Posts tagged 'kurt-hofstetter'

GC-01.03 · Lemoine–Reusch–Hofstetter 5-Step Division

Given points A and B on line AB, let unit vesica circles cAB and cBA meet at C and D. Circle cCA cuts cAB at E and chord CD at F; then circle cEF cuts AB internally at G and externally at G₁ so that \(|AG|/|GB| = |G_1A|/|AB| = \phi\).

GC-01.04 · Hofstetter’s 2004 Five-Step Secant Division

Given points A and B, draw line AB and unit circles cAB, cBA meeting at C and D, with cAB meeting ray BA beyond A at E. Circle cEB cuts cBA above AB at F, and secant DF divides AB at G in the golden ratio \(|AG|/|GB| = \phi\) in exactly five Euclidean loci.

GC-01.05 · Mascheroni Five-Circle Compass-Only Construction

Using a compass alone and zero straightedge lines, five circles constructed from given points A and B generate four collinear points Y, C, D, X such that \(|CX|/|CD| = |CD|/|DX| = \phi\).

GC-01.06 · Hofstetter’s Fixed-Aperture Rusty-Compass Division

With a rusty compass locked permanently to aperture \(r = |AB|\), circles cAB and cBA determine midpoint M via CD; a third unit circle cM centered at M meets cBA above AB at F, and line DF cuts AB at G in the golden ratio \(|AG|/|GB| = \phi\).