Integer triangle common divisor. Integer triangles with a 60° angle can also be generated by with coprime integers "m", "n" with 0 < "n" < "m" (the angle of 60° is opposite to the side of length "a"). From here, all primitive solutions can be obtained by dividing "a", "b", and "c" by their greatest common divisor (e.g. an equilateral triangle solution is obtained by taking "m" = 2 and "n" = 1, but this produces "a" = "b" = "c" = 3, which is not a primitive solution). See also More precisely, If formula_109, then formula_110, otherwise formula_111. Two different pairs
Equilateral triangle root formula_33 of 1 the triangle is equilateral if and only if Given a point "P" in the interior of an equilateral triangle, the ratio of the sum of its distances from the vertices to the sum of its distances from the sides is greater than or equal to 2, equality holding when "P" is the centroid. In no other triangle is there a point for which this ratio is as small as 2. This is the Erdős–Mordell inequality; a stronger variant of it is Barrow's inequality, which replaces the perpendicular distances to the sides with the distances from "P"