Posts tagged 'nguyen-thanh-dung'

GC-03.03 · Nguyen Thanh Dung’s 2×2 Grid Compass Arc

On a \(2 \times 2\) square grid P1P2P3P4 with horizontal midline AB, center O, and top midpoint D, extend AB by one grid unit to C. Circle cCD centered at C through D cuts AB at M in the golden ratio: \(|MB|/|AM| = |AB|/|MB| = \phi\).

GC-02.07 · Butterfly Chords Astride an Equilateral Triangle

Let I be the midpoint of radius OJ of circle cO, XT the chord perpendicular to OJ through I, and ICD an equilateral triangle symmetric about OJ with C and D on cO. If rays CI and DI meet cO again at A and B, then chords BC and AD cut XT at Y and Z with \(|YZ|/|ZT| = |YT|/|YZ| = |YZ|/|XY| = \phi\).