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°.
Isosceles triangle as a satire of social hierarchy: isosceles triangles represented the working class, with acute isosceles triangles higher in the hierarchy than right or obtuse isosceles triangles. As well as the isosceles right triangle, several other specific shapes of isosceles triangles have been studied. These include the Calabi triangle (a triangle with three congruent inscribed squares), the golden triangle and golden gnomon (two isosceles triangles whose sides and base are in the golden ratio), the 80-80-20 triangle appearing in the Langley’s Adventitious Angles puzzle, and the 30-30-120 triangle of the triakis triangular tiling. Five Catalan solids, the triakis tetrahedron, triakis octahedron,