters: `cover` Why a Foucault Pendulum Turns; `pantheon` The Panthéon, 1851; `stars` The Floor Turns; `globe` Slower Away From the Poles; `tour` Four Places; `ring` Keeping It a Line; `pegs` A Ring of Pegs; `lab` The Bench
  - Lab settings: `play` Run (1/0); `choice` Place (paris | north | singapore | sydney); `lat` Latitude (-90–90, step 0.1); `stars` From the stars (1/0); `ring` Charron ring (1/0); `labels` Labels (1/0)
- [The Solar System Today (今天的太阳系)](https://world.lapla.si/en/planets/): plate 24. Where are the eight planets right now? The farther from the Sun, the slower they go, and the longer a lap takes. Markdown: [en](https://world.lapla.si/en/planets/index.html.md), [中文](https://world.lapla.si/zh/planets/index.html.md).
  - 中文: [今天的太阳系](https://world.lapla.si/zh/planets/) — 八颗行星此刻在哪里？离太阳越远的，走得越慢，绕一圈也越久。
  - This is the solar system as it is today: the eight planets where orbit data from NASA’s Jet Propulsion Laboratory puts them. The farther a planet is from the Sun, the slower it moves and the longer its year — a rule Johannes Kepler found four centuries ago.
  - Embed: https://world.lapla.si/embed/en/planets/ · https://world.lapla.si/embed/zh/planets/
  - Chapters: `cover` The Solar System Today; `today` The Inner Planets Now; `race` The Inside Track Is Faster; `outer` The Giants Outside; `light` How Long Sunlight Takes; `size` All in a Row; `lab` Your Turn
  - Lab settings: `play` Run time (1/0); `date` Date (-3650–3650, step 1); `speed` Time speed (5–400, step 5); `labels` Labels (1/0)
- [What Pushes a Rocket (火箭靠什么飞上天)](https://world.lapla.si/en/rocket/): plate 27. A rocket doesn’t push against the air. It throws a large part of itself backwards very fast, and the rest of it is pushed forwards. Markdown: [en](https://world.lapla.si/en/rocket/index.html.md), [中文](https://world.lapla.si/zh/rocket/index.html.md).
  - 中文: [火箭靠什么飞上天](https://world.lapla.si/zh/rocket/) — 火箭不是推着空气飞起来的。它把自己的一大部分高速向后扔出去，剩下的部分就被推向前。
  - A rocket can speed up in the airless vacuum of space, because it doesn’t fly by pushing on air. It burns its fuel into hot gas and blasts that gas backwards at tremendous speed. The more it throws out, and the faster, the faster what is left of the rocket goes.
  - Embed: https://world.lapla.si/embed/en/rocket/ · https://world.lapla.si/embed/zh/rocket/
  - Chapters: `cover` What Pushes a Rocket; `push` Throw Back, Move Forward; `equation` The Rocket Equation; `stages` Dropping It in Stages; `orbit` How Fast Is Fast Enough; `lab` Your Turn
  - Lab settings: `play` Launch (1/0); `ve` Exhaust speed (1.5–4.5, step 0.05); `fuel` Share of the rocket that is fuel (0.5–0.9, step 0.01); `staging` Three stages (1/0); `labels` Labels (1/0)
- [Where Not Even Light Escapes (连光都逃不出来的地方)](https://world.lapla.si/en/blackhole/): plate 38. A black hole packs so much matter into so small a space that not even light can get out. It is dark itself, but the light it bends around it draws a bright ring. Markdown: [en](https://world.lapla.si/en/blackhole/index.html.md), [中文](https://world.lapla.si/zh/blackhole/index.html.md).
  - 中文: [连光都逃不出来的地方](https://world.lapla.si/zh/blackhole/) — 黑洞把大量物质挤在极小的地方，引力大到连光都逃不出来。它自己是黑的，可周围被它弯折的光，会画出一圈明亮的光环。
  - Squeeze a heavy enough star into a small enough space and its gravity grows so strong that not even light can escape: a black hole. You can’t see the hole itself, but the light around it is bent into a bright ring. In 2019, people saw a picture of such a ring for the first time.
  - Embed: https://world.lapla.si/embed/en/blackhole/ · https://world.lapla.si/embed/zh/blackhole/
  - Chapters: `cover` Where Not Even Light Escapes; `dark` The Edge of No Return; `bend` Bending Light; `ring` Where the Ring Comes From; `bright` Bright on One Side; `photo` The First Picture; `lab` Your Turn
  - Lab settings: `view` View (2–88, step 1); `disc` Accretion disc (1/0); `labels` Labels (1/0)

## Nature / Earth & Sky

- [How Rain Carves a Mountain (雨水如何雕刻一座山)](https://world.lapla.si/en/erosion/): plate 01. A single storm changes almost nothing. But the rain never stops. Markdown: [en](https://world.lapla.si/en/erosion/index.html.md), [中文](https://world.lapla.si/zh/erosion/index.html.md).
  - 中文: [雨水如何雕刻一座山](https://world.lapla.si/zh/erosion/) — 一场雨几乎改变不了什么，可雨从未停过。
  - A single storm changes almost nothing. But the rain never stops. The island below will live through an age of it in a few minutes.
  - Embed: https://world.lapla.si/embed/en/erosion/ · https://world.lapla.si/embed/zh/erosion/
  - Chapters: `cover` How Rain Carves a Mountain; `island` A New Island; `runoff` Water Knows Only Downhill; `valleys` The Valleys Deepen; `coast` Where the Soil Goes; `forest` A Forest Is a Net; `compare` Before and After; `taranaki` Taranaki: The Beginning; `kauai` Kauai: Much Later; `canyon` Grand Canyon: One River, Five or Six Million Years; `lab` Your Turn
  - Lab settings: `play` Start the rain (1/0); `choice` Place (island | taranaki | kauai | grand-canyon); `rain` Rainfall (0.3–3, step 0.1); `soft` Soil (0.3–3, step 0.1); `trees` Forest (1/0); `rivers` Streams (1/0); `labels` Labels (1/0); `sound` Sound (1/0)
- [The Wave That Hides in Deep Water (藏在深海里的浪)](https://world.lapla.si/en/tsunami/): plate 02. Out at sea it is almost impossible to notice. At the coast it can drown a town. Markdown: [en](https://world.lapla.si/en/tsunami/index.html.md), [中文](https://world.lapla.si/zh/tsunami/index.html.md).
  - 中文: [藏在深海里的浪](https://world.lapla.si/zh/tsunami/) — 在大洋中央，它几乎无法察觉；到了岸边，它能淹没一座城镇。
  - Out at sea, a tsunami is almost impossible to notice. At the coast, it can drown a town. The stretch of coast below shows what happens in between.
  - Embed: https://world.lapla.si/embed/en/tsunami/ · https://world.lapla.si/embed/zh/tsunami/
  - Chapters: `cover` The Wave That Hides in Deep Water; `calm` Wind Stirs Only the Surface; `quake` The Seafloor Lurches; `deep` As Fast as a Jet, and Nearly Invisible; `retreat` When the Sea Pulls Back; `shore` Shallow Water Makes It Stand Up; `runup` Not One Wave but Many; `pacific` March 11, 2011; `lab` Your Turn
  - Lab settings: `play` Run time (1/0); `slip` Earthquake size (1–10, step 0.5); `rate` Time (30–600, step 10); `sink` Landward side sinks (1/0); `colors` Color the wave (1/0); `labels` Labels (1/0)
- [The Engine of a Hurricane (飓风的引擎)](https://world.lapla.si/en/hurricane/): plate 04. It runs on warm water, and the turning Earth sets it spinning. Markdown: [en](https://world.lapla.si/en/hurricane/index.html.md), [中文](https://world.lapla.si/zh/hurricane/index.html.md).
  - 中文: [飓风的引擎](https://world.lapla.si/zh/hurricane/) — 它靠暖海运转，地球的自转让它旋转起来。
  - It runs on warm water, and the turning Earth sets it spinning. Above the patch of ocean below, a storm is taking shape.
  - Embed: https://world.lapla.si/embed/en/hurricane/ · https://world.lapla.si/embed/zh/hurricane/
  - Chapters: `cover` The Engine of a Hurricane; `engine` The Warmth of the Sea Is the Fuel; `spin` The Spinning Earth Sets It Turning; `eye` The Eye; `equator` No Hurricanes at the Equator; `land` After Landfall; `isabel` Isabel, 2003; `lab` Your Turn
  - Lab settings: `play` Let it develop (1/0); `sst` Sea temperature (24–31, step 0.1); `lat` Latitude (-30–30, step 0.5); `land` Make landfall (1/0); `cut` Cut it open (1/0); `labels` Labels (1/0)
- [Curtains in the Sky (天上的帘幕)](https://world.lapla.si/en/aurora/): plate 11. An aurora is light given off when electrons from space crash into the air high overhead. Markdown: [en](https://world.lapla.si/en/aurora/index.html.md), [中文](https://world.lapla.si/zh/aurora/index.html.md).
  - 中文: [天上的帘幕](https://world.lapla.si/zh/aurora/) — 极光是太空里飞来的电子，撞上高空的空气时发出的光。
  - An aurora is light given off when electrons from space crash into the air high overhead. Why does it appear mostly near the poles, and why is it green and red?
  - Embed: https://world.lapla.si/embed/en/aurora/ · https://world.lapla.si/embed/zh/aurora/
  - Chapters: `cover` Curtains in the Sky; `wind` A Wind From the Sun; `field` Only in Two Rings; `abisko` A Valley Under the Oval; `curtain` Curtains a Hundred Kilometers High; `colours` Green, Red and Pink; `storm` When the Sun Is Busy; `now` The Aurora Right Now; `lab` Your Turn
  - Lab settings: `play` Let the solar wind blow (1/0); `activity` Solar activity (0–1, step 0.01); `lines` Field lines (1/0); `labels` Labels (1/0)
- [The Cracks in the Earth (地球的裂缝)](https://world.lapla.si/en/quakes/): plate 14. A year’s 7,700 strong earthquakes fall mostly along a few lines: the edges of the pieces of the Earth’s shell. Markdown: [en](https://world.lapla.si/en/quakes/index.html.md), [中文](https://world.lapla.si/zh/quakes/index.html.md).
  - 中文: [地球的裂缝](https://world.lapla.si/zh/quakes/) — 一年里七千多次较强的地震，大多排在同几条线上：那是地壳碎片相接的地方。
  - Put a year of earthquakes on the globe and they do not scatter at random. They line up along a few thin seams — the cracks in the Earth’s hard outer shell.
  - Embed: https://world.lapla.si/embed/en/quakes/ · https://world.lapla.si/embed/zh/quakes/
  - Chapters: `cover` The Cracks in the Earth; `year` A Year of Earthquakes; `plates` A Shell in Pieces; `kinds` Three Ways to Meet; `speed` As Slow as Fingernails; `deep` The Sinking Plate; `size` One Step Up; `now` This Week; `lab` Your Turn
  - Lab settings: `play` Run the year (1/0); `time` Date (0–365, step 1); `mag` Smallest magnitude (4.5–7.5, step 0.1); `bounds` Plate boundaries (1/0); `labels` Labels (1/0)
- [Where Volcanoes Come From (火山从哪里来)](https://world.lapla.si/en/volcano/): plate 19. There is no sea of magma under the crust. Magma forms in only a few kinds of places, and that is where volcanoes grow. Markdown: [en](https://world.lapla.si/en/volcano/index.html.md), [中文](https://world.lapla.si/zh/volcano/index.html.md).
  - 中文: [火山从哪里来](https://world.lapla.si/zh/volcano/) — 地球的地壳下面并没有一片岩浆海。岩浆只在少数几种地方生成，火山也就只长在那里。
  - Beneath the crust there is no sea of melted rock. The rock inside the Earth is almost entirely solid; rock melts only in a few special kinds of places, and that is where volcanoes grow.
  - Embed: https://world.lapla.si/embed/en/volcano/ · https://world.lapla.si/embed/zh/volcano/
  - Chapters: `cover` Where Volcanoes Come From; `where` The World’s Volcanoes; `dive` A Sinking Plate Carries Water; `apart` Where Plates Pull Apart; `hotspot` Hot Spots; `chain` A Chain That Tells Time; `fuji` A Cone Above Sinking Plates; `shield` A Shield Over a Hot Spot; `base` Measured From Its Base; `now` Erupting Lately; `lab` Your Turn
  - Lab settings: `play` Move the plate (1/0); `speed` Plate speed (2–20, step 0.5); `labels` Labels (1/0)
- [Where a Compass Points (指南针指向哪里)](https://world.lapla.si/en/compass/): plate 23. A compass doesn’t point at the North Pole. It lines up with Earth’s magnetic field — and the magnetic pole it heads for keeps moving. Markdown: [en](https://world.lapla.si/en/compass/index.html.md), [中文](https://world.lapla.si/zh/compass/index.html.md).
  - 中文: [指南针指向哪里](https://world.lapla.si/zh/compass/) — 指南针并不指向北极点，而是顺着地球的磁场。那个它“指着”的磁北极，还在一年年地移动。
  - A compass needle doesn’t point at the North Pole. It lines up with the Earth’s magnetic field, and the north magnetic pole lies hundreds of kilometres from the North Pole and keeps moving: in recent decades it has been racing from northern Canada towards Siberia.
  - Embed: https://world.lapla.si/embed/en/compass/ · https://world.lapla.si/embed/zh/compass/
  - Chapters: `cover` Where a Compass Points; `needle` A Little Magnet That Turns; `field` Invisible Field Lines; `notnorth` Magnetic North Isn’t True North; `wander` A Pole That Walks; `why` A Dynamo Deep Inside; `lab` Your Turn
  - Lab settings: `play` Run the years (1/0); `year` Year (1590–2025, step 1); `labels` Labels (1/0)
- [Seeing Through the Earth With Earthquakes (用地震看穿地球)](https://world.lapla.si/en/core/): plate 25. No one has been to the centre of the Earth. We know it holds a liquid outer core and a solid inner core because earthquake waves went for us. Markdown: [en](https://world.lapla.si/en/core/index.html.md), [中文](https://world.lapla.si/zh/core/index.html.md).
  - 中文: [用地震看穿地球](https://world.lapla.si/zh/core/) — 没有人去过地心。我们知道地球里面有一个液态的外核和一个固态的内核，是因为地震波替我们去了。
  - The deepest hole ever drilled is 12 kilometres deep — less than a five-hundredth of the way to the centre. Yet we know the Earth has a ball of liquid iron at its heart, with a solid ball inside that. Earthquake waves told us.
  - Embed: https://world.lapla.si/embed/en/core/ · https://world.lapla.si/embed/zh/core/
  - Chapters: `cover` Seeing Through the Earth With Earthquakes; `waves` Two Kinds of Wave; `bend` Curving Paths; `sshadow` The Missing S Waves; `shadow` The P-Wave Shadow; `lehmann` Lehmann’s Inner Core; `lab` Your Turn
  - Lab settings: `play` Send a burst of waves (1/0); `choice` Wave (P | S); `angle` Angle leaving the quake (1–85, step 0.5); `labels` Labels (1/0)
- [Why Clouds Don’t Fall (云为什么不会掉下来)](https://world.lapla.si/en/cloud/): plate 30. An ordinary cumulus cloud holds hundreds of tonnes of water, yet it floats. The secret is how astonishingly small its droplets are. Markdown: [en](https://world.lapla.si/en/cloud/index.html.md), [中文](https://world.lapla.si/zh/cloud/index.html.md).
  - 中文: [云为什么不会掉下来](https://world.lapla.si/zh/cloud/) — 一朵普通的积云里有几百吨水，却稳稳地飘在天上。秘密在于云里的水滴小得出奇。
  - A fluffy cumulus cloud holds hundreds of tonnes of water, yet there it floats. Not because water is lighter than air, but because its droplets are so tiny they hardly fall at all.
  - Embed: https://world.lapla.si/embed/en/cloud/ · https://world.lapla.si/embed/zh/cloud/
  - Chapters: `cover` Why Clouds Don’t Fall; `heavy` Hundreds of Tonnes of Fluff; `slow` A Very Slow Fall; `grow` A Million Into One; `shape` Raindrops Aren’t Teardrop-Shaped; `lab` Your Turn
  - Lab settings: `size` Drop diameter (-2–0.7781512503836436, step 0.01); `updraft` Rising air (0–5, step 0.05); `labels` Labels (1/0)
- [See the Flash, Then Hear the Thunder (先看见闪电，再听见雷)](https://world.lapla.si/en/thunder/): plate 33. Lightning and thunder happen at the same moment, but light arrives almost at once while sound covers only about 340 metres a second. Count the seconds between them and you know how far away the storm is. Markdown: [en](https://world.lapla.si/en/thunder/index.html.md), [中文](https://world.lapla.si/zh/thunder/index.html.md).
  - 中文: [先看见闪电，再听见雷](https://world.lapla.si/zh/thunder/) — 闪电和雷声是同时发生的，可光几乎一瞬间就到，声音却每秒只走三百多米。数一数中间隔了几秒，就知道雷暴有多远。
  - Lightning and thunder happen at the same instant, in the same place. You see the flash first and hear the thunder later because sound is far slower than light. Count the seconds in between and you can work out how far away the storm is.
  - Embed: https://world.lapla.si/embed/en/thunder/ · https://world.lapla.si/embed/zh/thunder/
  - Chapters: `cover` See the Flash, Then Hear the Thunder; `flash` Made Together, Arriving Apart; `count` Three Seconds, One Kilometre; `rumble` Why Thunder Rumbles; `where` Where Lightning Strikes Most; `catatumbo` The Lighthouse of Catatumbo; `safe` When Thunder Roars, Go Indoors; `lab` Your Turn
  - Lab settings: `distance` Storm distance (1–20, step 0.5); `labels` Labels (1/0)
- [The V Behind a Ship (船尾的 V 字)](https://world.lapla.si/en/wake/): plate 35. A big ship, a small boat, even a swimming duck: the V-shaped wake behind them opens at almost exactly the same angle, about 19.5° on each side. Markdown: [en](https://world.lapla.si/en/wake/index.html.md), [中文](https://world.lapla.si/zh/wake/index.html.md).
  - 中文: [船尾的 V 字](https://world.lapla.si/zh/wake/) — 大船、小艇，甚至一只游泳的鸭子，身后拖出的 V 字形水波，张开的角度几乎一模一样：两边各约 19.5°。
  - Look down on a moving ship and you will see a V of waves trailing behind it. Strangely, for most boats, fast or slow, giant ship or duck, the V opens at nearly the same angle: about 19.5° on each side.
  - Embed: https://world.lapla.si/embed/en/wake/ · https://world.lapla.si/embed/zh/wake/
  - Chapters: `cover` The V Behind a Ship; `wake` A V Behind; `same` Fast or Slow, the Same; `why` Why 19.5°; `two` Two Kinds of Wave; `fast` Fast Boats Make Narrower Vs; `lab` Your Turn
  - Lab settings: `speed` Ship speed (3–14, step 0.1); `lines` Angle lines (1/0); `labels` Labels (1/0)
- [Ice Rings Around the Sun (太阳周围的冰晶光环)](https://world.lapla.si/en/halos/): plate 49. In thin high cloud, the ice crystals are tiny hexagonal prisms. Sunlight passing through them paints rings, spots and coloured arcs around the Sun. Markdown: [en](https://world.lapla.si/en/halos/index.html.md), [中文](https://world.lapla.si/zh/halos/index.html.md).
  - 中文: [太阳周围的冰晶光环](https://world.lapla.si/zh/halos/) — 高空薄云里的冰晶是一个个六棱柱。阳光穿过它们，在太阳四周画出光环、光斑和彩色的弧。
  - Cirrostratus is thin enough for the Sun to shine through. Its ice crystals are small hexagonal prisms. Light crossing them is turned through an angle, and it gathers where that turn is smallest: a ring of light 22° from the Sun.
  - Embed: https://world.lapla.si/embed/en/halos/ · https://world.lapla.si/embed/zh/halos/
  - Chapters: `cover` Ice Rings Around the Sun; `ring` A Ring 22° from the Sun; `crystal` Every Crystal Is a Prism; `minimum` Light Crowds at the Smallest Turn; `colour` Red on the Inside; `sundogs` Sundogs: Spots Beside the Sun; `arcs` More Arcs; `clouds` Why Not Every Cloud; `lab` The Bench
  - Lab settings: `turn` Turntable (18–80, step 0.1); `random` Tumbling (1/0); `plates` Level plates (1/0); `columns` Level columns (1/0); `labels` Labels (1/0)
- [Why Rivers Wind (河流为什么弯来弯去)](https://world.lapla.si/en/meander/): plate 50. Rivers on plains are rarely straight. In each bend the water swirls, cutting the outer bank and building the inner one, until the loop is cut off and left as an oxbow lake. Markdown: [en](https://world.lapla.si/en/meander/index.html.md), [中文](https://world.lapla.si/zh/meander/index.html.md).
  - 中文: [河流为什么弯来弯去](https://world.lapla.si/zh/meander/) — 平原上的河很少是直的。弯道里水打着旋，冲外岸、淤内岸，弯越走越大，直到被截断，留下一个牛轭湖。
  - Rivers on plains are rarely straight. In each bend the water swirls: it cuts away the outer bank and piles sand on the inner one, so the bend grows and slowly moves downstream. When a loop gets too tight, the river cuts across its neck, and the old loop is left behind as a crescent lake.
  - Embed: https://world.lapla.si/embed/en/meander/ · https://world.lapla.si/embed/zh/meander/
  - Chapters: `cover` Why Rivers Wind; `wiggle` Rivers on Plains Are Rarely Straight; `spiral` In a Bend, the Water Spirals; `banks` The Outer Bank Goes, the Inner Bank Grows; `grow` A Small Bend Grows; `cutoff` Cutoffs and Oxbow Lakes; `scale` Bends Scale with the River; `real` The Same River from Orbit; `lab` The Bench
  - Lab settings: `play` Let time run (1/0); `rate` Bank erodibility (0.5–2, step 0.05); `spiral` Secondary flow (1/0); `labels` Labels (1/0)

