## 字幕列表 影片播放

• It makes intuitive sense that objects like circles and spheres are round - but what is

我们都知道圆形和球体是圆的

• it about a sphere that makes it round?

但什么才是"圆"呢

• If you're talking about how effective a shape is at enclosing a large volume, you mean "sphericity".

我们用"球性"这个词

• And a sphere is the shape that contains the most volume with the least surface area, that

来描述一个形状围住容量的有效性

• is, a sphere is the most "spherical" shape.

显然球形能利用更少的面积围住更多体积

• But roundness has more to do with rolling than with volume, right?

也就是说球是最有"球性"的形状

• A round object can roll smoothly - like a wheel or ball bearing.

但圆常常被用做移动而不是装物体

• And the main feature that ball bearings need in order to roll smoothly is to be the same

圆形的物体可以平滑的滚动 比如轮子和滚珠

• width from bottom to top/one side to the other.

而它们最大的特点就是在滚动过程中 顶部到底部的距离不变

• It turns out there are plenty of non-circular 'shapes of constant width' that are excellent

事实上许多不是圆形的形状也可以用作轴承

• bearings as well.

比如 勒洛三角形

• The Reuleaux rotor, for example, is made up of segments from three circles intersecting

它是由三个交叉圆的圆心连接而成

• at their centers - so every point on a side is the same distance from the opposite corner,

形上任何一点到对边的距离都相等

• and the rotor rolls around wonderfully.

所以它也能平滑地滚动

• In fact, the Reuleaux rotor can even turn smoothly in a square hole!

事实上 勒洛三角形甚至能在正方形的洞中平滑地滚动

• But don't try to use a Reuleaux rotor for the wheel on your car - since they're not

但你别指望它代替车轮

• a constant distance from the axle, those points will make for a bumpy ride!

因为它能颠的你够呛

• In fact, the points on a Reuleaux rotor are just that - pointy.

勒洛三角形的顶点都很尖

• Doesn't that go against the idea of roundness?

这是否意味着它同时具有磨圆度呢

• Geology has the answer: stones with sharp or rough edges that are worn away become "rounded."

在地质学中 这又是另一码事

• So we might say a Reuleaux rotor is round but not rounded.

磨圆度是指石头被磨圆的程度

• On the other hand, certain British coins are round AND rounded, though they're still not

所以我们说勒洛三角形有"圆性"但没有磨圆度

• circles: the 20 and 50-p coins are shapes of constant width, which means they look un-circularly

而一种英国的硬币既有"圆性"也有磨圆度

• cool but don't get stuck in coin machines!

尽管它们也不是圆形

• And isn't if funny that "rouleau" means "roll" in French and Franz Reuleaux invented a rolling

这种20和50的便士有7个等边

• rotor?

也就是说它们不会卡在投币机的狭缝里

It makes intuitive sense that objects like circles and spheres are round - but what is

# 圓三角！ (Round Triangles!)

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林宜悉 發佈於 2021 年 01 月 14 日