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

  • it about a sphere that makes it round?

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

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

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

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

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

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

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

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

  • bearings as well.

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

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

  • and the rotor rolls around wonderfully.

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

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

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

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

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

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

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

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

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

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

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

  • rotor?

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

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B1 中級

丸い三角形! (Round Triangles!)

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    林宜悉 に公開 2021 年 01 月 14 日
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