## Nature / Life & Medicine

- [The Arithmetic of a Sunflower (向日葵的算术)](https://world.lapla.si/en/sunflower/): plate 06. Count the spirals its seeds make, and you will arrive at a famous sequence of numbers. Markdown: [en](https://world.lapla.si/en/sunflower/index.html.md), [中文](https://world.lapla.si/zh/sunflower/index.html.md).
  - 中文: [向日葵的算术](https://world.lapla.si/zh/sunflower/) — 数一数它的种子排成的螺旋，你会数到一串著名的数字。
  - Count the spirals its seeds make, and you will arrive at a famous sequence of numbers. All it takes to produce them is a single angle.
  - Embed: https://world.lapla.si/embed/en/sunflower/ · https://world.lapla.si/embed/zh/sunflower/
  - Chapters: `cover` The Arithmetic of a Sunflower; `count` Count Them; `fib` A Famous Sequence; `angle` Turn by 137.5 Degrees; `other` Even Slightly Off Won’t Do; `why` Nobody Is Counting; `real` 657 Sunflowers; `lab` Your Turn
  - Lab settings: `play` Grow them one by one (1/0); `angle` Turn per seed (90–180, step 0.05); `seeds` Number of seeds (50–2400, step 10); `left` Mark spirals one way (1/0); `right` Mark spirals the other way (1/0); `labels` Labels (1/0)
- [No Bird in Charge (没有领头的鸟)](https://world.lapla.si/en/murmuration/): plate 09. Thousands of starlings turn together at dusk like a shape-shifting cloud of smoke. No one is giving orders. Markdown: [en](https://world.lapla.si/en/murmuration/index.html.md), [中文](https://world.lapla.si/zh/murmuration/index.html.md).
  - 中文: [没有领头的鸟](https://world.lapla.si/zh/murmuration/) — 几千只椋鸟在黄昏里一起转向，像一团会变形的烟。没有谁在指挥。
  - Thousands of starlings turn together at dusk like a shape-shifting cloud of smoke. No one is giving orders; each bird watches only a few of its neighbors.
  - Embed: https://world.lapla.si/embed/en/murmuration/ · https://world.lapla.si/embed/zh/murmuration/
  - Chapters: `cover` No Bird in Charge; `cloud` A Cloud That Changes Shape; `rules` Three Rules; `seven` Watching Six or Seven; `wave` A Falcon; `why` Why Gather at All; `lab` Your Turn
  - Lab settings: `play` Release a falcon (1/0); `k` Neighbors each bird watches (1–20, step 1); `align` Fly the way they fly (0–3, step 0.05); `cohere` Move toward them (0–2, step 0.05); `separate` Keep your distance (0–4, step 0.05); `labels` Labels (1/0)
- [Where Spots and Stripes Come From (斑点和条纹从哪里来)](https://world.lapla.si/en/patterns/): plate 16. A leopard’s spots and a fish’s stripes may come from the same simple recipe: two ingredients, one fast and one slow. Markdown: [en](https://world.lapla.si/en/patterns/index.html.md), [中文](https://world.lapla.si/zh/patterns/index.html.md).
  - 中文: [斑点和条纹从哪里来](https://world.lapla.si/zh/patterns/) — 豹子的斑点、鱼身上的条纹，可能都出自同一个简单的配方：两种东西，一种跑得快，一种跑得慢。
  - Nobody paints the spots on a leopard or draws the stripes on a fish. In 1952 the mathematician Alan Turing realized that if two substances react with each other while spreading at different speeds, a pattern can grow all by itself.
  - Embed: https://world.lapla.si/embed/en/patterns/ · https://world.lapla.si/embed/zh/patterns/
  - Chapters: `cover` Where Spots and Stripes Come From; `recipe` A Copier and Its Fuel; `spacing` Keeping Their Distance; `recipes` Change the Recipe; `size` Bigger Body, More Spots; `real` Real Animals; `lab` Your Turn
  - Lab settings: `play` Let it grow (1/0); `choice` Recipe (spots | stripes | holes); `labels` Labels (1/0)
- [The Breathing Planet (会呼吸的地球)](https://world.lapla.si/en/breath/): plate 20. A tree’s wood is made mostly from air. Every summer the northern forests breathe in together, and the whole atmosphere holds less carbon dioxide. Markdown: [en](https://world.lapla.si/en/breath/index.html.md), [中文](https://world.lapla.si/zh/breath/index.html.md).
  - 中文: [会呼吸的地球](https://world.lapla.si/zh/breath/) — 一棵大树的木头，大部分来自空气。每年夏天，北半球的森林一起吸气，整个大气里的二氧化碳都会变少。
  - Most of a tree’s wood comes not from the soil but from the air. Every summer, countless leaves across the north breathe in together — and even the air high on a Hawaiian volcano changes.
  - Embed: https://world.lapla.si/embed/en/breath/ · https://world.lapla.si/embed/zh/breath/
  - Chapters: `cover` The Breathing Planet; `leaf` A Leaf Is a Factory; `air` Trees Are Made of Air; `breathe` One Deep Breath a Year; `north` The North Breathes Harder; `rise` Beyond the Breathing; `lab` Your Turn
  - Lab settings: `play` Run the year (1/0); `day` Day of the year (0–364, step 1); `labels` Labels (1/0)
- [MRI Scanner (磁共振成像仪)](https://world.lapla.si/en/mri/): plate F03. A clinical MRI scanner: a superconducting magnet, gradient coils and RF coils, one inside another. Hydrogen nuclei precess in the field; their signal fills k-space, and a Fourier transform turns it into an image. Markdown: [en](https://world.lapla.si/en/mri/index.html.md), [中文](https://world.lapla.si/zh/mri/index.html.md).
  - 中文: [磁共振成像仪](https://world.lapla.si/zh/mri/) — 一台临床磁共振扫描仪：超导磁体、梯度线圈、射频线圈，一层套一层。氢原子核在磁场里进动，信号填满 k 空间，再经傅里叶变换成像。
  - Magnetic resonance imaging uses no X-rays. It sets the hydrogen nuclei in the body precessing in step in a strong magnetic field, reads the signal they give off with radio waves, and computes a cross-section from it.
  - Embed: https://world.lapla.si/embed/en/mri/ · https://world.lapla.si/embed/zh/mri/
  - Chapters: `cover` MRI Scanner; `detail` A Millimetre of Soft Tissue; `spins` Ten in a Million; `resonance` 42.58 MHz per Tesla; `relax` T1 and T2; `section` Cut Open: Layer within Layer; `magnet` Coils at 4 Kelvin; `gradients` Position Becomes Frequency; `rf` Sending and Receiving; `kspace` k-Space; `room` Shielded Room, Safety Zone; `apart` Taken Apart; `lab` Field Strength
  - Lab settings: `choice` weighted (t1 | t2); `labels` Labels (1/0)
- [Surgical Robot (手术机器人)](https://world.lapla.si/en/surgical-robot/): plate F04. The surgeon operates from a console nearby; the arms pivot each instrument about its incision. Hand motion is scaled down and stripped of tremor on its way to a tip 8 mm across. Markdown: [en](https://world.lapla.si/en/surgical-robot/index.html.md), [中文](https://world.lapla.si/zh/surgical-robot/index.html.md).
  - 中文: [手术机器人](https://world.lapla.si/zh/surgical-robot/) — 医生坐在一旁操纵，机械臂让器械绕着切口转动。手的动作被缩小、滤去颤抖，再传到 8 毫米粗的器械尖上。
  - Laparoscopic surgery works through a few holes 8 to 12 mm wide in the body wall. Robot-assisted surgery uses the same approach, but the surgeon no longer holds the instruments: from a console, the hands’ motion is scaled down, stripped of tremor, and passed by arms at the bedside to the instruments inside. The most widely used system is the da Vinci.
  - Embed: https://world.lapla.si/embed/en/surgical-robot/ · https://world.lapla.si/embed/zh/surgical-robot/
  - Chapters: `cover` Surgical Robot; `scale` Eight Millimetres; `fulcrum` A Fulcrum in the Body Wall; `rcm` The Point That Stays Still; `section` Cut Open: Cables in the Wrist; `console` The Surgeon’s Console; `cart` Four Arms at the Bedside; `wrist` Seven Degrees of Freedom; `scaling` Scaled Down, Tremor Out; `apart` An Instrument Taken Apart; `limits` What It Can’t Do; `lab` Hand and Tip
  - Lab settings: `labels` Labels (1/0)
- [A Pattern Painted One Line at a Time (壳口一行行画出的花纹)](https://world.lapla.si/en/seashell/): plate 48. The triangles on a cone shell are painted at the edge of its opening, one line at a time. Each line is set by the cells along that edge: where one grows strong, it holds its neighbours back. Markdown: [en](https://world.lapla.si/en/seashell/index.html.md), [中文](https://world.lapla.si/zh/seashell/index.html.md).
  - 中文: [壳口一行行画出的花纹](https://world.lapla.si/zh/seashell/) — 芋螺壳上的三角形，是在壳口边缘一行一行画上去的。每一行由边缘上的细胞决定：一处变强，就压住旁边。
  - A shell grows only at its lip. Each new strip of shell keeps the pigment the lip carried at that moment. Turn after turn, the surface becomes a picture of time.
  - Embed: https://world.lapla.si/embed/en/seashell/ · https://world.lapla.si/embed/zh/seashell/
  - Chapters: `cover` A Pattern Painted One Line at a Time; `lip` Growing Only at the Edge; `record` A Picture of Time; `rule` Boost Yourself, Hold Back Your Neighbours; `waves` Waves That Vanish When They Meet; `kinds` One Set of Equations, Several Patterns; `automaton` Like a Cellular Automaton, but Not One; `spiral` Every Turn Grows by the Same Factor; `lab` The Bench
  - Lab settings: `choice` Pattern (textile | porphyria | stripes | dots); `production` Activator made (0.6–1.6, step 0.01); `decay` Inhibitor breakdown (0.5–2, step 0.01); `flatten` Flatten (1/0); `labels` Labels (1/0)
- [Hearing a Moth in the Dark (在黑暗里听见飞蛾)](https://world.lapla.si/en/echo/): plate 52. A bat hunts at night by its own voice. It sends out calls too high for us to hear and listens for the echo off a moth; how late the echo comes back tells it how far away the moth is. Markdown: [en](https://world.lapla.si/en/echo/index.html.md), [中文](https://world.lapla.si/zh/echo/index.html.md).
  - 中文: [在黑暗里听见飞蛾](https://world.lapla.si/zh/echo/) — 蝙蝠在夜里捕虫，靠的是自己的叫声。它发出人耳听不到的超声，再听飞蛾反射回来的回声，从回声晚到的时间里读出距离。
  - A pipistrelle flies at night, calling about ten times a second. Its calls are above human hearing and bounce back off a moth. However many milliseconds the echo takes, that is how far away the moth is.
  - Embed: https://world.lapla.si/embed/en/echo/ · https://world.lapla.si/embed/zh/echo/
  - Chapters: `cover` Hearing a Moth in the Dark; `dark` Calls No One Heard; `call` One Call; `range` The Late Echo; `ultra` Why Ultrasound; `ears` Two Ears; `wing` A Wing Made of a Hand; `hunt` Search, Approach, the Final Buzz; `doppler` Horseshoe Bats Retune; `moth` The Moth Can Hear; `lab` The Bench
  - Lab settings: `freq` Frequency (15–120, step 1); `dur` Call length (0–100, step 0.5); `rate` Calls a second (5–200, step 1); `labels` Labels (1/0)
- [How the Cochlea Takes Sound Apart (耳蜗怎样把声音拆开)](https://world.lapla.si/en/cochlea/): plate 53. Sound entering the ear ends up in a coiled tube. A membrane inside it is pushed into a wave that swells highest near the entrance for high notes and far along for low ones. A few thousand hair cells turn that motion into nerve signals. Markdown: [en](https://world.lapla.si/en/cochlea/index.html.md), [中文](https://world.lapla.si/zh/cochlea/index.html.md).
  - 中文: [耳蜗怎样把声音拆开](https://world.lapla.si/zh/cochlea/) — 声音进了耳朵，最后落在一条盘起来的细管里。管里一层膜被声波推着起伏，高音在入口处鼓得最高，低音在尽头。几千个毛细胞把这种起伏变成神经信号。
  - Deep in the inner ear is a tube coiled two and a half times, about 35 mm long when straightened. Sound sets a membrane inside it moving, and the motion runs inwards as a wave that swells to its highest at a place set by the frequency: high notes near the entrance, low notes at the far end.
  - Embed: https://world.lapla.si/embed/en/cochlea/ · https://world.lapla.si/embed/zh/cochlea/
  - Chapters: `cover` How the Cochlea Takes Sound Apart; `ear` From the Ear Canal to the Inner Ear; `lever` Getting Sound from Air into Fluid; `uncoil` Uncoiling a 35-Millimetre Tube; `wave` A Wave That Runs Inwards; `map` Every Frequency Has Its Place; `hair` Hair Cells on the Membrane; `channel` A Thread That Opens a Gate; `amp` Hair Cells That Change Length; `loud` A Trillionfold Range; `implant` Cochlear Implants; `lab` The Bench
  - Lab settings: `play` Play (1/0); `freq` Frequency (0–100, step 0.1); `level` Level (0–100, step 1); `freq2` Second tone (0–100, step 0.1); `two` Add a second tone (1/0); `amp` Outer-hair-cell gain (1/0); `labels` Labels (1/0)
- [CRISPR-Cas9 Genome Editing (CRISPR-Cas9 基因编辑)](https://world.lapla.si/en/crispr/): plate F15. A ladder of DNA and a Cas9 built from its crystal coordinates: a guide RNA finds twenty letters among three billion, the PAM first, then base by base, and two domains cut one strand each. Markdown: [en](https://world.lapla.si/en/crispr/index.html.md), [中文](https://world.lapla.si/zh/crispr/index.html.md).
  - 中文: [CRISPR-Cas9 基因编辑](https://world.lapla.si/zh/crispr/) — 一条 DNA 梯子和一台按晶体结构做出来的 Cas9：向导 RNA 带着它在三十亿个字母里找到二十个，先认 PAM，再逐个碱基配对，然后两个结构域各切一条链。
  - A real window of the human genome on a ladder of brass and glass, with Cas9 clamped on it where its crystal structure puts it. Every score on the page is computed from published tables, on that sequence, as you watch.
  - Embed: https://world.lapla.si/embed/en/crispr/ · https://world.lapla.si/embed/zh/crispr/
  - Chapters: `cover` CRISPR-Cas9 Genome Editing; `address` Twenty Letters in Three Billion; `pam` The PAM First; `rloop` Pairing, Base by Base; `cut` Two Strands, Two Blades; `inside` The Protein Taken Apart; `seed` What It Will Forgive; `repair` The Break Goes to the Cell; `editors` Editing Without a Break; `therapy` Switching Fetal Haemoglobin Back On; `lab` The Bench
  - Lab settings: `choice` Gene (bcl11a | hbb)

