Posts tagged 'dao-thanh-oai'

GC-05.02 — Dao Thanh Oai's Regular Pentagon Edge Perpendicular AB: y = 0 DE: x*sqrt(10 - 2*sqrt(5))/2 + y*(-sqrt(5)/2 - 1/2) + sqrt(5 - sqrt(5))*(sqrt(2) + sqrt(10)/2) = 0 EF: x*(1/2 + sqrt(5)/2) + y*sqrt(10 - 2*sqrt(5))/2 - sqrt(5)/2 + 3/2 = 0 Golden major FB = -1 + sqrt(5) Golden minor AF = 3 - sqrt(5) C = (1/2 + sqrt(5)/2, sqrt(2)*sqrt(5 - sqrt(5))/4 + sqrt(10)*sqrt(5 - sqrt(5))/4) D = (0, sqrt(10)*sqrt(5 - sqrt(5))/4 + 3*sqrt(2)*sqrt(5 - sqrt(5))/4) E = (-sqrt(5)/2 - 1/2, sqrt(2)*sqrt(5 - sqrt(5))/4 + sqrt(10)*sqrt(5 - sqrt(5))/4) A = (-1, 0) B = (1, 0) F = (2 - sqrt(5), 0) C D E A B F

GC-05.02 · Dao Thanh Oai’s Regular Pentagon Edge Perpendicular

In regular pentagon ABCDE, erect line EF perpendicular to side DE at vertex E. Line EF intersects opposite non-adjacent side AB internally at F such that \(|FB|/|AF| = |AB|/|FB| = \phi\).