Geometry — Arondale Withers

←The Geometry Practice

“Geometry will draw the soul toward truth and create the spirit of philosophy.”
Plato · Republic VII

Polyhedral compounds and geometric form studies using phi golden ratio and classical plane constructions. My math and geometry studies opened new insights into how I see the world. The great pyramid constants and improbabilities. Squaring the circle and Heptadecagon studies. All drawings using compass and straightedge only.

George Leoniak

Teacher

George taught me most of what I know, and he is the greatest single inspiration behind the majority of the compass-and-straightedge work in these journals. From him I learned how φ and π actually behave on paper, and the golden-ratio circle templates he teaches — the scaffolding that lets a geometer draw complex forms and compounds of every kind: the Platonic solids, the Archimedean solids, the Catalan solids, and a great deal beyond them.

My respect, appreciation, and gratitude are hard to overstate. Nearly every sheet that follows carries something he handed me.

Knew Geometry Courses →

The Geometers

Alongside George, two others shaped the practice — one I have sat across from, and one who settled the question two centuries before I ever picked up a compass.

Robert Edward Grant

Polymath

“Enjoy the journey of geometry.”Inscribed · Polymath

I own his books — one of them signed, there. We first met at CPAK, the Conference on Precession & Ancient Knowledge, in Palm Springs, and have talked one-on-one since, in person and over video, about geometry and the polymathic connections between fields most people keep apart.

A hand-drawn heptadecagon construction sheet titled Heptadecagon, 17-sided figure, with labelled compass arcs

My heptadecagon, drawn by hand — the figure Gauss proved possible.

Carl Friedrich Gauss

1777 – 1855

On the morning of March 30, 1796, a nineteen-year-old in Braunschweig proved that the regular seventeen-sided polygon could be drawn with compass and straightedge alone. It was not a clever drawing — it was a proof that the drawing must exist, and the first worked construction followed a few years later.

The Mighty Heptadecagon →

The Films

Timelapse constructions — hours of drawing compressed into seconds — and rotation studies of the finished forms.

The Great Rhombicosidodecahedron — twenty hours of drawing, in sixty seconds.

Geometry Journal — Superclip — a timelapse montage across the constructions.

Compound of Five Cubes — in the hand — the finished compound, turned.

Geometry Journal — Stills — plates from the working journals.

Inside the Sketchbook — Great Pyramid studies and moon phases.

Questions about the constructions?

Ask about any figure, or the method behind it.

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