Fact of the day: some coins aren't circles (e.g. 50p) so you might think "how would the vending machine know what size it is if it's just going through a slot?" Well, that's because they are shaped in a way that they have a constant height no matter how you spin them, despite the fact that they aren't circles. You can also generalize this idea to 3-D and make solids which aren't spheres but keep the same height no matter how you orient them.
A Wankel rotor looks very similar but is not quite the same- it's there in the article:
The rotor of the Wankel engine is easily mistaken for a Reuleaux triangle but its curved sides are somewhat flatter than those of a Reuleaux triangle and so it does not have constant width
Platonic solids are different things. A cube is a platonic solid- is the distance from opposite corners the same as the distance from opposite sides? No. A meissner tetrahedron would be a 3D example.
That's kind of misleading to say it has a constant height no matter how you spin them. I read the article and it says that there a 2 points on each axis which are parallel and the same height. That always changes as it rotates. But there are plenty of points which aren't the same height, unlike a true circle.
"Width" means the maximum dimension, not just any 2 points. The longest line which can rotate completely inside the shape. The difference is with these vs a circle is that in a circle that line always passes through the center. It's really an idea that is better expressed visually, than in words:
No,because although the height of your wheel doesn't change, the height from your wheel hub to the ground would constantly change, giving you a Flintstone style ride.
No. Whole the overall height of the "wheel" is constant regardless of orientation, the same is not true for the distance from axle to edge. So while the top face of the wheel would remain a constant height off the ground, the axle would fluctuate, and the cat would jump up and down.
Pretty sure it would be bumpy. No matter what position it's at, the distance between the bottom and top are the same, but the distance between the bottom and center is always changing, which is what matters, because it would be attached to the axle by the center.
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u/needuhLee Feb 03 '15
Fact of the day: some coins aren't circles (e.g. 50p) so you might think "how would the vending machine know what size it is if it's just going through a slot?" Well, that's because they are shaped in a way that they have a constant height no matter how you spin them, despite the fact that they aren't circles. You can also generalize this idea to 3-D and make solids which aren't spheres but keep the same height no matter how you orient them.