# Why are some coins Reuleaux triangles?

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?

The Blaschke-Lebesgue Theorem states that among all planar convex domains of given constant width $B$ the Reuleaux triangle has minimal area.$^\dagger$
The area of the Reuleaux triangle of unit width is $\frac{\pi - \sqrt{3}}{2} \approx 0.705$, 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.
$\dagger$ Evans M. Harrell, A direct proof of a theorem of Blaschke and Lebesgue, September 2000.