Why are some coins Reuleaux triangles?

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


         
Coin

         

(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 π320.705, 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

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