Reuleaux triangle any curve of given constant width. This area is where "s" is the constant width. One method for deriving this area formula is to partition the Reuleaux triangle into an inner equilateral triangle and three curvilinear regions between this inner triangle and the arcs forming the Reuleaux triangle, and then add the areas of these four sets. At the other extreme, the curve of constant width that has the maximum possible area is a circular disk, which has area formula_2. The angles made by each pair of arcs at the corners of a Reuleaux triangle are all equal to 120°.
Schwarz triangle function classification of arithmetic triangle groups (there are only finitely many) and determined when two of them are commensurable. The particular example is related to Bring's curve and the arithmetic theory implies that the triangle group for Δ contains the triangle group for the triangle Δ with angles /4, /4 and /5 as a non-normal subgroup of index 6. Doubling the triangles Δ and Δ, this implies that there should be a relation between 6 triangles Δ with angles /2, /5 and /5 and hyperbolic area /10 and a triangle Δ with angles /5, /5 and /10 and hyperbolic area 3/5.