## Nature / Matter, Light & Sound

- [Why a Rainbow Is Round (彩虹为什么是圆的)](https://world.lapla.si/en/rainbow/): plate 07. It does not hang anywhere in the sky. It is a ring of light 42 degrees around the shadow of your own head. Markdown: [en](https://world.lapla.si/en/rainbow/index.html.md), [中文](https://world.lapla.si/zh/rainbow/index.html.md).
  - 中文: [彩虹为什么是圆的](https://world.lapla.si/zh/rainbow/) — 它并不挂在天上的某个地方。它是一圈光，以你头部的影子为中心，半径 42°。
  - It does not hang anywhere in the sky. It is a ring of light 42 degrees around the shadow of your own head. And all of it happens inside a raindrop.
  - Embed: https://world.lapla.si/embed/en/rainbow/ · https://world.lapla.si/embed/zh/rainbow/
  - Chapters: `cover` Why a Rainbow Is Round; `drop` Light in a Raindrop; `angle` 42 Degrees; `sky` Back to the Sun; `own` Your Own Rainbow; `double` The Second Bow; `noon` No Rainbows at a Summer Noon; `lab` Your Turn
  - Lab settings: `play` Let the Sun rise (1/0); `sun` Sun’s height (0–60, step 0.5); `second` Second bow (1/0); `friend` Someone beside you (1/0); `labels` Labels (1/0)
- [Why Snowflakes Have Six Points (雪花为什么有六个角)](https://world.lapla.si/en/snowflake/): plate 08. Every snowflake grows from one tiny six-sided crystal of ice. Markdown: [en](https://world.lapla.si/en/snowflake/index.html.md), [中文](https://world.lapla.si/zh/snowflake/index.html.md).
  - 中文: [雪花为什么有六个角](https://world.lapla.si/zh/snowflake/) — 每一片雪花，都从一粒小小的六角冰晶长起。
  - Every snowflake grows from one tiny six-sided crystal of ice. Its shape records the path it took through the cloud.
  - Embed: https://world.lapla.si/embed/en/snowflake/ · https://world.lapla.si/embed/zh/snowflake/
  - Chapters: `cover` Why Snowflakes Have Six Points; `six` Six Begins With Water; `grow` From One Small Crystal; `branch` The Corners Lead; `shapes` Temperature Decides the Shape; `unique` No Two Quite Alike; `nakaya` Letters From Heaven; `lab` Your Turn
  - Lab settings: `choice` Shape (plate | sectored | stellar); `vapour` Water vapor in the air (0–100, step 1); `labels` Labels (1/0)
- [Why the Sky Is Blue (天空为什么是蓝的)](https://world.lapla.si/en/sky/): plate 13. The sky is not reflecting the sea. The air itself is throwing the blue in sunlight across the sky. Markdown: [en](https://world.lapla.si/en/sky/index.html.md), [中文](https://world.lapla.si/zh/sky/index.html.md).
  - 中文: [天空为什么是蓝的](https://world.lapla.si/zh/sky/) — 天空不是大海的倒影，而是空气把阳光里的蓝光撒向了四面八方。
  - The sky is not reflecting the sea, and there is nothing blue floating in the air. The air itself is throwing the blue in sunlight in every direction.
  - Embed: https://world.lapla.si/embed/en/sky/ · https://world.lapla.si/embed/zh/sky/
  - Chapters: `cover` Why the Sky Is Blue; `white` A Rainbow Inside White Light; `scatter` Bumping Into Air; `blue` Blue From Everywhere; `violet` Why Not Violet?; `sunset` Red at Sunset; `paths` One Sunbeam, Two Paths; `space` A Black Sky in Space; `lab` Your Turn
  - Lab settings: `play` Move the Sun (1/0); `sun` Sun’s height (-2–90, step 0.5); `air` Amount of air (0–4, step 0.05); `colour` Colors scatter differently (1/0); `labels` Labels (1/0)
- [How Sound Crosses the Air (声音怎样穿过空气)](https://world.lapla.si/en/sound/): plate 15. Sound is a push passed along through the air. The air doesn’t travel to you; the push does. Markdown: [en](https://world.lapla.si/en/sound/index.html.md), [中文](https://world.lapla.si/zh/sound/index.html.md).
  - 中文: [声音怎样穿过空气](https://world.lapla.si/zh/sound/) — 声音是在空气里传递的一阵阵推挤。空气没有流过来，传过来的是那阵推挤。
  - Every sound you hear is a push passed along through the air. The air itself doesn’t travel to your ear — only the push does.
  - Embed: https://world.lapla.si/embed/en/sound/ · https://world.lapla.si/embed/zh/sound/
  - Chapters: `cover` How Sound Crosses the Air; `push` Push, and Pass It On; `wave` Squeeze and Stretch; `pitch` Pitch; `loud` Loudness; `speed` Which Is Fastest?; `space` Silence in Space; `lab` Your Turn
  - Lab settings: `choice` Through (air | water | steel); `hz` Frequency (100–1000, step 10); `loud` Loudness (0.1–1, step 0.01); `listen` Listen (1/0); `mic` Use my voice (1/0); `labels` Labels (1/0)
- [Why Ice Floats (冰为什么浮在水上)](https://world.lapla.si/en/ice/): plate 17. Freeze most liquids and the solid sinks in its own liquid. Ice floats. The secret is in the little hexagons water molecules build. Markdown: [en](https://world.lapla.si/en/ice/index.html.md), [中文](https://world.lapla.si/zh/ice/index.html.md).
  - 中文: [冰为什么浮在水上](https://world.lapla.si/zh/ice/) — 大多数东西冻成固体后会沉下去，冰却浮了起来。秘密在水分子搭成的小六边形里。
  - Freeze most liquids and the solid sinks. Water does the opposite — and that is why lakes freeze from the top down, and fish survive the winter underneath.
  - Embed: https://world.lapla.si/embed/en/ice/ · https://world.lapla.si/embed/zh/ice/
  - Chapters: `cover` Why Ice Floats; `float` The Tip of the Iceberg; `molecules` Crowded, or Holding Hands; `four` Heaviest Cupful at 4°C; `lake` A Lake That Freezes From the Top; `rare` A Rare Exception; `lab` Your Turn
  - Lab settings: `play` Change the temperature (1/0); `temp` Temperature (-10–20, step 0.5); `labels` Labels (1/0)
- [Three Cones, a Million Colors (三种视锥，百万种颜色)](https://world.lapla.si/en/color/): plate 21. Sunlight holds a smooth sweep of colors, but our eyes see it with just three kinds of cells. Every color you see is those three cells taking a vote. Markdown: [en](https://world.lapla.si/en/color/index.html.md), [中文](https://world.lapla.si/zh/color/index.html.md).
  - 中文: [三种视锥，百万种颜色](https://world.lapla.si/zh/color/) — 阳光里的颜色连成一片，眼睛却只用三种细胞去看它们。我们看到的每一种颜色，都是这三种细胞一起“投票”的结果。
  - Sunlight is a smooth sweep of colors, not just red, green and blue. It is our eyes that have only three kinds of color-sensing cells — which is why three lamps can fool us into seeing so many colors.
  - Embed: https://world.lapla.si/embed/en/color/ · https://world.lapla.si/embed/zh/color/
  - Chapters: `cover` Three Cones, a Million Colors; `mix` Three Lamps Make White; `shadows` Colored Shadows; `spectrum` Sunlight Isn’t Three Colors; `cones` Three Kinds of Cones; `fooled` Fooling the Eye; `lab` Your Turn
  - Lab settings: `red` Red lamp (0–1, step 0.01); `green` Green lamp (0–1, step 0.01); `blue` Blue lamp (0–1, step 0.01); `labels` Labels (1/0)
- [Why a Siren Changes Its Tune (救护车为什么会变调)](https://world.lapla.si/en/doppler/): plate 26. An ambulance sounds higher coming towards you and lower going away. The siren hasn’t changed; its sound waves have been squeezed or stretched. Markdown: [en](https://world.lapla.si/en/doppler/index.html.md), [中文](https://world.lapla.si/zh/doppler/index.html.md).
  - 中文: [救护车为什么会变调](https://world.lapla.si/zh/doppler/) — 救护车开过来时，警笛声尖一些；开走时，又低一些。警笛本身并没有变，变的是声波被挤紧还是拉开。
  - As an ambulance comes towards you, its siren sounds high; the moment it passes, the note drops. The siren plays the same note the whole time. What changes are the sound waves on their way to your ear — squeezed together, or stretched apart.
  - Embed: https://world.lapla.si/embed/en/doppler/ · https://world.lapla.si/embed/zh/doppler/
  - Chapters: `cover` Why a Siren Changes Its Tune; `still` A Siren Standing Still; `bunch` Squeezed in Front, Stretched Behind; `pass` The Moment It Passes; `boom` Faster Than Sound; `stars` Light Shifts Too; `lab` Your Turn
  - Lab settings: `play` Drive (1/0); `speed` Speed (0–1800, step 10); `listen` Listen (1/0); `labels` Labels (1/0)
- [Where a Bubble’s Colours Come From (肥皂泡的颜色从哪里来)](https://world.lapla.si/en/bubble/): plate 28. Soapy water has no colour, yet bubbles shimmer with every hue. The colour isn’t in the soap — it is in how thick the film is. Markdown: [en](https://world.lapla.si/en/bubble/index.html.md), [中文](https://world.lapla.si/zh/bubble/index.html.md).
  - 中文: [肥皂泡的颜色从哪里来](https://world.lapla.si/zh/bubble/) — 肥皂水是无色的，泡泡却五彩缤纷。颜色不在肥皂里，而在泡泡膜的厚度里。
  - Soapy water is colourless, yet blow it into a bubble and it shimmers like a rainbow, its colours forever flowing. They aren’t dyes. The light is being sorted by a film hundreds of times thinner than a hair.
  - Embed: https://world.lapla.si/embed/en/bubble/ · https://world.lapla.si/embed/zh/bubble/
  - Chapters: `cover` Where a Bubble’s Colours Come From; `two` Two Reflections; `add` Adding Up, or Cancelling Out; `thickness` Thickness Makes the Colour; `drain` A Flowing Rainbow; `nature` Colour From Structure; `lab` Your Turn
  - Lab settings: `play` Let the film drain (1/0); `thick` Average film thickness (100–1200, step 10); `labels` Labels (1/0)
- [A Curved Piece of Glass (一块弯曲的玻璃)](https://world.lapla.si/en/lens/): plate 29. Light bends a little as it passes from air into glass. Shape the glass into a curve and light passing through every part of it can meet at one point — which is how magnifying glasses, cameras and your eyes work. Markdown: [en](https://world.lapla.si/en/lens/index.html.md), [中文](https://world.lapla.si/zh/lens/index.html.md).
  - 中文: [一块弯曲的玻璃](https://world.lapla.si/zh/lens/) — 光从空气进入玻璃会拐个弯。把玻璃磨成弯曲的形状，就能让穿过它各处的光汇聚到一点：放大镜、相机和你的眼睛都靠这个。
  - Light bends slightly as it passes from air into glass. Grind the glass thick in the middle and thin at the edges, and all the light bends towards a single point. Magnifying glasses, cameras, telescopes and the lens inside your eye all work this way.
  - Embed: https://world.lapla.si/embed/en/lens/ · https://world.lapla.si/embed/zh/lens/
  - Chapters: `cover` A Curved Piece of Glass; `bend` Light Takes a Turn; `focus` Coming to a Point; `image` An Upside-Down Picture; `eye` The Lens in Your Eye; `myopia` Short Sight and Glasses; `lab` Your Turn
  - Lab settings: `curve` Lens curvature (30–160, step 1); `object` Object distance (60–400, step 1); `labels` Labels (1/0)
- [Why Metal Feels Cold (为什么金属摸起来更凉)](https://world.lapla.si/en/touch/): plate 31. A metal spoon and a wooden spoon left in the same room are exactly the same temperature, yet the metal one feels much colder. What your hand feels is how fast heat leaves it. Markdown: [en](https://world.lapla.si/en/touch/index.html.md), [中文](https://world.lapla.si/zh/touch/index.html.md).
  - 中文: [为什么金属摸起来更凉](https://world.lapla.si/zh/touch/) — 放在同一个房间里的铁勺和木勺，温度一模一样，摸起来铁勺却凉得多。你的手感觉到的，其实是热量流走得有多快。
  - Leave a metal spoon and a wooden spoon in the same room overnight and they end up exactly the same temperature. Touch them, though, and the metal feels cold, the wood warm. Your hand isn’t feeling their temperature. It is feeling how fast heat flows out of it.
  - Embed: https://world.lapla.si/embed/en/touch/ · https://world.lapla.si/embed/zh/touch/
  - Chapters: `cover` Why Metal Feels Cold; `same` The Same Temperature; `flow` Heat Leaves Your Hand; `contact` The Temperature Your Skin Feels; `hot` The Other Way Round; `lab` Your Turn
  - Lab settings: `choice` Material (copper | steel | stone | glass | wood | foam); `temp` Material temperature (-10–70, step 1); `labels` Labels (1/0)
- [Why Mountain Water Isn’t Hot Enough (山顶上的水为什么不够烫)](https://world.lapla.si/en/boil/): plate 32. At the top of Everest, water boils at about 70°C — too cool to hard-boil an egg, however long you wait. The temperature water boils at depends on how much air is pressing down on it. Markdown: [en](https://world.lapla.si/en/boil/index.html.md), [中文](https://world.lapla.si/zh/boil/index.html.md).
  - 中文: [山顶上的水为什么不够烫](https://world.lapla.si/zh/boil/) — 在珠穆朗玛峰顶，水大约 70°C 就开了，煮再久也煮不成一个硬邦邦的白煮蛋。水在哪个温度沸腾，取决于头顶有多少空气压着它。
  - At the seaside, water boils at 100°C. At the top of Mount Everest it boils at about 70°C, too cool to hard-boil an egg. The water hasn’t changed. The air pressing on it has.
  - Embed: https://world.lapla.si/embed/en/boil/ · https://world.lapla.si/embed/zh/boil/
  - Chapters: `cover` Why Mountain Water Isn’t Hot Enough; `bubbles` What the Bubbles Are; `air` The Air Above Us; `mountain` One Mountain, Four Pots; `everest` The Real Summit; `lapaz` One City, Three Boiling Points; `cook` Why Mountain Kitchens Use Pressure Cookers; `lab` Your Turn
  - Lab settings: `choice` Place (sea | denver | lapaz | elalto | camp | summit); `height` Altitude (0–8849, step 1); `lid` Pressure-cooker lid on (1/0); `labels` Labels (1/0)
- [Why a Steel Ship Floats (钢铁做的船为什么能浮起来)](https://world.lapla.si/en/float/): plate 34. Drop a lump of steel in water and it sinks at once, yet the same steel built into a ship floats with ten thousand tonnes of cargo aboard. The secret is how much water the ship pushes aside. Markdown: [en](https://world.lapla.si/en/float/index.html.md), [中文](https://world.lapla.si/zh/float/index.html.md).
  - 中文: [钢铁做的船为什么能浮起来](https://world.lapla.si/zh/float/) — 一块钢扔进水里立刻沉底，可用同样多的钢造成的船，却能载着上万吨货物浮在海上。秘密在于船排开了多少水。
  - A steel screw dropped in water sinks straight to the bottom. Yet a cargo ship built from thousands of tonnes of steel can take on more than ten thousand tonnes of cargo and still float. The steel is the same. What changed is its shape.
  - Embed: https://world.lapla.si/embed/en/float/ · https://world.lapla.si/embed/zh/float/
  - Chapters: `cover` Why a Steel Ship Floats; `steel` The Same Steel; `push` The Water Pushes Back; `load` Load It, and It Sinks Deeper; `salt` Deeper in a River Than at Sea; `lab` Your Turn
  - Lab settings: `choice` Water (fresh | sea | dead); `cargo` Cargo (0–22000, step 100); `labels` Labels (1/0)
- [Where Is the Electron? (电子在哪里)](https://world.lapla.si/en/atom/): plate 36. Textbooks often draw electrons as little balls circling the nucleus. In fact an electron has no orbit. It is more like a cloud: all we can say is where it is likely to be. Markdown: [en](https://world.lapla.si/en/atom/index.html.md), [中文](https://world.lapla.si/zh/atom/index.html.md).
  - 中文: [电子在哪里](https://world.lapla.si/zh/atom/) — 课本上常把电子画成绕着原子核转圈的小球。其实电子没有轨道，它更像一团云：我们只能说它在哪里出现的可能性大。
  - Textbooks often draw an atom as a tiny solar system, its electrons circling the nucleus like planets. A hundred years ago, scientists found that electrons don’t behave like that. An electron has no fixed path, only a cloud of places it might turn up.
  - Embed: https://world.lapla.si/embed/en/atom/ · https://world.lapla.si/embed/zh/atom/
  - Chapters: `cover` Where Is the Electron?; `planets` Not a Tiny Solar System; `empty` Atoms Are Almost Empty; `cloud` A Cloud of Chances; `shapes` More Energy, More Shapes; `light` A Jump Makes Light; `lab` Your Turn
  - Lab settings: `choice` Electron cloud (1s | 2s | 2p | 3p | 3d | 3dxy); `cut` Cut open (1/0); `labels` Labels (1/0)
- [When Two Ripples Meet (两圈水波相遇时)](https://world.lapla.si/en/ripple/): plate 37. Drop two stones in water and their rings of ripples pass straight through each other. In some places they cancel out, and the water there barely moves. Markdown: [en](https://world.lapla.si/en/ripple/index.html.md), [中文](https://world.lapla.si/zh/ripple/index.html.md).
  - 中文: [两圈水波相遇时](https://world.lapla.si/zh/ripple/) — 往水里扔两颗石子，两圈波纹相遇，会穿过彼此继续前进；在有些地方，它们会互相抵消，水面几乎不动。
  - Drop two stones into still water and two rings of ripples spread out and meet. They don’t smash into each other; they pass through and carry on. Where they overlap, some spots rise higher, while others hardly move, and lines of calm water appear.
  - Embed: https://world.lapla.si/embed/en/ripple/ · https://world.lapla.si/embed/zh/ripple/
  - Chapters: `cover` When Two Ripples Meet; `drop` Rings Moving Out; `through` Passing Through; `calm` Lines of Calm; `floor` Bright Lines on the Bottom; `lab` Your Turn
  - Lab settings: `freq` Tapping speed (3–14, step 0.5); `gap` Distance between fingers (0.5–3, step 0.1); `phase` Half a beat apart (1/0); `labels` Labels (1/0)
- [The Invisible Lines Around a Magnet (磁铁周围看不见的线)](https://world.lapla.si/en/magnet/): plate 39. Lay a sheet of paper over a magnet, sprinkle iron filings on it and tap gently: the filings line up in curves running from one end of the magnet to the other. They are drawing the shape of its magnetic field. Markdown: [en](https://world.lapla.si/en/magnet/index.html.md), [中文](https://world.lapla.si/zh/magnet/index.html.md).
  - 中文: [磁铁周围看不见的线](https://world.lapla.si/zh/magnet/) — 在磁铁上面放一张纸，撒上铁屑，轻轻敲几下，铁屑就排成一条条弧线，从磁铁的一头连到另一头。它们画出的，是磁场的样子。
  - A magnet pulls a nail towards it without touching it, so something invisible must surround it. Lay a sheet of paper over a magnet, sprinkle fine iron filings on it and tap gently, and the filings arrange themselves into curved lines. Those lines draw the shape of the magnetic field.
  - Embed: https://world.lapla.si/embed/en/magnet/ · https://world.lapla.si/embed/zh/magnet/
  - Chapters: `cover` The Invisible Lines Around a Magnet; `still` It Pulls Through Paper; `filings` Filings Fall Into Line; `poles` Crowded at the Ends; `two` Two Magnets; `earth` The Earth Is a Magnet Too; `lab` Your Turn
  - Lab settings: `choice` Setup (one | attract | repel); `compass` Compasses (1/0); `labels` Labels (1/0)
- [Sand That Draws a Sound (沙子画出的振动)](https://world.lapla.si/en/chladni/): plate 47. Sprinkle sand on a metal plate and make it ring. The sand jumps away from the moving parts and gathers on the lines that stay still, drawing the shape of the vibration. Markdown: [en](https://world.lapla.si/en/chladni/index.html.md), [中文](https://world.lapla.si/zh/chladni/index.html.md).
  - 中文: [沙子画出的振动](https://world.lapla.si/zh/chladni/) — 在金属板上撒一层沙，让板振动起来，沙子会跳开，聚到板上不动的线上，画出这块板振动的形状。
  - A thin metal plate is ringing. Sand on it is thrown off wherever the plate moves and comes to rest on the lines where it does not. Each pitch draws a different figure.
  - Embed: https://world.lapla.si/embed/en/chladni/ · https://world.lapla.si/embed/zh/chladni/
  - Chapters: `cover` Sand That Draws a Sound; `bow` A Violin Bow, 1787; `nodes` Sand Stops Where the Plate Is Still; `sweep` Tuning to Resonance; `modes` Finer and Finer Figures; `finger` A Finger Picks the Figure; `pairs` Two Figures in One; `theory` A Prize Question; `violin` The Top of a Violin; `lab` The Bench
  - Lab settings: `choice` Plate (square | violin); `freq` Frequency (0–1, step 0.0005); `thick` Top thickness (2.2–3.6, step 0.05); `sound` Sound (1/0); `labels` Labels (1/0)
- [Patterns Shaken Out of Oil (摇出来的花纹)](https://world.lapla.si/en/faraday/): plate 51. Shake a dish of oil up and down hard enough and the still surface suddenly wrinkles into squares, hexagons or stripes. It rises and falls at half the rate of the shaking. Markdown: [en](https://world.lapla.si/en/faraday/index.html.md), [中文](https://world.lapla.si/zh/faraday/index.html.md).
  - 中文: [摇出来的花纹](https://world.lapla.si/zh/faraday/) — 把一盘油上下摇动，摇得够快，平静的油面会突然起皱，排成方格、六边形或条纹。它起伏的频率只有摇动的一半。
  - A thin layer of oil sits on a shaker, moving up and down. At low acceleration the surface stays flat; past a threshold it breaks into a regular pattern. Each time the pattern rises and falls, the dish has gone up and down twice.
  - Embed: https://world.lapla.si/embed/en/faraday/ · https://world.lapla.si/embed/zh/faraday/
  - Chapters: `cover` Patterns Shaken Out of Oil; `crispations` Wrinkled Water, 1831; `half` Half the Frequency; `swing` Like a Swing; `threshold` A Threshold; `patterns` Stripes, Squares, Hexagons; `wavelength` Faster Shaking, Shorter Waves; `quasi` Two Frequencies; `bounce` A Drop That Does Not Land; `walk` A Drop That Walks; `analogy` An Analogy; `lab` The Bench
  - Lab settings: `choice` Silicone oil (oil10 | oil20 | oil50 | oil100); `freq` Frequency (15–120, step 1); `accel` Acceleration (0–12, step 0.05); `two` Second frequency (1/0); `labels` Labels (1/0)

