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
Equilateral triangle area of all those circumscribed around a given circle is equilateral. The ratio of the area of the incircle to the area of an equilateral triangle, formula_30, is larger than that of any non-equilateral triangle. The ratio of the area to the square of the perimeter of an equilateral triangle, formula_31 is larger than that for any other triangle. If a segment splits an equilateral triangle into two regions with equal perimeters and with areas "A" and "A", then If a triangle is placed in the complex plane with complex vertices "z", "z", and "z", then for either non-real cube