Index of Geometers & Contributors

Biographical registry of classical, modern, and contemporary geometers whose theorems, constructions, and archival curations are represented in this catalog.

Euclid of Alexandria (fl. c. 300 BCE) — Alexandrian Geometer; Author of the Elements

Formulated division in extreme and mean ratio in Elements Book II Proposition 11 and Book VI Proposition 30, applying it to construct the regular pentagon (IV.11) and the icosahedron and dodecahedron (Book XIII). Cataloged constructions: GC-01.01, GC-01.02, GC-05.01

Claudius Ptolemy (c. 100 – c. 170 CE) — Alexandrian Astronomer & Geometer

Introduced the streamlined circle-and-midpoint construction of the regular decagon and pentagon in Almagest Book I, Chapter 10 to compute his trigonometric table of chords. Cataloged constructions: GC-05.01

Luca Pacioli (c. 1447 – 1517) — Franciscan Mathematician; Author of De Divina Proportione (1509)

Chronicled thirteen ‘effects’ of extreme and mean ratio in De Divina Proportione (1509, illustrated by Leonardo da Vinci), popularizing the Renaissance title Divina Proportione.

Johannes Kepler (1571 – 1630) — Astronomer & Geometer

Described the Pythagorean theorem and division in extreme and mean ratio as the ‘two great treasures of geometry’ (1597 letter to Michael Mästlin) and studied the 1 : √φ : φ right triangle and rhombic triacontahedron. Cataloged constructions: GC-04.02

William Hooper (fl. 1770 – 1794) — Author of Rational Recreations

Published the earliest known geometric missing-area rectangle dissection fallacy in Rational Recreations (1774/1794), whose vanishing-gap limit is governed by φ. Cataloged constructions: GC-07.06

Émile Michel Hyacinthe Lemoine (1840 – 1912) — French Geometer; Founder of Géométrographie

Founded Géométrographie (1902), a quantitative operational calculus measuring the simplicity and exactitude of ruler-and-compass constructions, and recorded early minimal divisions in extreme and mean ratio. Cataloged constructions: GC-01.03

Paul Curry (1917 – 1986) — Magician & Recreational Geometer

Invented the Curry Paradox (1953) of area-discrepant triangle and rectangle rearrangements driven by Fibonacci slopes approaching 1/φ. Cataloged constructions: GC-07.06

H. E. Huntley (1892 – 1978) — Physicist & Mathematical Expositor

Author of The Divine Proportion: A Study in Mathematical Beauty (Dover, 1970), highlighting unexpected appearances of φ such as the angle-bisector circle in the 3-4-5 right triangle. Cataloged constructions: GC-04.01

H. S. M. Coxeter (1907 – 2003) — Geometer; University of Toronto

Communicated George Odom’s equilateral midline golden-section problem in the American Mathematical Monthly (Problem E3007, 1983) and championed classical synthetic and projective geometry. Cataloged constructions: GC-02.01

George Odom (1941 – 2010) — Artist & Amateur Geometer

Discovered the celebrated two-line equilateral-triangle midline construction of φ (1982–1983) through visual exploration of polyhedra and three-dimensional models. Cataloged constructions: GC-02.01

Alexander Bogomolny (1948 – 2018) — Mathematician, Educator & Creator of Cut-the-Knot

Founded Interactive Mathematics Miscellany and Puzzles (Cut-the-Knot, 1996–2018), curating, proving, and illustrating dozens of classical and contemporary Golden Ratio constructions contributed by geometers worldwide. Cataloged constructions: GC-06.07, GC-07.05, GC-07.06

Ron Knott (b. c. 1950) — Mathematician & Educator; University of Surrey

Creator of the encyclopedic Fibonacci Numbers and the Golden Section resource (cataloged in sibling repository geometor/knott).

Viktor Vasil’evich Prasolov (b. 1956) — Russian Geometer & Author; Independent University of Moscow

Author of Problems in Plane and Solid Geometry, documenting affine equi-area characterizations of golden diagonal ratios in general convex pentagons. Cataloged constructions: GC-05.03

Alexandre Borovik (b. 1956) — Mathematician; University of Manchester

Observed the golden rectangle embedded inside Bùi Quang Tuân’s concentric Greek cross and square configuration on Cut-the-Knot. Cataloged constructions: GC-03.07

Jerzy Kocik (fl. 1990 – present) — Mathematician & Physicist; Southern Illinois University

Discovered and analyzed the Apollonian ‘Golden Window’ circle packing (Mathematics Magazine, 2010), showing how simultaneous tangency forces powers of φ. Cataloged constructions: GC-06.05