## Technology / Chips & Information

- [How a Phone Knows Where It Is (手机怎么知道你在哪里)](https://world.lapla.si/en/gps/): plate 41. Thirty-odd satellites, 20,200 km up, keep announcing the time. A phone only listens, and from how late each announcement arrives it works out where it is, to within a few metres. Markdown: [en](https://world.lapla.si/en/gps/index.html.md), [中文](https://world.lapla.si/zh/gps/index.html.md).
  - 中文: [手机怎么知道你在哪里](https://world.lapla.si/zh/gps/) — 三十多颗卫星在两万多公里高空不停地报时。手机只是听，从每一声报时晚到了多久，算出自己在哪里，误差只有几米。
  - Far above the clouds, thirty-odd satellites circle the Earth twice a day. Each carries atomic clocks and says, over and over: this is the time, and this is where I am. Your phone never answers. It only listens, and from how late each message arrives it works out where it is standing, to within a few metres.
  - Embed: https://world.lapla.si/embed/en/gps/ · https://world.lapla.si/embed/zh/gps/
  - Chapters: `cover` How a Phone Knows Where It Is; `ring` Six Rings of Satellites; `signal` A Message at the Speed of Light; `circles` One Distance, One Sphere; `clock` The Fourth Satellite; `einstein` Einstein in Orbit; `systems` Not Only GPS; `lab` Your Turn
  - Lab settings: `choice` You are in (beijing | london | nairobi | newyork | sydney); `clock` Phone clock error (0–3, step 0.1); `fix` Correct the clock (4th satellite) (1/0); `bunched` Bunched satellites (1/0); `systems` All navigation systems (1/0); `labels` Labels (1/0)
- [Light in a Glass Thread (光在玻璃丝里走)](https://world.lapla.si/en/fibre/): plate 42. Shine a light into a stream of water and the light bends with the stream. Today the same trick traps the internet in glass threads as fine as a hair and sends it across the Pacific. Markdown: [en](https://world.lapla.si/en/fibre/index.html.md), [中文](https://world.lapla.si/zh/fibre/index.html.md).
  - 中文: [光在玻璃丝里走](https://world.lapla.si/zh/fibre/) — 一束光照进水流，水流弯，光也跟着弯。今天，越洋的网络信号就是这样，被困在和头发差不多细的玻璃丝里，穿过整个太平洋。
  - Shine a light into a stream of water and something strange happens: the light bends with the falling water and is carried all the way to where it lands. The idea behind that experiment of 1841 now turns your messages into flashes of light, traps them in glass threads as fine as a hair, and carries them across the floor of the Pacific.
  - Embed: https://world.lapla.si/embed/en/fibre/ · https://world.lapla.si/embed/zh/fibre/
  - Chapters: `cover` Light in a Glass Thread; `fountain` Light That Follows Water; `mirror` A Perfect Mirror; `thread` A Thread of Glass; `pulses` Ones and Zeros in Light; `cable` As Thick as a Garden Hose; `ocean` Across the Pacific; `lab` Your Turn
  - Lab settings: `speed` Stream speed (0.45–2.3, step 0.01); `tilt` Laser angle (0–55, step 1); `labels` Labels (1/0)
- [A Code That Survives Sand (埋掉一块，照样能扫)](https://world.lapla.si/en/qr/): plate 45. Bury part of a QR code in sand and a phone still reads it. The secret is in its spare bytes, which say nothing at all but can work out what went wrong and how to put it right. Markdown: [en](https://world.lapla.si/en/qr/index.html.md), [中文](https://world.lapla.si/zh/qr/index.html.md).
  - 中文: [埋掉一块，照样能扫](https://world.lapla.si/zh/qr/) — 二维码被沙子埋掉一块，手机照样读得出来。秘密在那些不写任何内容的“备用字节”里：它们能算出哪里错了，又该改成什么。
  - In 2013, Rio de Janeiro laid QR codes into its seafront promenade in black and white stone. When the wind blows sand over part of one, a phone still reads it. Some of the squares in a QR code say nothing at all; they are there to repair the rest. How do they know what went wrong?
  - Embed: https://world.lapla.si/embed/en/qr/ · https://world.lapla.si/embed/zh/qr/
  - Chapters: `cover` A Code That Survives Sand; `square` A Code Made of Stones; `eyes` Three Eyes; `bytes` Letters in a Zigzag; `mask` The Mask; `sand` Sand on the Promenade; `limit` Where It Gives Up; `lab` Your Turn
  - Lab settings: `choice` How much spare (L | M | Q | H); `sand` Sand (0–100, step 1); `wrong` Mark wrong bytes (1/0); `labels` Labels (1/0)
- [EUV Lithography Machine (极紫外光刻机)](https://world.lapla.si/en/euv/): plate F01. Light 13.5 nm long prints a chip’s circuits on silicon, four times smaller than the mask. It comes from tin droplets turned to plasma, and travels only by mirrors. Markdown: [en](https://world.lapla.si/en/euv/index.html.md), [中文](https://world.lapla.si/zh/euv/index.html.md).
  - 中文: [极紫外光刻机](https://world.lapla.si/zh/euv/) — 用 13.5 纳米的光，把芯片电路缩小四倍印在硅片上。光由锡滴炸成的等离子体发出，一路只靠反射镜传递。
  - The finest lines on a chip are a dozen nanometres wide. The machines that print them use extreme ultraviolet light with a wavelength of 13.5 nm. Everything absorbs this light, air included, so the whole path from source to wafer runs in vacuum and is passed along by about a dozen mirrors.
  - Embed: https://world.lapla.si/embed/en/euv/ · https://world.lapla.si/embed/zh/euv/
  - Chapters: `cover` EUV Lithography Machine; `scale` Thirteen Nanometres; `light` Why 13.5 Nanometres; `mirror` A Mirror of Forty Layers; `section` Cut Open: Mirror after Mirror; `source` Tin Droplets and Plasma; `optics` Illuminator, Mask, Projection; `stages` Scanning Opposite Ways; `apart` Taken Apart; `lab` Source Power
  - Lab settings: `labels` Labels (1/0)
- [The Dilution Refrigerator (稀释制冷机)](https://world.lapla.si/en/dilution/): plate F05. A superconducting quantum computer hangs from a gold-plated “chandelier”. Each stage is colder than the one above; the last is about 10 mK, hundreds of times colder than space. Markdown: [en](https://world.lapla.si/en/dilution/index.html.md), [中文](https://world.lapla.si/zh/dilution/index.html.md).
  - 中文: [稀释制冷机](https://world.lapla.si/zh/dilution/) — 超导量子计算机挂在一盏镀金的“吊灯”下面。一层比一层冷，最底下约 10 毫开，比宇宙空间冷几百倍。
  - Superconducting qubits only work close to absolute zero. The machine that takes them there is a dilution refrigerator: its upper stages are cooled by a pulse-tube cooler, the last stretch by a mixture of helium-3 and helium-4.
  - Embed: https://world.lapla.si/embed/en/dilution/ · https://world.lapla.si/embed/zh/dilution/
  - Chapters: `cover` The Dilution Refrigerator; `cold` Ten Millikelvin; `why` Why So Cold; `section` Cut Open: Stage by Stage; `pulse` The Pulse Tube: Down to 4 K; `mixture` Helium-3 Floats on Helium-4; `loop` Round the Loop; `wiring` Lines That Shed Heat; `apart` Taken Apart; `lab` Cooldown
  - Lab settings: `labels` Labels (1/0)
- [Gate-All-Around Transistor (环栅晶体管)](https://world.lapla.si/en/gaa/): plate F14. In today’s most advanced chips each switch is a few sheets of silicon 5 nm thick, wrapped on all four sides by a metal gate. The tighter the wrap, the more firmly it switches off. Markdown: [en](https://world.lapla.si/en/gaa/index.html.md), [中文](https://world.lapla.si/zh/gaa/index.html.md).
  - 中文: [环栅晶体管](https://world.lapla.si/zh/gaa/) — 今天最先进的芯片里，每个开关是几片 5 纳米厚的硅，四面被金属栅极包住。包得越紧，关得越死，漏的电越少。
  - As the switches in chips get shorter, their gates find it harder to hold them. The answer was to wrap the silicon: from one side, to three, to all four. A few thin sheets are stacked and the metal gate closes round each one. This is a piece of a logic cell cut open: five gates, two stacks of sheets, the source and drain crystals, contacts and the first two layers of copper.
  - Embed: https://world.lapla.si/embed/en/gaa/ · https://world.lapla.si/embed/zh/gaa/
  - Chapters: `cover` Gate-All-Around Transistor; `scale` A Switch You Can Count in Atoms; `count` Tens of Billions on a Chip; `switch` The Gate Lowers a Barrier; `why` Why Wrap All Four Sides; `section` Cut Open; `stack` Stacked Sheets; `making` Build It, Then Hollow It; `node` “2 nm” Is Not 2 nm; `next` What Comes Next; `apart` Taken Apart; `lab` Bench
  - Lab settings: `choice` Structure (planar | fin | gaa); `vg` Gate voltage (-0.2–1, step 0.01); `vd` Drain voltage (0–1, step 0.01); `L` Gate length (8–40, step 1); `count` Sheets (1–4, step 1); `W` Sheet width (10–50, step 1); `T` Sheet thickness (3–10, step 0.5); `labels` Labels (1/0)

## Technology / AI

- [More Features Than Neurons (比神经元更多的特征)](https://world.lapla.si/en/superposition/): plate 43. A single neuron in a neural network often stands for several unrelated things. A model with just two neurons can arrange five features into a pentagon and keep them all. Markdown: [en](https://world.lapla.si/en/superposition/index.html.md), [中文](https://world.lapla.si/zh/superposition/index.html.md).
  - 中文: [比神经元更多的特征](https://world.lapla.si/zh/superposition/) — 一个神经网络里的神经元，往往同时管着好几件毫不相干的事。一个只有两个神经元的小模型，能把五样东西排成一个五边形，全部记住。
  - Researchers looking inside an image-recognition network found a neuron that fired for cat faces, for the fronts of cars and for cat legs. Why would one neuron take on several jobs? A model small enough to watch at every step suggests an answer: as long as things rarely happen together, a network can stack more features than it has neurons into the same space.
  - Embed: https://world.lapla.si/embed/en/superposition/ · https://world.lapla.si/embed/zh/superposition/
  - Chapters: `cover` More Features Than Neurons; `neuron` One Neuron, Three Meanings; `squeeze` Five Things, Two Numbers; `share` Rare Things Can Share; `cost` The Price Is Interference; `shapes` Shapes in Three Dimensions; `read` Pulling Features Apart; `lab` Your Turn
  - Lab settings: `choice` Features → neurons (5in2 | 6in3 | 8in3); `density` How often each feature turns up (0–6, step 1); `shape` Shape (1/0); `labels` Labels (1/0)
- [Pictures Out of Noise (从噪声里长出来的图)](https://world.lapla.si/en/diffusion/): plate 44. Many AI image generators start from random static and remove it, one step at a time. A small network does the same in your browser, and a cloud of dots slowly condenses into a knot. Markdown: [en](https://world.lapla.si/en/diffusion/index.html.md), [中文](https://world.lapla.si/zh/diffusion/index.html.md).
  - 中文: [从噪声里长出来的图](https://world.lapla.si/zh/diffusion/) — 许多会画画的 AI，都从一团随机的噪点开始：一步一步，把噪声擦掉。一个小网络在你的浏览器里做同样的事，让一团乱点慢慢凝成一个结。
  - Many of today’s image generators begin every picture with meaningless random static. They don’t look up a picture and paste it together; they guess, over and over, which part of what they have is noise, and wipe a little of it away. Watch a model small enough to follow at every step, and you find that it makes things it has never seen precisely because it hasn’t learned perfectly.
  - Embed: https://world.lapla.si/embed/en/diffusion/ · https://world.lapla.si/embed/zh/diffusion/
  - Chapters: `cover` Pictures Out of Noise; `noise` Every Picture Starts as Static; `forward` Ruining a Picture Is Easy; `reverse` Learning to Walk It Back; `copy` A Perfect Student Only Copies; `twins` Two Networks, One New Answer; `lab` Your Turn
  - Lab settings: `choice` Denoiser (exact | net | twins); `examples` Examples (0–2, step 1); `knot` Knot (1/0); `labels` Labels (1/0)
- [Learning by Heart, Then Learning the Rule (先背答案，再学会规律)](https://world.lapla.si/en/grokking/): plate 46. A small neural network learns to add hours on a 24-hour clock. It gets its practice questions right almost at once, by memorising them, and only long afterwards answers questions it has never seen. Inside, it has built clocks. Markdown: [en](https://world.lapla.si/en/grokking/index.html.md), [中文](https://world.lapla.si/zh/grokking/index.html.md).
  - 中文: [先背答案，再学会规律](https://world.lapla.si/zh/grokking/) — 一个小神经网络学 24 小时制的钟点加法。练习题它很快全做对了，靠的是死记；过了很久，它才忽然答对从没见过的题。它的里面，长出了几只钟。
  - Train a neural network on half the sums of clock arithmetic and it soon answers all of them perfectly, but only those: on the half it never saw, it does no better than a guess. Keep training, long after the practice questions have nothing left to teach, and something odd happens. Researchers call it grokking.
  - Embed: https://world.lapla.si/embed/en/grokking/ · https://world.lapla.si/embed/zh/grokking/
  - Chapters: `cover` Learning by Heart, Then Learning the Rule; `clock` Clock Arithmetic; `heart` Learning by Heart; `downhill` Walking Downhill; `grok` The Jump; `clocks` Clocks Inside; `why` Why It Waited; `lab` Your Turn
  - Lab settings: `wd` Weight decay (0–4, step 1); `frac` Squares to practise on (0–5, step 1); `marks` Dim wrong answers (1/0); `labels` Labels (1/0)
- [Attention in Transformers (Transformer 的注意力)](https://world.lapla.si/en/attention/): plate F13. A two-layer, eight-head Transformer reads a sentence in your browser, one character at a time, and guesses the next. Each thread is one act of attention; its brightness is the weight. Markdown: [en](https://world.lapla.si/en/attention/index.html.md), [中文](https://world.lapla.si/zh/attention/index.html.md).
  - 中文: [Transformer 的注意力](https://world.lapla.si/zh/attention/) — 一个两层、八个头的小 Transformer，在你的浏览器里逐字读一句话，猜下一个字母。每条丝线是一次“注意”，亮度就是它的权重。
  - A language model reads what came before and guesses what comes next. Attention decides where it looks back. This machine holds a small model that was really trained; every thread and needle on it is a number it is computing now.
  - Embed: https://world.lapla.si/embed/en/attention/ · https://world.lapla.si/embed/zh/attention/
  - Chapters: `cover` Attention in Transformers; `predict` One Character at a Time; `tokens` Characters Become Numbers; `scores` Queries and Keys; `softmax` Only Looking Back; `values` Bringing Back What It Found; `stream` Cut Open; `heads` Eight Heads, Eight Jobs; `induction` Copying What Came Next Last Time; `forming` It Appears Suddenly; `ablate` Pulling a Head Out; `cache` The Square and the Cache; `lab` The Bench

