#constant width

[szimmetria-airtemmizs]

On the sides you can see two curves of constant width, that is a curve whose width is the same in all directions. This is the reason they always touch the two lines as they rotate. The existence of curves of constant width is well known by now. What is much less known is that you can morph between any two such curves such that during the morph the curve stays a curve of constant width. For these two curves the morphing can be seen in the middle. (Actually, you can see two different morphs. )

[tradeshanty]

The most well-known example of a curve of constant width is a circle, but many other constructions are known. Any triangle can also be used to construct such a curve, and the simplest example of this is the Reuleaux triangle, often used in machinery to convert rotational motion to reciprocating motion.

Image: Wikipedia

[mathhombre]

Constant Width

@malinchristersson posted this super clever GeoGebra sketch of shapes of constant width, which got me thinking about these today. This GeoGebra sketch shows one with radial symmetry and odd number of vertices, and a non symmetric one built on three directions. Fun to make & I feel like I understand the geometry a bit better.