Integer triangle cosine equals 0, ±1/2, or ±1. The only ones of these giving an angle strictly between 0° and 180° are the cosine value 1/2 with the angle 60°, the cosine value –1/2 with the angle 120°, and the cosine value 0 with the angle 90°. The only combination of three of these, allowing multiple use of any of them and summing to 180°, is three 60° angles. Conditions are known in terms of elliptic curves for an integer triangle to have an integer ratio "N" of the circumradius to the inradius. The smallest case, that of the equilateral triangle, has
Spring Triangle with Cor Caroli. Spring Triangle The Spring Triangle is an astronomical asterism involving an imaginary triangle drawn upon the celestial sphere, with its defining vertices at Arcturus, Spica, and Regulus. This triangle connects the constellations of Boötes, Virgo, and Leo. It is visible rising in the south eastern sky of the northern hemisphere between March and May. George Lovi of Sky & Telescope magazine had a slightly different "Spring triangle", including the tail of Leo, Denebola, instead of Regulus. Denebola is dimmer, but the triangle is more nearly equilateral. These stars form parts of a larger Spring asterism called the