## Ideas / Mathematics

- [Life from a Smooth Rule (规则里游出的生命)](https://world.lapla.si/en/lenia/): plate M01. Melt the squares, the ticks and the life-or-death of Conway’s Game of Life, and a small thing swims out of the numbers, with a body and a tail, healing when it is bitten. Its whole law is one ring and one bell-shaped curve. Markdown: [en](https://world.lapla.si/en/lenia/index.html.md), [中文](https://world.lapla.si/zh/lenia/index.html.md).
  - 中文: [规则里游出的生命](https://world.lapla.si/zh/lenia/) — 把康威“生命游戏”的格子、节拍与生死都化开，一个小东西便从数里游了出来：有身子，有尾巴，被咬一口还会长好。它的全部天理，只是一个圆环、一条钟形的曲线。
  - A sheet of squares, three rules, and patterns crawl across the page: the Game of Life, 1970. Let the squares, the ticks and the life-or-death run smooth, and out of the dish swims something no one has drawn: it glides, it heals, and it comes in species.
  - Embed: https://world.lapla.si/embed/en/lenia/ · https://world.lapla.si/embed/zh/lenia/
  - Chapters: `cover` Life from a Smooth Rule; `life` The Game of Life; `smooth` Smoothing It Out; `growth` The Growth Curve; `orbium` Orbium; `tune` A Narrow Law; `heal` The Wound; `zoo` A Field Guide; `meaning` Is It Alive?; `lab` The Bench
  - Lab settings: `play` Play (1/0); `choice` Species (orbium | gyrorbium | scutium | paraptera | hydrogeminium | kronium); `mu` μ, curve centre (0.1–0.4, step 0.001); `sigma` σ, curve width (0.005–0.07, step 0.0005); `rate` Speed of time (0.25–3, step 0.05); `labels` Labels (1/0)
- [Counting Clacks, Finding π (碰撞数出 π)](https://world.lapla.si/en/blocks/): plate M02. Two blocks and a wall, and a count of the collisions. Each time the large block gets 100 times heavier, the count gains another digit of π. Markdown: [en](https://world.lapla.si/en/blocks/index.html.md), [中文](https://world.lapla.si/zh/blocks/index.html.md).
  - 中文: [碰撞数出 π](https://world.lapla.si/zh/blocks/) — 两块方块，一面墙，数一数撞了几次。大块每重 100 倍，次数就多出 π 的一位数字。
  - Two blocks sit on a smooth rail with a wall at the left end. The large block slides in, and the small one bounces between it and the wall. With a mass ratio of 100 there are 31 collisions; with 10,000, 314; with 1,000,000, 3141.
  - Embed: https://world.lapla.si/embed/en/blocks/ · https://world.lapla.si/embed/zh/blocks/
  - Chapters: `cover` Counting Clacks, Finding π; `puzzle` Two Blocks; `digits` The Digits of π; `rules` Two Conservation Laws; `phase` A Circle; `angle` Equal Arcs; `why` Why π; `echo` The Same Geometry; `lab` The Bench
  - Lab settings: `play` Play (1/0); `choice` Mass ratio M/m (1 | 100 | 10000 | 1000000 | 100000000); `rate` Speed of time (0.05–1, step 0.05); `sound` Sound (1/0); `labels` Labels (1/0)
- [Any Closed Line, Drawn by Turning Circles (转动的圆，画出闭合的线)](https://world.lapla.si/en/fourier/): plate M03. A chain of arrows, head to tail, each turning at a whole-number speed: the last tip can draw any closed line. Markdown: [en](https://world.lapla.si/en/fourier/index.html.md), [中文](https://world.lapla.si/zh/fourier/index.html.md).
  - 中文: [转动的圆，画出闭合的线](https://world.lapla.si/zh/fourier/) — 一串首尾相接的箭头，各以整数倍的速度转动，最后一支的箭尖能画出任何一条闭合的线。
  - An arrow turning steadily about its foot draws a circle with its tip. Join many arrows head to tail, each turning at a different whole-number speed, and the last tip can draw a treble clef, or any other closed line. The length and starting angle of every arrow are worked out from the line itself.
  - Embed: https://world.lapla.si/embed/en/fourier/ · https://world.lapla.si/embed/zh/fourier/
  - Chapters: `cover` Any Closed Line, Drawn by Turning Circles; `arrow` One Arrow; `two` Two Arrows; `many` Many Arrows; `find` Where the Arrows Come From; `fit` More Terms, Closer Fit; `heat` It Began with Heat; `lab` The Bench
  - Lab settings: `play` Play (1/0); `choice` Drawing (clef | square | star | own); `terms` Terms (1–201, step 1); `speed` Speed (0.25–2, step 0.05); `rings` Circles (1/0); `labels` Labels (1/0)
- [One in Eight Random Tetrahedra Hold the Centre (随机四面体包住球心：八分之一)](https://world.lapla.si/en/tetra/): plate M04. Four random points on a sphere make a tetrahedron that holds the centre one time in eight. Three points on a circle: one in four. Markdown: [en](https://world.lapla.si/en/tetra/index.html.md), [中文](https://world.lapla.si/zh/tetra/index.html.md).
  - 中文: [随机四面体包住球心：八分之一](https://world.lapla.si/zh/tetra/) — 球面上随机取四个点，连成的四面体有八分之一的机会包住球心。圆上三点是四分之一。
  - Pick four points at random on a sphere and join them into a tetrahedron. The centre lies inside it with probability exactly 1/8. Three random points on a circle make a triangle that holds the centre with probability 1/4. Both answers can be counted out the same way.
  - Embed: https://world.lapla.si/embed/en/tetra/ · https://world.lapla.si/embed/zh/tetra/
  - Chapters: `cover` One in Eight Random Tetrahedra Hold the Centre; `circle` Three Points on a Circle; `lines` Lines First; `sphere` Four Points on a Sphere; `eight` Eight Outcomes; `reframe` A Different Question; `lab` The Bench
  - Lab settings: `play` Run (1/0); `choice` Space (circle | sphere); `points` Points (3–8, step 1); `speed` Trials a second (1–1000, step 1); `labels` Labels (1/0)
- [Why a Slanted Cut Through a Cone Is an Ellipse (斜切圆锥，切口是椭圆)](https://world.lapla.si/en/dandelin/): plate M05. Slice a cone at a slant and the cut is the same curve two pins and a string draw. Two spheres prove it. Markdown: [en](https://world.lapla.si/en/dandelin/index.html.md), [中文](https://world.lapla.si/zh/dandelin/index.html.md).
  - 中文: [斜切圆锥，切口是椭圆](https://world.lapla.si/zh/dandelin/) — 斜着切开圆锥，切口和两枚图钉加一根线画出的椭圆是同一种曲线。两个球证明了这一点。
  - Cut a cone with a slanted plane and the edge of the cut is a closed curve. Two pins and a string draw an ellipse. They are the same curve: drop two spheres into the cone, and the points where they touch the cut are the ellipse’s foci.
  - Embed: https://world.lapla.si/embed/en/dandelin/ · https://world.lapla.si/embed/zh/dandelin/
  - Chapters: `cover` Why a Slanted Cut Through a Cone Is an Ellipse; `slices` Four Cuts; `string` Two Pins and a String; `same` The Same Curve?; `spheres` Two Spheres; `tangents` Equal Tangents; `parabola` One Sphere Left; `lab` The Bench
  - Lab settings: `play` Move P (1/0); `choice` Curve (ellipse | parabola); `tilt` Tilt of the cut (0–46, step 1); `where` Where P is (0–359, step 1); `labels` Labels (1/0)
- [Half a Turn Is e to the iπ (转半圈，是 e 的 iπ 次方)](https://world.lapla.si/en/euler/): plate M06. eⁱᵗ is a point walking round the unit circle at a steady pace, its velocity always i times its position. After time π it is at −1. Markdown: [en](https://world.lapla.si/en/euler/index.html.md), [中文](https://world.lapla.si/zh/euler/index.html.md).
  - 中文: [转半圈，是 e 的 iπ 次方](https://world.lapla.si/zh/euler/) — eⁱᵗ 是一个沿单位圆匀速行走的点，速度永远是位置的 i 倍。走过时间 π，它到了 −1。
  - eⁱᵗ describes a motion: the velocity is always the position times i, which means at right angles to the radius and of length 1. Such a point walks round the unit circle at a steady pace, so after time t it has covered an arc t. Half the circle is an arc of π, so e^(iπ) = −1.
  - Embed: https://world.lapla.si/embed/en/euler/ · https://world.lapla.si/embed/zh/euler/
  - Chapters: `cover` Half a Turn Is e to the iπ; `turn` Times i: a Quarter Turn; `grow` Growth at the Rate of Itself; `walk` Velocity at Right Angles; `steps` A Hundred Small Steps; `rotate` Rotation as a Motion; `lab` The Bench
  - Lab settings: `play` Play (1/0); `choice` Steps n (1 | 2 | 4 | 8 | 16 | 32 | 100); `t` Time t (0–6.2832, step 0.01); `rule` Rule (1/0); `riders` Riders (1/0); `labels` Labels (1/0)
- [Determined, Yet Unpredictable (确定，却无法预测)](https://world.lapla.si/en/lorenz/): plate M07. Three simple equations, nothing random in them. Two starts a millionth apart have nothing in common twenty time units later. Markdown: [en](https://world.lapla.si/en/lorenz/index.html.md), [中文](https://world.lapla.si/zh/lorenz/index.html.md).
  - 中文: [确定，却无法预测](https://world.lapla.si/zh/lorenz/) — 三条简单的方程，没有任何随机。两个只差百万分之一的起点，二十个时间单位后已经毫不相干。
  - Three variables, three equations, nothing random anywhere. From the same start it traces the same path every time; move the start by a millionth and the two paths run together, then pull apart, then have nothing in common. That is chaos.
  - Embed: https://world.lapla.si/embed/en/lorenz/ · https://world.lapla.si/embed/zh/lorenz/
  - Chapters: `cover` Determined, Yet Unpredictable; `flow` Convection in Three Numbers; `wheel` A Leaking Waterwheel; `restart` Three Decimals Short; `nudge` A Millionth Apart; `attractor` Never Repeating, Never Crossing; `rho` How Hard It Is Heated; `forecast` Two Weeks; `lab` The Bench
  - Lab settings: `play` Play (1/0); `rho` ρ (0–35, step 0.1); `wheel` Wheel (1/0); `labels` Labels (1/0)
- [Random Bounces Pile Up into a Bell Curve (随机碰撞，堆出钟形曲线)](https://world.lapla.si/en/galton/): plate M08. On a Galton board each steel ball goes left or right at random at every pin. After a thousand balls, the bins always show the same bell curve. Markdown: [en](https://world.lapla.si/en/galton/index.html.md), [中文](https://world.lapla.si/zh/galton/index.html.md).
  - 中文: [随机碰撞，堆出钟形曲线](https://world.lapla.si/zh/galton/) — 高尔顿板上，每颗钢珠在每颗钉上随机向左或向右。上千颗落完，格子里总是同一条钟形曲线。
  - Steel balls fall through rows of brass pins, going left or right at random at every pin. Where one lands can’t be told, yet a thousand always pile up into the same bell curve. Swap the coin for a die and the curve stays the same: that is the central limit theorem.
  - Embed: https://world.lapla.si/embed/en/galton/ · https://world.lapla.si/embed/zh/galton/
  - Chapters: `cover` Random Bounces Pile Up into a Bell Curve; `board` The Board; `path` One Ball’s Path; `count` Counting Paths; `bell` Into a Bell; `clt` Swap in a Die; `where` Where It Shows Up; `real` A Real Board; `lab` The Bench
  - Lab settings: `choice` Nudge (coin | die | uniform); `rows` Rows (1–14, step 1); `bias` Chance of right, p (0.05–0.95, step 0.01); `overlay` Exact law (1/0); `labels` Labels (1/0)
- [A Matrix Moves the Whole Plane (矩阵，是搬动整个平面的方式)](https://world.lapla.si/en/linear/): plate M09. A 2 × 2 matrix moves the whole plane at once: grid lines stay straight, parallel and evenly spaced, and the origin stays put. Its columns are where the two basis arrows land; its determinant is the factor by which areas grow. Markdown: [en](https://world.lapla.si/en/linear/index.html.md), [中文](https://world.lapla.si/zh/linear/index.html.md).
  - 中文: [矩阵，是搬动整个平面的方式](https://world.lapla.si/zh/linear/) — 一个 2 × 2 矩阵把整个平面一起搬动：网格线保持笔直、平行、等距，原点不动。两列是两根基准箭头的落点，行列式是面积放大的倍数。
  - A 2 × 2 matrix moves the whole plane at once: grid lines stay straight, parallel and evenly spaced, and the origin stays put. The matrix’s two columns are where the basis arrows î and ĵ land. The unit square becomes a parallelogram, and the factor by which its area grows is the determinant.
  - Embed: https://world.lapla.si/embed/en/linear/ · https://world.lapla.si/embed/zh/linear/
  - Chapters: `cover` A Matrix Moves the Whole Plane; `grid` A Grid and Two Arrows; `columns` Two Columns, Two Landing Points; `examples` Turn, Shear, Stretch, Flip; `compose` One Map, Then Another; `det` How Much Area Grows; `sign` Flipped and Flattened; `eigen` Arrows That Keep Their Line; `lab` The Bench
  - Lab settings: `snap` Snap (1/0); `eigen` Eigen-lines (1/0); `labels` Labels (1/0)
- [A Fold That Opens in One Pull (一拉就开的折痕)](https://world.lapla.si/en/miura/): plate M10. A sheet folded into parallelograms opens all at once when one corner is pulled, and closes all at once when it is pushed back. One angle sets every crease. Markdown: [en](https://world.lapla.si/en/miura/index.html.md), [中文](https://world.lapla.si/zh/miura/index.html.md).
  - 中文: [一拉就开的折痕](https://world.lapla.si/zh/miura/) — 一张纸按平行四边形折好，拉住一角，整张纸一起展开，一松手又一起收拢。所有折痕只由一个角度决定。
  - A sheet is folded along a pattern of parallelograms. Pull one corner and the whole sheet opens together; push it back and it closes together. No panel bends; each only turns about its creases. The shape of the whole sheet is set by a single angle.
  - Embed: https://world.lapla.si/embed/en/miura/ · https://world.lapla.si/embed/zh/miura/
  - Chapters: `cover` A Fold That Opens in One Pull; `pull` Pull a Corner, Open It All; `pattern` Straight One Way, Zig-Zag the Other; `rigid` Panels Stay Flat; Only the Creases Turn; `vertex` Two Counts at One Vertex; `angle` One Angle Sets Every Crease; `poisson` Longer One Way, Longer the Other; `uses` Maps, Solar Arrays, Sandwich Panels; `lab` The Bench
  - Lab settings: `alpha` Acute angle α (50–80, step 1); `a` Straight side a (40–54, step 1); `b` Slanted side b (44–58, step 1); `mv` Mountain / valley (1/0); `labels` Labels (1/0)
- [Slope and Area Undo Each Other (斜率与面积互为逆运算)](https://world.lapla.si/en/calculus/): plate M11. The derivative is the slope of a curve at a point; the integral is the area under it. The rate at which the area grows as the right edge moves is exactly the curve’s height there, so each operation undoes the other. Markdown: [en](https://world.lapla.si/en/calculus/index.html.md), [中文](https://world.lapla.si/zh/calculus/index.html.md).
  - 中文: [斜率与面积互为逆运算](https://world.lapla.si/zh/calculus/) — 导数是曲线在一点的斜率，积分是曲线下的面积。面积随右边界增长的速度，正好等于曲线在那里的高度：两种运算互相抵消。
  - The derivative is the slope of a curve at a point; the integral is the area piled up under it. Push the right edge, and the area grows at a rate equal to the curve’s height there. So the two are inverse operations: integrate, then differentiate, and you are back at the curve you began with.
  - Embed: https://world.lapla.si/embed/en/calculus/ · https://world.lapla.si/embed/zh/calculus/
  - Chapters: `cover` Slope and Area Undo Each Other; `car` Speedometer and Odometer; `zoom` Zoom In, and It Is a Slope; `strips` Area Is Many Thin Strips; `ftc` How Fast the Area Grows; `square` A Square Gains Two Strips; `circle` Sine on the Unit Circle; `exp` Growing at Its Own Value; `lab` The Bench
  - Lab settings: `choice` Curve (square | sine | exp | draw); `dx` Strip width dx (-5–-1, step 0.01); `car` Car (1/0); `aCurve` Area curve (1/0); `tangent` Tangent (1/0); `labels` Labels (1/0)
- [Every Two Circles Linked (每两个圆都扣在一起)](https://world.lapla.si/en/hopf/): plate M12. The three-dimensional sphere in four-dimensional space falls apart into circles that never meet, one for each point of an ordinary sphere. Projected into three dimensions, every two of them are linked. Markdown: [en](https://world.lapla.si/en/hopf/index.html.md), [中文](https://world.lapla.si/zh/hopf/index.html.md).