Jingcheng Tong (fl. 1985 – 2015) — Mathematician; University of North Florida

Characterized area-bisecting chords in trapezoids whose parallel bases stand in ratio 1 : 3, dividing both legs in the golden ratio. Cataloged constructions: GC-07.03

Jo Niemeyer (b. 1946) — German Concrete Artist & Designer

Constructivist artist whose sculptures and geometric studies feature the golden division generated by three equal leaning segments. Cataloged constructions: GC-04.03

Kurt Hofstetter (b. 1959) — Austrian Artist & Geometer

Published a remarkable series of minimal 5-step Euclidean, 5-circle Mascheroni compass-only, and fixed-opening rusty-compass Golden Ratio constructions in Forum Geometricorum (2002–2005). Cataloged constructions: GC-01.03, GC-01.04, GC-01.05, GC-01.06

Michel Bataille (fl. 2000 – present) — French Geometer & Problemist; Rouen

Prolific contributor to Crux Mathematicorum and Forum Geometricorum; devised the equilateral-triangle-and-square radical-axis construction of φ (2011). Cataloged constructions: GC-02.02

Bùi Quang Tuân (fl. 2010 – present) — Vietnamese Geometer

Discovered numerous synthetic Golden Ratio theorems curated on Cut-the-Knot, including a 5-step collinear circle construction, the Greek Cross & Square, Four Golden Circles, Van Obel isosceles division, and infinite circle-secant families. Cataloged constructions: GC-01.07, GC-02.03, GC-03.07, GC-04.04, GC-05.03, GC-06.01, GC-06.03

Tran Quang Hung (fl. 2012 – present) — Vietnamese Geometer; Hanoi University of Science High School

Contributed an extraordinary suite of synthetic Golden Ratio discoveries across equilateral triangles, squares, 3×3 grids, hexagons, pentagon stars, Wu Xing rotations, rhombi, trapezoids, and mixtilinear circles. Cataloged constructions: GC-02.04, GC-02.05, GC-02.06, GC-03.01, GC-03.02, GC-03.04, GC-03.05, GC-04.01, GC-05.02, GC-05.04, GC-05.05, GC-05.06, GC-06.04, GC-07.01, GC-07.04, GC-07.05

Dao Thanh Oai (fl. 2013 – present) — Vietnamese Geometer

Known for discoveries in Euclidean and projective triangle/polygon geometry, including the regular-pentagon edge-perpendicular division in φ. Cataloged constructions: GC-05.02

Nguyen Thanh Dung (fl. 2015 – present) — Vietnamese Geometer

Contributed butterfly-chord equilateral constructions and 2×2 square lattice divisions in extreme and mean ratio on Cut-the-Knot. Cataloged constructions: GC-02.07, GC-03.03

Quang Duong (fl. 2015) — Geometer & Problem Solver

Contributed synthetic proofs for Tran Quang Hung’s reflected equilateral and incircle Golden Ratio theorems.

Grégoire Nicollier (fl. 2010 – present) — Swiss Mathematician; University of Applied Sciences of Western Switzerland

Contributed analytic and synthetic proofs of polygonal and equilateral Golden Ratio configurations on Cut-the-Knot.

Leonard Giugiuc (fl. 2010 – present) — Romanian Mathematician & Problemist

Co-solved and generalized several trigonometric, mixtilinear, and butterfly Golden Ratio problems curated by Alexander Bogomolny. Cataloged constructions: GC-07.05

Ercole Suppa (fl. 2005 – present) — Italian Geometer; Teramo

Researcher in triangle centers and sangaku-style circle configurations; discovered the golden ratio of inradii in a midpoint-partitioned square (2015). Cataloged constructions: GC-03.06

Elliot McGucken (fl. 2015 – present) — Physicist & Recreational Geometer

Contributed golden-section constructions in two and three tangent equal circles and 3×3 square grids on Cut-the-Knot. Cataloged constructions: GC-03.04, GC-06.02, GC-06.04

Thanos Kalogerakis (fl. 2016) — Greek Geometer

Observed the diameter-to-secant golden ratio across two externally tangent equal circles. Cataloged constructions: GC-06.02

John Arioni (fl. 2016) — Geometer

Contributed the Yin-Yang twin-circle secant construction and the 30°-rotated unit square diagonal-circle construction of φ on Cut-the-Knot. Cataloged constructions: GC-03.08, GC-06.06

John Molokach (fl. 2013 – present) — Recreational Geometer

Devised the construction of a golden rhombus and consecutive powers of φ from two unit-shifted 1×3 rectangles and an inscribed unit circle. Cataloged constructions: GC-07.02