A question that you might have heard is "What shape other than a circle can serve as a manhole cover?" That is, a shape which ensures that the manhole cover will not fall into the hole that it is meant to cover. The requirement for the shape is that it has constant diameter at any measured angle. The circle is not the only shape with this property. Reuleaux triangles and other odd-numbered polygons with arcs around their edges have constant diameter as well. However, they are impractical for uses such as wheels because an axle fixed to the center of the triangle would not move in a straight line as the wheel rolls.
Drag the slider to change the number of points in the polygon. Press Roll to see the shape spin around inside the square. Observe that the square always lies tangent to the sides of the object.
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