  - 中文: [每两个圆都扣在一起](https://world.lapla.si/zh/hopf/) — 四维空间里的三维球面，可以分成无数个互不相交的圆，每个圆对应普通球面上的一个点。投影到三维，任意两个圆都扣在一起。
  - Four-dimensional space holds a three-dimensional sphere. It can be taken apart into circles that never meet, one for each point of an ordinary sphere. Projected into three-dimensional space, the circles nest into tori, and every two of them are linked.
  - Embed: https://world.lapla.si/embed/en/hopf/ · https://world.lapla.si/embed/zh/hopf/
  - Chapters: `cover` Every Two Circles Linked; `circle` A Circle Over Every Point; `project` Down to Three Dimensions; `link` Linked in Pairs; `tori` Latitudes Become Tori; `fill` Filling Space; `spin` Rotations and Qubits; `invariant` It Cannot Be Shrunk; `lab` The Bench
  - Lab settings: `play` Run the bead (1/0); `height` Height of P, p₁ (-1–1, step 0.01); `lon` Longitude of P (0–360, step 1); `tori` Tori (1/0); `lat` Latitude (1/0); `labels` Labels (1/0)
- [Opposite Points, Same Weather (对面的点，同样的天气)](https://world.lapla.si/en/borsuk/): plate M13. At any moment there are two exactly opposite points on Earth with the same temperature and the same pressure. That is the Borsuk–Ulam theorem: a continuous map from the sphere to the plane always sends some pair of opposite points to the same place. Markdown: [en](https://world.lapla.si/en/borsuk/index.html.md), [中文](https://world.lapla.si/zh/borsuk/index.html.md).
  - 中文: [对面的点，同样的天气](https://world.lapla.si/zh/borsuk/) — 任何时刻，地球上都有两个正相对的点，温度相同，气压也相同。这是 Borsuk–Ulam 定理：球面到平面的连续映射，总把某一对对径点送到同一处。
  - At any moment there are two exactly opposite points on Earth with the same temperature and the same pressure. It follows from the shape of a sphere, not from the weather.
  - Embed: https://world.lapla.si/embed/en/borsuk/ · https://world.lapla.si/embed/zh/borsuk/
  - Chapters: `cover` Opposite Points, Same Weather; `circle` Two Opposite Points on the Equator; `globe` Temperature and Pressure at Once; `why` Why There Must Be One; `ham` One Cut, Three Halves; `necklace` Two People, One Necklace; `ls` Three Pieces Are Not Enough; `lab` The Bench
  - Lab settings: `curves` Curves (1/0); `labels` Labels (1/0)
- [One Shape, Never Repeating (只用一种形状，永不重复)](https://world.lapla.si/en/hat/): plate M14. A thirteen-sided shape made of eight kites covers the whole plane, yet however it is laid, the pattern never repeats periodically. Markdown: [en](https://world.lapla.si/en/hat/index.html.md), [中文](https://world.lapla.si/zh/hat/index.html.md).
  - 中文: [只用一种形状，永不重复](https://world.lapla.si/zh/hat/) — 一块由 8 个风筝形拼成的十三边形，可以铺满整个平面，但无论怎样铺，图案都不会周期性地重复。
  - A single shape that covers the plane, but only in patterns that never repeat periodically, is called an aperiodic monotile. The search took more than fifty years. In 2023 the “hat” turned up: a thirteen-sided shape made of eight kites.
  - Embed: https://world.lapla.si/embed/en/hat/ · https://world.lapla.si/embed/zh/hat/
  - Chapters: `cover` One Shape, Never Repeating; `shape` Eight Kites; `tile` Covering, Never Repeating; `flip` Some Turned Over; `meta` Four Clusters; `inflate` Larger, and Larger Again; `family` A Family of Shapes; `proof` Why It Cannot Repeat; `spectre` A Tile That Never Turns; `lab` The Bench
  - Lab settings: `choice` Level (0 | 1 | 2 | 3); `shape` Shape Tile(a, b) (0–90, step 0.5); `frames` Frames (1/0); `labels` Labels (1/0)
- [A Sphere Will Not Lie Flat (球面摊不平)](https://world.lapla.si/en/projection/): plate M15. A sphere cannot be flattened without distortion. Every map projection gives something up: area, angles, distance or straight lines. Markdown: [en](https://world.lapla.si/en/projection/index.html.md), [中文](https://world.lapla.si/zh/projection/index.html.md).
  - 中文: [球面摊不平](https://world.lapla.si/zh/projection/) — 球面不能不变形地摊成平面。每一种地图投影都要放弃一些东西：面积、角度、距离，或者直线。
  - Peel the skin off a globe and press it flat, and it tears or stretches. A sphere is curved and a plane is not, so every world map chooses what to keep.
  - Embed: https://world.lapla.si/embed/en/projection/ · https://world.lapla.si/embed/zh/projection/
  - Chapters: `cover` A Sphere Will Not Lie Flat; `peel` The Peeled Skin; `gauss` Gauss’s Remarkable Theorem; `surfaces` Surfaces That Do Unroll; `mercator` Mercator Keeps the Angles; `rhumb` Why Sailors Wanted It; `size` Greenland and Africa; `equal` Keeping Area; `gnomonic` A Lamp at the Centre; `azimuthal` Distances from the Centre; `dymaxion` Cut Into Twenty Faces; `tissot` An Honest Ruler; `lab` The Bench
  - Lab settings: `choice` Projection (mercator | lambert | mollweide | equalearth | conic | equidistant | dymaxion); `discs` Discs (1/0); `labels` Labels (1/0)
- [More Than One Parallel (平行线不止一条)](https://world.lapla.si/en/hyperbolic/): plate M16. Replace Euclid’s fifth postulate by “through a point off a line there is more than one parallel”, and you get a world just as consistent: triangles add up to less than 180°, and space grows exponentially. Markdown: [en](https://world.lapla.si/en/hyperbolic/index.html.md), [中文](https://world.lapla.si/zh/hyperbolic/index.html.md).
  - 中文: [平行线不止一条](https://world.lapla.si/zh/hyperbolic/) — 欧几里得第五公设换成「过直线外一点有不止一条平行线」，得到的是一个同样自洽的世界：三角形内角和小于 180°，空间向外指数增长。
  - For two thousand years people tried to derive Euclid’s fifth postulate from the others, and failed. In the nineteenth century several people found, each on their own, that replacing it gives a geometry with no contradiction. Every tile on this enamel plate is the same size.
  - Embed: https://world.lapla.si/embed/en/hyperbolic/ · https://world.lapla.si/embed/zh/hyperbolic/
  - Chapters: `cover` More Than One Parallel; `postulate` The Fifth Postulate; `parallels` More Than One; `pseudosphere` A Real Surface; `disc` Infinity in a Disc; `halfplane` The Upper Half-Plane; `triangle` Less Than 180°; `tilings` Regular Tilings; `mirrors` Made by Mirrors; `escher` Circle Limit; `growth` Space That Grows Exponentially; `crochet` Made With a Hook; `lab` The Bench
  - Lab settings: `choice` Tool (move | geodesic | triangle); `p` Sides p (3–10, step 1); `q` At each corner q (3–10, step 1)
- [The Fourth Direction (第四个方向)](https://world.lapla.si/en/polytope/): plate M17. Four-dimensional space holds six regular polytopes. We cannot see them, only their slices and their shadows: a three-dimensional hyperplane passing through, or a projection into our space. Markdown: [en](https://world.lapla.si/en/polytope/index.html.md), [中文](https://world.lapla.si/zh/polytope/index.html.md).
  - 中文: [第四个方向](https://world.lapla.si/zh/polytope/) — 四维空间里有六种正多胞体。我们看不到它们，只能看它们的截面和投影：一个三维的超平面切过去，或者把它的影子投到我们的空间里。
  - Three dimensions have five regular solids, four have six regular polytopes, and every dimension above that has only three. This model builds their projections into our space from brass struts and steel nodes, and shows their slices in coloured glass.
  - Embed: https://world.lapla.si/embed/en/polytope/ · https://world.lapla.si/embed/zh/polytope/
  - Chapters: `cover` The Fourth Direction; `flatland` Flatland; `ladder` From a Point to a Tesseract; `net` Unfolding It; `six` Six Regular Polytopes; `slices` A Hyperplane Passes Through; `stott` Sections in Card; `schlegel` Perspective: the Schlegel Diagram; `stereo` Stereographic Projection; `rotate` Turning in a Plane; `higher` Only Three From Five Dimensions Up; `lab` The Bench
  - Lab settings: `choice` Polytope (5 | 8 | 16 | 24 | 120 | 600); `choice2` Plane of turning (0 | 1 | 2 | 3 | 4 | 5 | stop); `choice3` Projection (ortho | persp | stereo); `h` Hyperplane w (-1–1, step 0.01)
- [A Line That Fills a Square (一条线填满正方形)](https://world.lapla.si/en/hilbert/): plate M18. A continuous curve can pass through every point of a square. In 1891 Hilbert drew how: split into four, then four again, without end. Markdown: [en](https://world.lapla.si/en/hilbert/index.html.md), [中文](https://world.lapla.si/zh/hilbert/index.html.md).
  - 中文: [一条线填满正方形](https://world.lapla.si/zh/hilbert/) — 一条连续的曲线可以经过正方形里的每一点。希尔伯特 1891 年画出了它的构造：一分为四，再一分为四，无限地分下去。
  - Which has more points, a line segment or a square? Cantor’s answer was neither. A decade later Peano and Hilbert found something stranger: a continuous line through every point of the square. The wire in the tray is the fifth step towards it.
  - Embed: https://world.lapla.si/embed/en/hilbert/ · https://world.lapla.si/embed/zh/hilbert/
  - Chapters: `cover` A Line That Fills a Square; `cantor` As Many Points; `peano` Through Every Point, Continuously; `hilbert` Hilbert’s Picture; `limit` The Limit; `onto` Some Points, Three Times; `local` Near Stays Near; `zorder` Z-Order; `family` A Family of Curves; `dither` Scanning Along the Curve; `index` Maps and Databases; `sphere` Cells on a Sphere; `lab` The Bench
  - Lab settings: `order` Order (1–8, step 1); `k` k cells either side (1–64, step 1); `nb` Neighbourhood (1/0)
- [How Evidence Moves Belief (证据如何改变相信)](https://world.lapla.si/en/bayes/): plate M19. Start with how much you believe something, see some evidence, and change your belief by the weight of that evidence. Bayes’ theorem says exactly how: the posterior is proportional to the prior times the likelihood. Markdown: [en](https://world.lapla.si/en/bayes/index.html.md), [中文](https://world.lapla.si/zh/bayes/index.html.md).
  - 中文: [证据如何改变相信](https://world.lapla.si/zh/bayes/) — 先有一个相信的程度，看到证据，再按证据的分量改一改。贝叶斯定理说的就是怎样改：后验正比于先验乘以似然。
  - Balls on a table tell where another ball lies; one peg in a thousand is ill, yet most positive results are false; on a sea chart, places searched in vain send the sand to places not yet searched. Three models, each computed exactly by Bayes’ theorem.
  - Embed: https://world.lapla.si/embed/en/bayes/ · https://world.lapla.si/embed/zh/bayes/
  - Chapters: `cover` How Evidence Moves Belief; `table` A Level Table; `curve` From Counts to a Curve; `general` Prior Times Likelihood; `test` One in a Thousand; `areas` As Areas; `odds` Odds and the Likelihood Ratio; `sequence` One at a Time; `converge` Different Priors, One Answer; `sand` Probability as Sand; `scorpion` Scorpion; `af447` Air France 447; `lab` The Bench
  - Lab settings: `choice` Piece (table | tray | chart); `choice2` Prior (flat | right | left); `base` Base rate (-3–-0.3010299956639812, step 0.01); `sens` Sensitivity (ill test positive) (0.5–0.999, step 0.001); `spec` Specificity (well test negative) (0.5–0.999, step 0.001); `areas` Lay out by area (1/0); `d` Chance one look finds it, d (0.1–0.95, step 0.05)
- [Every Loop Holds a Rectangle (每个圈上都有长方形)](https://world.lapla.si/en/mobius/): plate M20. Every closed curve in the plane has four points that form a rectangle. The proof lifts the pairs of points on the curve into space, where they make a Möbius strip; the strip cannot lie flat, it has to pass through itself, and where it does is a rectangle. Markdown: [en](https://world.lapla.si/en/mobius/index.html.md), [中文](https://world.lapla.si/zh/mobius/index.html.md).
  - 中文: [每个圈上都有长方形](https://world.lapla.si/zh/mobius/) — 任何一条闭合的曲线上都有四个点构成长方形。证明把曲线上的点对举到空间里，铺成一条莫比乌斯带；这条带子放不平，必然穿过自己，穿过的地方就是长方形。
  - On every closed curve that does not cross itself there are four points forming a rectangle. The reason is not the curve’s shape but the Möbius strip.
  - Embed: https://world.lapla.si/embed/en/mobius/ · https://world.lapla.si/embed/zh/mobius/
  - Chapters: `cover` Every Loop Holds a Rectangle; `square` A Square on a Loop; `rect` One Step Back: Rectangles; `diagonals` Two Diagonals; `lift` Lifting Every Pair; `seam` The Surface Passes Through Itself; `mobius` The Pairs Are a Möbius Strip; `why` Why It Must Pass Through; `ratio` Every Shape of Rectangle; `open` The Square Is Still Open; `lab` The Bench
  - Lab settings: `angle` Diagonal angle (5–90, step 1); `arches` Wires (1/0); `cloth` Cloth (1/0); `squares` Squares (1/0)
- [Patterns Drawn by Diffusion (扩散画出的斑纹)](https://world.lapla.si/en/turing/): plate M21. Two substances: one makes more of itself, the other holds it down, and the one that holds it down spreads faster. An even mixture then breaks into spots or stripes on its own, at a spacing the equations set. Markdown: [en](https://world.lapla.si/en/turing/index.html.md), [中文](https://world.lapla.si/zh/turing/index.html.md).
  - 中文: [扩散画出的斑纹](https://world.lapla.si/zh/turing/) — 两种物质，一种让自己变多，一种压住它，而压住它的那种跑得更快。均匀的混合于是自己长出斑点或条纹，间距由方程决定。
  - Diffusion usually smooths things out. In 1952 Alan Turing worked out the opposite case: two substances that react with each other, spreading at different enough speeds, break an even state into spots or stripes a set distance apart. The gel, the ceramic tail and the strip of fish skin are all computed live.
  - Embed: https://world.lapla.si/embed/en/turing/ · https://world.lapla.si/embed/zh/turing/
  - Chapters: `cover` Patterns Drawn by Diffusion; `two` Two Substances; `unstable` Diffusion That Makes Pattern; `spacing` The Spacing Is Computed; `shape` Spots or Stripes; `map` A Map of Parameters; `gel` Evidence in a Gel; `fish` A Growing Fish; `cells` Cells, Not Molecules; `tail` The Leopard’s Tail; `lab` The Bench
  - Lab settings: `choice` Model (gm | gs); `kappa` Saturation κ (0–0.2, step 0.005); `F` F (0.005–0.08, step 0.0005); `k` k (0.03–0.075, step 0.0005); `speed` Speed (0.25–3, step 0.05); `erase` Erase (1/0)
- [Life from a Table of Numbers (一张表里长出的生命)](https://world.lapla.si/en/particles/): plate M22. A few kinds of beads, and one number between every two kinds: pull or push. Make the table lopsided and Newton’s third law fails; the tank never settles again. Markdown: [en](https://world.lapla.si/en/particles/index.html.md), [中文](https://world.lapla.si/zh/particles/index.html.md).
  - 中文: [一张表里长出的生命](https://world.lapla.si/zh/particles/) — 几种珠子，每两种之间只有一个数：吸引或排斥。只要这张表不对称，牛顿第三定律就不成立，玻璃槽里便永远不会安静。
  - A few kinds of beads in a glass tank. Each kind has one number for each kind, attract or repel, and nothing else. A symmetric table lets them line up and stop. A lopsided one grows things that walk, chase, split and merge.
  - Embed: https://world.lapla.si/embed/en/particles/ · https://world.lapla.si/embed/zh/particles/
  - Chapters: `cover` Life from a Table of Numbers; `rule` One Number; `table` A Table; `third` The Third Law; `chase` Chase and Flight; `cells` Membrane and Core; `zoo` The Specimen Rack; `random` Any Table at All; `nature` Lopsided in Nature; `history` Where It Came From; `lab` The Bench
  - Lab settings: `play` Play (1/0); `rate` Speed of time (0.2–2, step 0.05); `count` Beads (200–4096, step 100); `sym` Symmetric table only (1/0)

