Reuleaux Triangles

• Applications of shapes of constant width. A Reuleaux triangle doesn't quite drill out a square hole (it leaves rounded corners) but a different and less-symmetric constant-width shape based on an isosceles right triangle can be used to do so. This web page also discusses coin design, cams, and rotary engines, all based on curves of constant width; see also discussion on Metafilter.

• constant-width shapes and Reuleaux triangle from Eric Weisstein's treasure trove.

• Geometry forum discussion on the Reuleux triangle and its ability to drill out (most of) a square hole.
  

• A magic geometric constant optimized by the Reuleaux triangle.

• Number patterns, curves, and topology, J. Britton. Includes sections on the golden ratio, conics, Moiré patterns, Reuleaux triangles, spirograph curves, fractals, and flexagons.

• Reuleaux triangle entry from Kunkel's mathematics lessons.

• Reuleaux Wheel. From Mudd Math Fun Facts.

• Rolling with Reuleaux from Ivars Peterson's MathLand.

• Shapes of constant width.

• Sketchpad demo includes a Reuleaux triangle rolling between two parallel lines.

• Square wheels. Bill Beatty describes how to make cubical-looking shapes that are round enough to roll smoothly on an axle.

• Star construction of shapes of constant width, animated in Java by A. Bogomolny.