Necessarily a Circle?
Geometry
Level
2
There is no doubt that the width of a circle is constant: its diameter.
If a given plane simple closed curve's width is constant in all directions, is it necessarily a circle?
Yes
No
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1 solution
The surprising answer is that there are many non-circular shapes of constant width. A nontrivial example is the Reuleaux triangle, a shape formed from the intersection of three circular disks, each having its center on the boundary of the other two.