Posts tagged 'emile-lemoine'

GC-01.03 — Lemoine–Reusch–Hofstetter 5-Step Division cAB: x**2 + y**2 - 1 = 0 cBA: y**2 + (x - 1)**2 - 1 = 0 cCA: (x - 1/2)**2 + (y - sqrt(3)/2)**2 - 1 = 0 cEF: (x + 1/2)**2 + (y - sqrt(3)/2)**2 - 2 = 0 AB: y = 0 CD: x - 1/2 = 0 Golden major AG = -1/2 + sqrt(5)/2 Golden minor GB = 3/2 - sqrt(5)/2 C = (1/2, sqrt(3)/2) D = (1/2, -sqrt(3)/2) E = (-1/2, sqrt(3)/2) F = (1/2, -1 + sqrt(3)/2) G1 = (-sqrt(5)/2 - 1/2, 0) A = (0, 0) B = (1, 0) G = (-1/2 + sqrt(5)/2, 0) C D E F G1 A B G

GC-01.03 · Lemoine–Reusch–Hofstetter 5-Step Division

Given points A and B on line AB, let unit vesica circles cAB and cBA meet at C and D. Circle cCA cuts cAB at E and chord CD at F; then circle cEF cuts AB internally at G and externally at G1 so that \(|AG|/|GB| = |G_1A|/|AB| = \phi\).