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Posts tagged 'field-algebraic'

GC-01.07 — Bùi Quang Tuân's Five-Step Three-Circle Secant cO: x**2 + y**2 - 1 = 0 cBA: y**2 + (x + 1)**2 - 4 = 0 cCO: y**2 + (x + 3)**2 - 9 = 0 L: y = 0 MN: x*(sqrt(35)/6 + 3*sqrt(7)/4) - 7*y/12 + sqrt(7)/8 + sqrt(35)/8 = 0 Golden major MP = sqrt(7)*sqrt(-sqrt(2)*sqrt(sqrt(5) + 3) + 4 + sqrt(10)*sqrt(sqrt(5) + 3))/4 Golden minor PN = sqrt(7)*sqrt(-5*sqrt(2)*sqrt(sqrt(5) + 3) + sqrt(10)*sqrt(sqrt(5) + 3) + 12)/4 A = (1, 0) C = (-3, 0) O = (0, 0) B = (-1, 0) M = (-1/6, sqrt(35)/6) N = (-3/4, -3*sqrt(7)/4) P = (-7*sqrt(2)*sqrt(sqrt(5) + 3)/32 - 7*sqrt(5)/48 - 1/48 + 7*sqrt(10)*sqrt(sqrt(5) + 3)/96, -17*sqrt(14)*sqrt(sqrt(5) + 3)/96 - sqrt(7)/48 + sqrt(35)/48 + sqrt(70)*sqrt(sqrt(5) + 3)/32) A C O B M N P

GC-01.07 · Bùi Quang Tuân’s Five-Step Three-Circle Secant

On line L through O, draw circle cO meeting L at A and B, circle cBA meeting L at C, and circle cCO meeting cO above L at M and cBA below L at N. Then chord MN cuts cO at P with \(|MN|/|MP| = |MP|/|PN| = \phi\).
01-minimal-compass field-algebraic bui-quang-tuan
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