## Technology / Classic Machines

- [Watt’s Steam Engine (瓦特的蒸汽机)](https://world.lapla.si/en/steam/): plate C01. An iron vessel standing in cold water saved most of the coal; two spinning balls taught the engine its own pace. Built in Birmingham in 1788, it stands at rest in London today. Markdown: [en](https://world.lapla.si/en/steam/index.html.md), [中文](https://world.lapla.si/zh/steam/index.html.md).
  - 中文: [瓦特的蒸汽机](https://world.lapla.si/zh/steam/) — 一只浸在冷水里的铁罐，省下了一大半的煤；两只飞球一转，机器便自己拿捏快慢。它 1788 年造于伯明翰，如今静立在伦敦。
  - James Watt did not invent the steam engine. Half a century before him, engines were already pumping water from English mines, but at every stroke they chilled their own cylinder and then had to warm it again. Watt gave cold and heat each a place of its own, and the same coal did twice the work; twenty years on, he and his partner were building engines that drove whole factories. This one, built in 1788, is the oldest rotative steam engine in the world to survive essentially unaltered.
  - Embed: https://world.lapla.si/embed/en/steam/ · https://world.lapla.si/embed/zh/steam/
  - Chapters: `cover` Watt’s Steam Engine; `waste` Between Cold and Hot; `condenser` A Separate Vessel; `double` Pushing Both Ways; `parallel` A Straight Line out of an Arc; `sun` Sun and Planet; `governor` The Flyball Governor; `apart` Taken Apart; `section` Cut Open; `changed` What It Changed; `lab` At the Regulator
  - Lab settings: `machines` Polishing machines running (0–43, step 1); `governor` Governor (1/0); `labels` Labels (1/0)
- [The SLR Camera (单反相机)](https://world.lapla.si/en/camera/): plate C02. While you frame, a mirror behind the lens sends the light up into a prism. Press the release and the mirror lifts; two cloth curtains cross the film one after the other. Markdown: [en](https://world.lapla.si/en/camera/index.html.md), [中文](https://world.lapla.si/zh/camera/index.html.md).
  - 中文: [单反相机](https://world.lapla.si/zh/camera/) — 取景时，镜头后的一面镜子把光送进五棱镜；按下快门，镜子抬起，两道布帘依次掠过胶片。
  - SLR stands for single-lens reflex. The same lens is used to frame and to take the picture: a mirror sends the lens’s light to the viewfinder, and at the moment of exposure it swings up and the light falls on the film. The model follows the Olympus OM-1 of 1972, a fully mechanical 35 mm film SLR.
  - Embed: https://world.lapla.si/embed/en/camera/ · https://world.lapla.si/embed/zh/camera/
  - Chapters: `cover` The SLR Camera; `real` A Real One; `parallax` What You See, What You Get; `mirror` A Mirror at 45°; `prism` The Roof Pentaprism; `release` Pressing the Release; `shutter` Two Curtains; `flash` Flash Sync; `advance` Winding On; `apart` Taken Apart; `section` Cut Open: One Light Path; `changed` What It Changed; `lab` At the Shutter
  - Lab settings: `flash` Flash (1/0); `labels` Labels (1/0)
- [The Escapement (擒纵机构)](https://world.lapla.si/en/escapement/): plate C03. A spring or a falling weight, let go, gives up its energy all at once. The escapement lets it out in equal small steps, one per beat, timed by something that swings back and forth. Markdown: [en](https://world.lapla.si/en/escapement/index.html.md), [中文](https://world.lapla.si/zh/escapement/index.html.md).
  - 中文: [擒纵机构](https://world.lapla.si/zh/escapement/) — 发条或重锤的力，放开就会一下子放完。擒纵机构把它分成相等的小份，一拍放一份，节拍由一个来回摆动的振子决定。
  - A mechanical clock or watch is driven by a falling weight or a wound spring, and timed by an oscillator with a rhythm of its own: a pendulum, or a balance wheel and hairspring. Between the two sits the escapement. Each beat it lets the wheels move on one small step and gives the oscillator a little energy back. The main exhibit is a watch movement beating 28,800 times an hour, with two older clocks beside it.
  - Embed: https://world.lapla.si/embed/en/escapement/ · https://world.lapla.si/embed/zh/escapement/
  - Chapters: `cover` The Escapement; `problem` All at Once; `verge` Verge and Foliot; `pendulum` A Rhythm of Its Own; `anchor` The Anchor; `lever` The Lever in a Watch; `cycle` One Beat in Five Steps; `detached` Left Alone; `tick` The Tick; `wind` Wound and Running Down; `apart` Taken Apart; `section` Cut Open; `changed` What It Changed; `lab` The Movement in Hand
  - Lab settings: `slow` Slow motion (1/0); `sound` Sound (1/0); `labels` Labels (1/0)
- [The Four-Stroke Engine (四冲程发动机)](https://world.lapla.si/en/engine/): plate C04. The fuel burns inside the cylinder. The piston makes four strokes and the crank turns twice; in one of them, the burning gas drives the piston down. Markdown: [en](https://world.lapla.si/en/engine/index.html.md), [中文](https://world.lapla.si/zh/engine/index.html.md).
  - 中文: [四冲程发动机](https://world.lapla.si/zh/engine/) — 燃料在汽缸里烧。活塞上下四次、曲轴转两圈，其中一次被燃气推下去。
  - A petrol engine burns its fuel inside the cylinder, with no boiler. In every two round trips of the piston it draws in, compresses, burns and pushes out its charge, and only one of those strokes is driven by the gas. The model follows the 1968 Alfa Romeo 1750, an inline four with two overhead camshafts: an aluminium block, cast-iron liners and a forged-steel crankshaft.
  - Embed: https://world.lapla.si/embed/en/engine/ · https://world.lapla.si/embed/zh/engine/
  - Chapters: `cover` The Four-Stroke Engine; `problem` Fire Inside the Cylinder; `strokes` Four Strokes; `valves` Camshafts at Half Speed; `crank` Crank and Connecting Rod; `four` Four Cylinders, 1-3-4-2; `efficiency` Compression and Efficiency; `apart` Taken Apart; `section` One Cylinder, Cut Open; `changed` What It Changed; `lab` Throttle in Hand
  - Lab settings: `slow` Stroke by stroke (1/0); `cut` Cut open (1/0); `labels` Labels (1/0)
- [The Printing Press (活字印刷机)](https://world.lapla.si/en/press/): plate C05. Metal letters set into a page, inked, covered with paper, one pull of the bar: a printed page. Mainz, about 1450. Markdown: [en](https://world.lapla.si/en/press/index.html.md), [中文](https://world.lapla.si/zh/press/index.html.md).
  - 中文: [活字印刷机](https://world.lapla.si/zh/press/) — 一个个金属字排成版，上墨，盖纸，拉一下压杆：一页印好了。约 1450 年，美因茨。
  - Around 1450 in Mainz, Johannes Gutenberg put several things together into one method: a hand mould that could change its width, type cast from a lead–tin alloy, oil-based ink, and a screw press. The letters could be taken apart and set again, and a page could be printed hundreds of times. The model follows the wooden hand press as later pictures show it; the tools for casting and setting type are on the bench beside it.
  - Embed: https://world.lapla.si/embed/en/press/ · https://world.lapla.si/embed/zh/press/
  - Chapters: `cover` The Printing Press; `copy` How a Book Was Made; `system` Gutenberg’s Method; `stick` Set Backwards; `forme` Locking Up and Inking; `pull` One Pull; `apart` Taken Apart; `section` Cut Open: Casting a Letter; `bible` Forty-Two Lines; `changed` What It Changed; `lab` At the Bar
  - Lab settings: `labels` Labels (1/0)
- [The Phonograph and the Gramophone (留声机)](https://world.lapla.si/en/phonograph/): plate C06. Sound pushes a needle that cuts wiggles into a groove; a needle running back along the wiggles brings the sound back. The whole machine runs without electricity. Markdown: [en](https://world.lapla.si/en/phonograph/index.html.md), [中文](https://world.lapla.si/zh/phonograph/index.html.md).
  - 中文: [留声机](https://world.lapla.si/zh/phonograph/) — 声音推着针在沟槽里刻出弯曲，针再沿着弯曲走一遍，声音就回来了。整台机器不用电。
  - Before 1877, no one had heard recorded sound. The phonograph cut the vibrations of sound into a fine groove, then let a steel needle run along it and shake a thin diaphragm. The model is a wind-up table gramophone: an oak cabinet, a 78 rpm shellac disc, a soundbox with a mica diaphragm and a brass petal horn.
  - Embed: https://world.lapla.si/embed/en/phonograph/ · https://world.lapla.si/embed/zh/phonograph/
  - Chapters: `cover` The Phonograph and the Gramophone; `problem` Sound Was Gone As Soon As It Was Made; `edison` A Cylinder of Tinfoil; `berliner` A Flat Disc; `needle` The Needle in the Groove; `groove` A Chord Cut into the Groove; `soundbox` The Soundbox; `horn` The Horn; `motor` Spring and Governor; `apart` Taken Apart; `section` The Sound’s Path, Cut Open; `changed` What It Changed; `lab` Crank in Hand
  - Lab settings: `brake` Brake (1/0); `labels` Labels (1/0)
- [The Typewriter (打字机)](https://world.lapla.si/en/typewriter/): plate C07. Press a key and a typebar swings up and strikes the paper through the ribbon; let go and the carriage steps one space to the left. Markdown: [en](https://world.lapla.si/en/typewriter/index.html.md), [中文](https://world.lapla.si/zh/typewriter/index.html.md).
  - 中文: [打字机](https://world.lapla.si/zh/typewriter/) — 按下一个键，一根字杆甩起来，隔着色带把字母压在纸上；松开键，滑架向左让出一格。
  - Handwriting is slow, and every hand is different. The typewriter cast each letter as a piece of type and printed it at the touch of a key, the same size and just as clear every time. The model is a frontstrike machine of the kind of the Underwood No. 5, made from 1900: a black enamelled cast frame, glass-topped keys, and forty-two nickelled typebars in a half circle, striking the front of a rubber platen. Type on it with your own keyboard.
  - Embed: https://world.lapla.si/embed/en/typewriter/ · https://world.lapla.si/embed/zh/typewriter/
  - Chapters: `cover` The Typewriter; `problem` The Trouble with Handwriting; `first` The First Typewriter on Sale; `qwerty` Why the Keyboard Says QWERTY; `strike` One Keystroke, Slowed Down; `escapement` A Carriage That Moves One Space at a Time; `line` Capitals, the Bell and a New Line; `apart` Taken Apart; `section` One Key, Cut Open; `changed` What It Changed; `lab` Type a Few Lines
  - Lab settings: `sound` Sound (1/0); `labels` Labels (1/0)
- [The Lockstitch Sewing Machine (缝纫机与锁式线迹)](https://world.lapla.si/en/sewing/): plate C08. The needle takes a loop of thread under the cloth; the hook carries it round the bobbin case and over the lower thread, and the loop is drawn back into the cloth. One turn of the handwheel, one stitch. Markdown: [en](https://world.lapla.si/en/sewing/index.html.md), [中文](https://world.lapla.si/zh/sewing/index.html.md).
  - 中文: [缝纫机与锁式线迹](https://world.lapla.si/zh/sewing/) — 针把一个线圈送到布下面，旋梭带着它绕过梭壳，套住底线，再拉回布中间。转一圈手轮，缝一针。
  - By hand, a few dozen stitches a minute. A sewing machine has its needle’s eye at the point and two threads, one above the cloth and one below, that lock in the middle of it, hundreds of times a minute. The model is a black japanned household machine with gold decals; the hook and bobbin sit under the cloth.
  - Embed: https://world.lapla.si/embed/en/sewing/ · https://world.lapla.si/embed/zh/sewing/
  - Chapters: `cover` The Lockstitch Sewing Machine; `problem` How Slow Sewing by Hand Is; `needle` The Eye at the Point; `lockstitch` How One Stitch Locks; `feed` The Feed Dogs; `timing` One Turn, One Stitch; `apart` Taken Apart; `inside` Inside the Machine; `changed` What It Changed; `lab` Sew a Few Stitches
  - Lab settings: `xray` X-ray (1/0); `labels` Labels (1/0)
- [The Enigma Cipher Machine (恩尼格玛密码机)](https://world.lapla.si/en/enigma/): plate C09. Press a key and the rotors step first; the current runs through the plugboard, three rotors and a reflector and back, and another letter lights up. Markdown: [en](https://world.lapla.si/en/enigma/index.html.md), [中文](https://world.lapla.si/zh/enigma/index.html.md).
  - 中文: [恩尼格玛密码机](https://world.lapla.si/zh/enigma/) — 按一个键，转子先走一格，电流穿过插线板、三个转子和反射器再折回来，另一个字母的灯亮了。
  - Anyone can pick up a radio message, so it has to be unreadable to all but its own side. The Enigma is an electromechanical rotor machine: press a key, the rotors move on a step, the current takes a path that is different every time, and another letter lights on the lamp board. The model is the Enigma I the German Army used from 1930: an oak case, black crackle finish, three rotors, reflector B and a plugboard with ten cables. Type on it with your own keyboard.
  - Embed: https://world.lapla.si/embed/en/enigma/ · https://world.lapla.si/embed/zh/enigma/
  - Chapters: `cover` The Enigma Cipher Machine; `problem` Messages Anyone Can Hear; `keys` Press a Key, a Lamp Lights; `path` The Path of the Current; `stepping` Rotors That Count Like an Odometer; `plugboard` The Plugboard; `rules` The Same Settings Decipher; `keyspace` How Many Settings; `apart` Taken Apart; `rotor` One Rotor, Cut Open; `broken` How It Was Broken; `changed` What It Changed; `lab` Encipher a Line Yourself
  - Lab settings: `labels` Labels (1/0)
- [The Difference Engine (差分机)](https://world.lapla.si/en/difference/): plate C10. Tables of polynomials by addition alone: eight columns of figure wheels, each added to the next, one result per turn of the cycle, printed straight away. Markdown: [en](https://world.lapla.si/en/difference/index.html.md), [中文](https://world.lapla.si/zh/difference/index.html.md).
  - 中文: [差分机](https://world.lapla.si/zh/difference/) — 只用加法算出多项式的表：八列数字轮，一列加到下一列，摇一圈曲柄出一个结果，直接印出来。
  - Navigation, astronomy and engineering in the nineteenth century ran on printed tables, and the tables were computed, copied and typeset by hand, with errors everywhere. Babbage designed a machine that does nothing but add, and left both the arithmetic and the printing to gears. The model is his Difference Engine No. 2, after the one the Science Museum in London built to his drawings of 1847–49: bronze figure wheels, an iron frame, steel carry arms, the crank and cam stack at one end and the printing and stereotyping apparatus at the other.
  - Embed: https://world.lapla.si/embed/en/difference/ · https://world.lapla.si/embed/zh/difference/
  - Chapters: `cover` The Difference Engine; `tables` Errors in the Tables; `differences` Addition Alone; `wheels` Eight Columns of Figure Wheels; `cycle` Two Halves to a Result; `carry` Carrying Tens; `print` Printed Straight Away; `apart` Taken Apart; `history` Built 150 Years Later; `changed` What It Changed; `lab` Turn It Yourself
  - Lab settings: `choice` Polynomial (euler | squares | cubes); `broken` Disconnect units carry lever (1/0); `labels` Labels (1/0)
- [The Picture Tube (显像管电视机)](https://world.lapla.si/en/crt/): plate C11. A beam of electrons in a vacuum, pushed about by magnetic fields more than fifteen thousand lines a second, paints a picture on phosphor one spot at a time. Markdown: [en](https://world.lapla.si/en/crt/index.html.md), [中文](https://world.lapla.si/zh/crt/index.html.md).
  - 中文: [显像管电视机](https://world.lapla.si/zh/crt/) — 一束电子在真空里被磁场推着走，一秒一万五千多行，把一幅画面一点一点画在荧光粉上。
  - From the 1950s into this century, television pictures were drawn inside an evacuated glass tube. A gun at the back fires a beam of electrons, coils round the neck steer it with magnetic fields to every part of the screen, and the phosphor on the inside of the screen glows where it is hit. The model is a colour set of about 1980: a walnut cabinet and a 22-inch class in-line shadow-mask tube, cut away at the left side and the top, and the tube can be cut open along its axis.
  - Embed: https://world.lapla.si/embed/en/crt/ · https://world.lapla.si/embed/zh/crt/
  - Chapters: `cover` The Picture Tube; `picture` One Spot at a Time; `inside` A Glass Bottle of Vacuum; `gun` Making a Beam; `steer` Steered by Magnets; `raster` Line by Line; `colour` Three Guns and a Mask; `glow` Afterglow; `voltage` Twenty-Five Thousand Volts; `apart` Taken Apart; `changed` What It Changed; `lab` Scan It Yourself
  - Lab settings: `choice` Raster (pal | ntsc | coarse); `h` Horizontal coil current (-100–100, step 1); `interlace` Interlace (1/0); `cut` Cut the tube open (1/0); `magnet` Magnet near the screen (1/0); `red` Red gun (1/0); `green` Green gun (1/0); `blue` Blue gun (1/0); `labels` Labels (1/0)
- [The Antikythera Mechanism (安提基西拉机械)](https://world.lapla.si/en/antikythera/): plate C12. A box of bronze gears from more than two thousand years ago: turn the crank, and the Sun, the Moon, its phase, the calendar and the eclipse cycles all move on together. Markdown: [en](https://world.lapla.si/en/antikythera/index.html.md), [中文](https://world.lapla.si/zh/antikythera/index.html.md).
  - 中文: [安提基西拉机械](https://world.lapla.si/zh/antikythera/) — 两千多年前的一盒青铜齿轮：转动曲柄，日月、月相、阴历和日月食的周期一起往前走。
  - In 1901 a corroded lump of bronze came up from an ancient wreck off southern Greece. Inside it is the earliest geared calculator known. It was made around the second century BC, it holds astronomical cycles in its tooth counts, and a turn of its crank works out, for any day, where the Sun and Moon stand, the phase of the Moon, the month of the calendar and the eclipses that may come. The model follows the reconstruction published by the UCL research team in 2021: a wooden case, bronze plates and gears, the zodiac and the display of the Cosmos at the front and two spiral dials at the back.
  - Embed: https://world.lapla.si/embed/en/antikythera/ · https://world.lapla.si/embed/zh/antikythera/
  - Chapters: `cover` The Antikythera Mechanism; `wreck` A Lump of Bronze from the Sea; `sky` Cycles That Don’t Line Up; `crank` Turning Time; `trains` Tooth Counts Are Periods; `pinslot` The Moon Speeds Up and Slows Down; `phase` The Moon Ball; `back` Two Spirals on the Back; `planets` The Planets: Evidence and Reconstruction; `apart` Taken Apart; `changed` What It Changed; `lab` Turn It Yourself
  - Lab settings: `year` Year (-260–-40, step 1); `survive` Surviving only (1/0); `found` As found (1/0); `back` Show the back (1/0); `labels` Labels (1/0)
- [The Tide-Predicting Machine (潮汐预报机)](https://world.lapla.si/en/tide/): plate C13. A row of cranks, one wire and a pen: Kelvin’s machine added ten cosines together and drew a year of a port’s tides in four hours. Markdown: [en](https://world.lapla.si/en/tide/index.html.md), [中文](https://world.lapla.si/zh/tide/index.html.md).
  - 中文: [潮汐预报机](https://world.lapla.si/zh/tide/) — 一排曲柄、一根钢丝和一支笔：开尔文的机器把十个余弦加在一起，四个小时画出一个港口一年的潮汐。
  - The tide at a port can be taken apart into many rises and falls with fixed periods, each set by some motion of the Moon or the Sun. In 1872 William Thomson, later Lord Kelvin, designed a machine that made each of them a crank, added them with one wire and drew the sum with a pen on a band of paper. For more than ninety years afterwards, most of the world’s tide tables came from machines like it.
  - Embed: https://world.lapla.si/embed/en/tide/ · https://world.lapla.si/embed/zh/tide/
  - Chapters: `cover` The Tide-Predicting Machine; `problem` A Port Needs a Table; `sum` Many Rises and Falls, Added; `yoke` One Crank per Term; `gears` Tooth Counts Set the Speeds; `wire` One Wire Does the Sum; `pen` A Pen Draws the Year; `apart` Taken Apart; `dday` “Position Z”, 1944; `changed` What It Changed; `lab` Turn It Yourself
  - Lab settings: `choice` Port (8443970 | 8410140 | 9414290 | 9447130 | 8729840 | 1612340); `labels` Labels (1/0)
- [The Wankel Rotary Engine (转子发动机)](https://world.lapla.si/en/wankel/): plate C14. A three-sided rotor goes round inside a waisted bore: three chambers work through the four strokes at once, with no pistons going up and down and no valves. Markdown: [en](https://world.lapla.si/en/wankel/index.html.md), [中文](https://world.lapla.si/zh/wankel/index.html.md).
  - 中文: [转子发动机](https://world.lapla.si/zh/wankel/) — 一个三角形的转子在一条「8」字形的缸里绕着转：三个腔同时做着四个冲程，没有活塞往复，也没有气门。
  - In a piston engine the pistons stop and reverse dozens of times a second. The rotary engine does away with that: a three-sided rotor on an eccentric shaft runs round a bore shaped as an epitrochoid, and the three chambers between rotor and bore take turns to draw in, compress, burn and expel. The model is built to the dimensions of Mazda’s 13B: R 105 mm, e 15 mm, 80 mm wide, two rotors.
  - Embed: https://world.lapla.si/embed/en/wankel/ · https://world.lapla.si/embed/zh/wankel/
  - Chapters: `cover` The Wankel Rotary Engine; `problem` An Engine That Doesn’t Reciprocate; `housing` An Epitrochoid; `gears` Three to Two; `strokes` Three Chambers, Four Strokes at Once; `ports` No Valves; `seals` The Apex Seals; `chamber` A Long, Thin Combustion Chamber; `apart` Taken Apart; `section` Cut Along the Shaft; `power` Small and Strong; `changed` What It Changed; `lab` Turn the Shaft
  - Lab settings: `choice` Ports (side | renesis | peripheral); `angle` Shaft angle (0–1080, step 1); `wear` Apex seal wear (0–1, step 0.01); `labels` Labels (1/0)
- [The Mark I Perceptron (感知机)](https://world.lapla.si/en/perceptron/): plate C15. A machine that learned letters from examples: four hundred photocells to see, 512 randomly wired units in between, and motor-driven potentiometers to remember. Markdown: [en](https://world.lapla.si/en/perceptron/index.html.md), [中文](https://world.lapla.si/zh/perceptron/index.html.md).
  - 中文: [感知机](https://world.lapla.si/zh/perceptron/) — 一台从例子里学会认字母的机器：四百个光电池看，五百一十二个随机接线的单元在中间，电动机转动的电位器记住学到的东西。
  - In 1958 a computer did only what a program spelled out step by step. Frank Rosenblatt wanted a machine that learned from examples. The Mark I Perceptron, built at the Cornell Aeronautical Laboratory, looked at a letter with 20 × 20 photocells, passed the signals through a randomly wired plugboard to 512 association units, and weighted those through motor-driven potentiometers for eight response units to answer. When an answer was wrong, the potentiometers turned a step.
  - Embed: https://world.lapla.si/embed/en/perceptron/ · https://world.lapla.si/embed/zh/perceptron/
  - Chapters: `cover` The Mark I Perceptron; `problem` Learning from examples; `embryo` “Embryo of computer”; `retina` Four hundred photocells; `wiring` Wired at random; `weights` Potentiometers that turn; `learning` Turned only when wrong; `apart` Taken apart; `camera` The camera, cut open; `results` What it learned; `limits` What it could not learn; `today` Today’s networks; `lab` Teach it letters
  - Lab settings: `choice` Task (ex | eight | parity); `speed` Pictures a second (1–60, step 1); `labels` Labels (1/0)

