Posts tagged 'john-molokach'

GC-07.02 — John Molokach's Golden Rhombus from Shifted 1×3 Rectangles cO: x**2 + y**2 - 1 = 0 BA: y - 1 = 0 Golden major T1K = 1 Golden minor KA = -1/2 + sqrt(5)/2 T2 = (0, -1) R1 = (-2, 1) R6 = (2, -1) R7 = (-1, -1) B = (1/2 - sqrt(5)/2, 1) C = (-sqrt(5)/2 - 1/2, -1) D = (-1/2 + sqrt(5)/2, -1) O = (0, 0) T1 = (0, 1) K = (1, 1) A = (1/2 + sqrt(5)/2, 1) T2 R1 R6 R7 B C D O T1 K A

GC-07.02 · John Molokach’s Golden Rhombus from Shifted 1×3 Rectangles

Stack two \(3 \times 1\) rectangles RECT1 and RECT2 shifted by one unit around center O, draw unit circle cO, and draw the two tangents to cO perpendicular to outer diagonal R1R6. Together with the horizontal outer edges, they bound a golden rhombus ABCD (\(|AC|/|BD| = \phi\)) with \(|T1K|/|KA| = \phi\).