Reuleaux Triangles Roll Just As Well As Circles

The most familiar Reuleaux triangles are guitar picks, but they're also used in architecture and engineering. As a drill bit, they can drill nearly square holes-the corners will just be slightly rounded. These shapes are named after Franz Reuleaux, a German engineer in the 19th century who incorporated Reuleaux triangles in his designs. He did not discover them, however, as evidence of their use in mapmaking stretches back to the 1500s.

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Key Facts In This Video

  1. Hexagons are not shapes of constant width—as they rotate, their vertical height changes. 00:36

  2. See what a three-dimensional Reuleaux triangle looks like: 05:02

  3. Like the Reuleaux triangle, a Meissner tetrahedron is a counterintuitive shape of constant width. 07:13