Integer triangle not) satisfy formula_151. We can generate the full equivalence class of similar triangles that satisfy B=3A by using the formulas where formula_28 and formula_27 are integers such that formula_157. Note that all triangles with B = 3A (whether with integer sides or not) satisfy formula_158. The only integer triangle with three rational angles (rational numbers of degrees, or equivalently rational fractions of a full turn) is the equilateral triangle. This is because integer sides imply three rational cosines by the law of cosines, and by Niven's theorem a rational cosine coincides with a rational angle if and only if the
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