Special right triangle triangles are used to aid in calculating common trigonometric functions, as below: The 45°–45°–90° triangle, the 30°–60°–90° triangle, and the equilateral/equiangular (60°–60°–60°) triangle are the three Möbius triangles in the plane, meaning that they tessellate the plane via reflections in their sides; see Triangle group. In plane geometry, constructing the diagonal of a square results in a triangle whose three angles are in the ratio 1 : 1 : 2, adding up to 180° or radians. Hence, the angles respectively measure 45° (), 45° (), and 90° (). The sides in this triangle are in the ratio 1 : 1
Reuleaux triangle circle within another of three times the radius. Other planar shapes with three curved sides include the arbelos, which is formed from three semicircles with collinear endpoints, and the Bézier triangle. The Reuleaux triangle may also be interpreted as the conformal image of a spherical triangle with 120° angles. This spherical triangle is one of the Schwarz triangles (with parameters 3/2, 3/2, 3/2), triangles bounded by great-circle arcs on the surface of a sphere that can tile the sphere by reflection. Reuleaux triangle A Reuleaux triangle is a shape formed from the intersection of three circular disks, each having its