Hyperbolic triangle relations between the sides "s" and the angles "A" of an equilateral triangle (a triangle where all sides have the same length and all angles are equal). The relations are: Whether "C" is a right angle or not, the following relationships hold: The hyperbolic law of cosines is as follows: Its dual theorem is There is also a "law of sines": and a four-parts formula: For hyperbolic trigonometry: Hyperbolic triangle In hyperbolic geometry, a hyperbolic triangle is a triangle in the hyperbolic plane. It consists of three line segments called "sides" or "edges" and three points called "angles" or "vertices".
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