Posts tagged 'field-q-sqrt2-phi'

GC-03.04 — Tran Quang Hung & Elliot McGucken's 3×3 Grid Circle cOT: x**2 + y**2 - 10 = 0 OA: -3*x + 3*y = 0 Golden major CB = -sqrt(2) + sqrt(10) Golden minor BA = -sqrt(10) + 3*sqrt(2) S1 = (-3, 3) S3 = (3, -3) S4 = (-3, -3) C1 = (-1, 1) C3 = (1, -1) C4 = (-1, -1) T = (1, 3) O = (0, 0) A = (3, 3) C = (1, 1) B = (sqrt(5), sqrt(5)) S1 S3 S4 C1 C3 C4 T O A C B

GC-03.04 · Tran Quang Hung & Elliot McGucken’s 3×3 Grid Circle

In a \(3 \times 3\) square grid S1AS3S4 centered at O, let C be the upper-right vertex of the central grid cell, A the outer upper-right corner, and T the adjacent trisection vertex on the top edge. Circle cOT cuts diagonal segment CA at B such that \(|CB|/|BA| = \phi\).
GC-03.05 — Tran Quang Hung's 3×3 Grid Incenter Division cPT: (x - 5/2 + sqrt(5)/2)**2 + (y - 5/2 + sqrt(5)/2)**2 - 2*(-1/2 + sqrt(5)/2)**2 = 0 AT: -3*x + 3*y = 0 Golden major PT = (-sqrt(2) + sqrt(10))/2 Golden minor SP = (-sqrt(10) + 3*sqrt(2))/2 Q2 = (3, 3) Q3 = (0, 3) K1 = (2, 1) K2 = (1, 2) U = (3, 1) V = (1, 3) A = (0, 0) Q1 = (3, 0) S = (1, 1) T = (2, 2) P = (5/2 - sqrt(5)/2, 5/2 - sqrt(5)/2) Q2 Q3 K1 K2 U V A Q1 S T P

GC-03.05 · Tran Quang Hung’s 3×3 Grid Incenter Division

In a \(3 \times 3\) grid AQ1Q2Q3 on \([0,3]^2\), let S \(= (1,1)\) and T \(= (2,2)\) be opposite corners of the central unit cell, and let U \(= (3,1)\) and V \(= (1,3)\). The incenter P of isosceles triangle AUV divides diagonal ST of the central cell in the golden ratio: \(|PT|/|SP| = \phi\).