Posts tagged 'equilateral'

W.11 Isosceles, Equilateral & Kepler’s Golden Right Triangle

In a non-null triangle, Q_1 = Q_2 iff s_1 = s_2 (with apex spread s_3 = (Q_3/Q_1)(1 - Q_3/(4*Q_1))), and Q_1 = Q_2 = Q_3 iff s_1 = s_2 = s_3 = 3/4; in Kepler’s Golden Right Triangle with side lengths (1, sqrt(phi), phi), the nested radical vanishes in quadrance to give Q = (1, phi, phi^2) and exact golden spreads (s_1, s_2, s_3) = (2 - phi, phi - 1, 1) = (1/phi^2, 1/phi, 1).