← divine / Posts tagged 'compass-only' Posts tagged 'compass-only' GC-01.05 — Mascheroni Five-Circle Compass-Only Construction c1: x**2 + y**2 - 1 = 0 c2: y**2 + (x - 1)**2 - 1 = 0 c3: (x - 1/2)**2 + (y - sqrt(3)/2)**2 - 3 = 0 c4: y**2 + (x - 1)**2 - 4 = 0 c5: x**2 + y**2 - 4 = 0 Golden major CD = sqrt(3) Golden minor DX = (-sqrt(3) + sqrt(15))/2 E = (-1, 0) F = (2, 0) Y = (1/2, sqrt(15)/2) A = (0, 0) B = (1, 0) C = (1/2, sqrt(3)/2) D = (1/2, -sqrt(3)/2) X = (1/2, -sqrt(15)/2) E F Y A B C D X GC-01.05 · Mascheroni Five-Circle Compass-Only Construction Using a compass alone and zero straightedge lines, five circles constructed from given points A and B generate four collinear points Y, C, D, X such that \(|CX|/|CD| = |CD|/|DX| = \phi\).
GC-01.05 — Mascheroni Five-Circle Compass-Only Construction c1: x**2 + y**2 - 1 = 0 c2: y**2 + (x - 1)**2 - 1 = 0 c3: (x - 1/2)**2 + (y - sqrt(3)/2)**2 - 3 = 0 c4: y**2 + (x - 1)**2 - 4 = 0 c5: x**2 + y**2 - 4 = 0 Golden major CD = sqrt(3) Golden minor DX = (-sqrt(3) + sqrt(15))/2 E = (-1, 0) F = (2, 0) Y = (1/2, sqrt(15)/2) A = (0, 0) B = (1, 0) C = (1/2, sqrt(3)/2) D = (1/2, -sqrt(3)/2) X = (1/2, -sqrt(15)/2) E F Y A B C D X GC-01.05 · Mascheroni Five-Circle Compass-Only Construction Using a compass alone and zero straightedge lines, five circles constructed from given points A and B generate four collinear points Y, C, D, X such that \(|CX|/|CD| = |CD|/|DX| = \phi\).