Peter Taylor pointed out at MathEduc that some BD$1 coins from 1997 are Reuleaux triangles:

^{ (Image from de.ucoin.net.) }

Does anyone know why they were shaped this way? Was there some

pragmatic reason connected to its constant-width property? Or was it just a design/aesthetic decision?

**Answer**

The Blaschke-Lebesgue Theorem states that among all planar convex domains of given constant width B the Reuleaux triangle has minimal area.†

The area of the Reuleaux triangle of unit width is π−√32≈0.705, which is approximately 90% of the area of the disk of unit diameter. Therefore, if one needs to mint (convex) coins of a given constant width and thickness, using Reuleaux triangles allows one to use approximately 10% less metal.

† Evans M. Harrell, A direct proof of a theorem of Blaschke and Lebesgue, September 2000.

**Attribution***Source : Link , Question Author : Joseph O’Rourke , Answer Author : Rodrigo de Azevedo*