## Technology / Energy, Flight & Sensing

- [Five-Axis Machining Centre (五轴加工中心)](https://world.lapla.si/en/cnc/): plate F02. Three straight axes move the spindle, two rotary axes turn the part, and all five move together to cut an impeller from a solid block of aluminium. Markdown: [en](https://world.lapla.si/en/cnc/index.html.md), [中文](https://world.lapla.si/zh/cnc/index.html.md).
  - 中文: [五轴加工中心](https://world.lapla.si/zh/cnc/) — 三根直线轴移动主轴，两根旋转轴转动工件，五根轴一起动，把一块实心铝切成叶轮。
  - Jet-engine blisks, turbocharger impellers, artificial joints and moulds are all complex curved surfaces, and in many places a cutter can only reach in at a slant. A five-axis machining centre tilts and turns the part so the cutter always meets it at a good angle. In the model, the machine is cutting an impeller from an aluminium billet 210 mm across.
  - Embed: https://world.lapla.si/embed/en/cnc/ · https://world.lapla.si/embed/zh/cnc/
  - Chapters: `cover` Five-Axis Machining Centre; `micron` Thousandths of a Millimetre; `axes` Five Axes; `reach` Why Five; `rtcp` The Tip Stays on the Path; `flank` Tip and Flank; `spindle` Cut Open: the Spindle; `scales` Scales and Heat; `changer` Tool Changer, Probe and Coolant; `makes` From a Solid Block; `apart` Taken Apart; `lab` Spindle Speed
  - Lab settings: `path` Toolpath (1/0); `coolant` Coolant (1/0); `labels` Labels (1/0)
- [Tokamak Fusion Reactor (托卡马克聚变装置)](https://world.lapla.si/en/tokamak/): plate F06. A tokamak like ITER: eighteen D-shaped superconducting coils round a ring-shaped vacuum vessel, inside which a deuterium–tritium plasma at about 150 million degrees hangs in a magnetic field. Markdown: [en](https://world.lapla.si/en/tokamak/index.html.md), [中文](https://world.lapla.si/zh/tokamak/index.html.md).
  - 中文: [托卡马克聚变装置](https://world.lapla.si/zh/tokamak/) — 一台像 ITER 那样的托卡马克：十八个 D 形超导线圈围着一圈真空室，里面的氘氚等离子体要烧到约 1.5 亿度，靠磁场悬在半空。
  - A tokamak holds a plasma hotter than a hundred million degrees in a ring-shaped vacuum vessel with magnetic fields, so that deuterium and tritium fuse. This is a cutaway model of one, in the proportions of ITER, under construction in France.
  - Embed: https://world.lapla.si/embed/en/tokamak/ · https://world.lapla.si/embed/zh/tokamak/
  - Chapters: `cover` Tokamak Fusion Reactor; `goal` 150 Million Degrees; `dt` 17.6 MeV; `lawson` Density, Temperature, Time; `gyrate` Round the Field Lines; `drift` Bent into a Ring, Still Drifting; `twist` Twisting the Field; `section` Cut Open: Layer within Layer; `magnets` Coils at −269 °C; `glow` The Edge You Can See; `wall` Blanket and Divertor; `heating` Heating; `status` Where Things Stand; `apart` Taken Apart; `lab` Plasma Current
  - Lab settings: `labels` Labels (1/0)
- [Turbofan Engine (涡扇发动机)](https://world.lapla.si/en/turbofan/): plate F07. A high-bypass turbofan of the kind under a widebody’s wing, a quarter cut away: fan, ten-stage high-pressure compressor, annular combustor, two turbines. At take-off it swallows about 1.2 tonnes of air a second. Markdown: [en](https://world.lapla.si/en/turbofan/index.html.md), [中文](https://world.lapla.si/zh/turbofan/index.html.md).
  - 中文: [涡扇发动机](https://world.lapla.si/zh/turbofan/) — 一台宽体客机用的大涵道比涡扇发动机，四分之一剖开：风扇、十级高压压气机、环形燃烧室、高低压涡轮，起飞时每秒吸进约 1.2 吨空气。
  - Under a widebody’s wing, a turbofan gets about 85 % of its thrust from the air its fan pushes round the core. This is a cutaway model of one on a ground-run stand, about the size of a Boeing 787’s engines.
  - Embed: https://world.lapla.si/embed/en/turbofan/ · https://world.lapla.si/embed/zh/turbofan/
  - Chapters: `cover` Turbofan Engine; `scale` 1.2 Tonnes of Air a Second; `brayton` Compress, Burn, Expand; `bypass` Most Thrust Comes from the Fan; `section` Cut Open; `spools` Two Shafts, Two Speeds; `fan` Twisted Blades; `compressor` Ten Stages; `combustor` Annular Combustor; `turbine` Hotter than Melting; `containment` Throwing a Blade; `numbers` Real Engines; `apart` Taken Apart; `lab` Throttle
  - Lab settings: `airflow` Airflow (1/0); `labels` Labels (1/0)
- [The Gravitational-Wave Interferometer (引力波干涉仪)](https://world.lapla.si/en/ligo/): plate F08. Two arms 4 km long measure changes in length more than ten thousand times smaller than a proton. In 2015 it recorded, for the first time, the gravitational waves from two black holes merging. Markdown: [en](https://world.lapla.si/en/ligo/index.html.md), [中文](https://world.lapla.si/zh/ligo/index.html.md).
  - 中文: [引力波干涉仪](https://world.lapla.si/zh/ligo/) — 两条 4 千米长的臂，测出比质子小一万多倍的长度变化。2015 年，它第一次记录到两个黑洞合并时发出的引力波。
  - When a gravitational wave passes, space is stretched in one direction and squeezed in the direction at right angles to it. A laser interferometer compares the two with a pair of long arms set at right angles. LIGO in the United States has two, one at Hanford, Washington, and one at Livingston, Louisiana.
  - Embed: https://world.lapla.si/embed/en/ligo/ · https://world.lapla.si/embed/zh/ligo/
  - Chapters: `cover` The Gravitational-Wave Interferometer; `precision` Smaller Than a Proton; `michelson` One Beam, Two Paths; `stretch` One Arm Longer, One Shorter; `arms` About 300 Trips Along Each Arm; `laser` Tens of Watts In, Hundreds of Kilowatts in the Arms; `section` Cut Open: Tube and Vacuum; `suspension` Mirrors on a Four-Stage Pendulum; `quiet` Cut Off From the Ground; `squeeze` Squeezed Light; `sites` Two Sites, 3,000 km Apart; `gw150914` 14 September 2015; `apart` Taken Apart; `lab` Laboratory
  - Lab settings: `play` Play GW150914 (1/0); `labels` Labels (1/0); `world` Earth scale (1/0); `sound` Sound (1/0)
- [The Webb Space Telescope (韦布空间望远镜)](https://world.lapla.si/en/webb/): plate F09. Eighteen gold-coated segments make one 6.5 m mirror, and five layers of film keep the Sun’s heat off it. It was launched folded and unfolded itself in space over two weeks. Markdown: [en](https://world.lapla.si/en/webb/index.html.md), [中文](https://world.lapla.si/zh/webb/index.html.md).
  - 中文: [韦布空间望远镜](https://world.lapla.si/zh/webb/) — 18 块镀金镜片拼成一面 6.5 米的主镜，五层薄膜挡住太阳的热。它折叠着发射，在太空里用两周时间一步步展开。
  - The James Webb Space Telescope is an infrared telescope that works about 1.5 million km from Earth. Too big for any rocket, it was launched folded and opened out in space. This is a model of it unfolded.
  - Embed: https://world.lapla.si/embed/en/webb/ · https://world.lapla.si/embed/zh/webb/
  - Chapters: `cover` The Webb Space Telescope; `precision` Eighteen Mirrors Acting as One; `phasing` Eighteen Stars Become One; `infrared` Why Infrared; `cold` Five Layers Against the Sun; `orbit` L2, 1.5 Million km Out; `section` Cut Open; `instruments` Four Instruments; `folded` Folded for Launch; `unfold` Two Weeks of Unfolding; `found` What It Has Seen; `apart` Taken Apart; `lab` The Deployment Timeline
  - Lab settings: `labels` Labels (1/0)
- [The Harmonic Drive (谐波减速器)](https://world.lapla.si/en/harmonic/): plate F10. The strain-wave gear inside a robot joint: an ellipse flexes a thin steel cup, and each turn the cup falls back just two teeth. A 100 : 1 reduction in one stage, with almost no backlash. Markdown: [en](https://world.lapla.si/en/harmonic/index.html.md), [中文](https://world.lapla.si/zh/harmonic/index.html.md).
  - 中文: [谐波减速器](https://world.lapla.si/zh/harmonic/) — 机器人关节里的谐波减速器：一个椭圆把薄钢杯压弯，转一圈，杯子只退两个齿。一级减速 100 倍，几乎没有间隙。
  - In a robot arm or a humanoid’s joint, the motor spins fast with little torque, and the joint must turn slowly, strongly and precisely. A strain-wave gear does it with a thin steel cup flexed by an ellipse: 100 : 1 in a single stage, with next to no backlash. Here is a joint module cut open, beside the same gear 2.4 times larger and taken into its three parts.
  - Embed: https://world.lapla.si/embed/en/harmonic/ · https://world.lapla.si/embed/zh/harmonic/
  - Chapters: `cover` The Harmonic Drive; `reach` 100 : 1 in One Stage; `problem` Fast Motors, Slow Joints; `parts` Three Parts; `ellipse` Flexed into an Ellipse; `walk` One Turn, Two Teeth Back; `mesh` Many Teeth at Once; `section` The Joint Module, Cut Open; `motor` Frameless Torque Motor; `sensors` Two Encoders and a Brake; `bearing` Cross-Roller Bearing; `uses` Where It Works; `numbers` Real Numbers; `apart` Taken Apart; `lab` Laboratory
  - Lab settings: `mark` Mark one tooth (1/0); `xray` Clear flexspline (1/0); `apart` Take the joint apart (1/0); `cut` Cut the joint open (1/0); `labels` Labels (1/0)
- [Lidar (激光雷达)](https://world.lapla.si/en/lidar/): plate F11. A lidar on a car’s roof times light: 6.67 nanoseconds there and back is one metre. 128 beams spin, and the street around turns into hundreds of thousands of points with coordinates. Markdown: [en](https://world.lapla.si/en/lidar/index.html.md), [中文](https://world.lapla.si/zh/lidar/index.html.md).
  - 中文: [激光雷达](https://world.lapla.si/zh/lidar/) — 车顶上的激光雷达给光计时：一个脉冲来回 6.67 纳秒就是 1 米。128 束激光转一圈，四周的街道变成几十万个带坐标的点。
  - Self-driving cars and robots see in 3D with lidar: a laser pulse goes out, bounces back, and the time it took gives the distance. A column of lasers spins and measures over two million points a second. Here is a street model at 1 : 100, every point on its ground and walls computed along real beam angles, and beside it the sensor head at full size, cut open.
  - Embed: https://world.lapla.si/embed/en/lidar/ · https://world.lapla.si/embed/zh/lidar/
  - Chapters: `cover` Lidar; `reach` Over Two Million Points a Second; `tof` Timing Light; `scan` Ring by Ring; `channels` 16, 32, 64, 128 Channels; `section` The Head, Cut Open; `emit` A Column of Lasers, One Lens; `receive` One Detector for Each Beam; `spin` Turning, Powering, Knowing Where It Points; `wavelength` 900 or 1,550 Nanometres; `solid` Lidars That Don’t Spin; `fmcw` Speed, Measured Directly; `weather` Fog and Black Paint; `ghost` Ghosts Behind the Glass; `apart` Taken Apart; `lab` Laboratory
  - Lab settings: `hz` Spin (5–20, step 5); `fog` Fog (0–1, step 0.01); `world` Show the street model (1/0); `apart` Take the head apart (1/0); `cut` Cut the head open (1/0); `labels` Labels (1/0)
- [The Phased Array (相控阵：不转的天线)](https://world.lapla.si/en/phased/): plate F12. A flat panel holds a thousand small antennas. Let each send a moment after its neighbour and the beam leans to one side. No motor: the direction is set by timing alone. Markdown: [en](https://world.lapla.si/en/phased/index.html.md), [中文](https://world.lapla.si/zh/phased/index.html.md).
  - 中文: [相控阵：不转的天线](https://world.lapla.si/zh/phased/) — 一块平板上排着上千个小天线。每一个比旁边的晚一点点发射，波束就偏向一边。没有电机，方向只由时间决定。
  - In radars, 5G base stations and satellite terminals there is an antenna that changes direction without turning: many small antennas send the same wave, and when their phases are staggered in order, the beam they add up to swings round. Here is a flat-panel terminal, cut open, and beside it a ripple tank whose light is the wave computed for the same arrangement.
  - Embed: https://world.lapla.si/embed/en/phased/ · https://world.lapla.si/embed/zh/phased/
  - Chapters: `cover` The Phased Array; `reach` One Flat Panel, Any Direction in the Sky; `wave` Many Small Waves Make One Beam; `steer` Each a Little Later, and the Wavefront Tilts; `spacing` Half a Wavelength Apart; `count` More Elements, a Narrower Beam; `section` The Panel, Cut Open; `apart` Layer by Layer; `chips` Where Each Element’s Phase Comes From; `systems` Where They Are Used; `receive` Receiving Works the Same Way; `lab` Laboratory
  - Lab settings: `choice` Elements (4 | 8 | 16 | 32); `d` Spacing (0.25–1.5, step 0.01); `phases` Show phases (1/0); `avg` Show average strength (1/0); `taper` Taper (strong middle, weak edges) (1/0); `apart` Take the panel apart (1/0); `cut` Cut the panel open (1/0); `labels` Labels (1/0)