Persons

Mathematicians, geometers, and scholars referenced across the GEOMETOR Knott Mathematical Catalog.

Dr. Ron Knott (fl. 1979–2025)

Mathematician & computer scientist (formerly Dept. of Mathematics, University of Surrey); author and curator of Fibonacci Numbers, the Golden Section and the Golden String (1996–2025).

Euclid of Alexandria (fl. c. 300 BCE)

Author of the Elements; formalized division in extreme and mean ratio (II.11, VI.30), the golden 72°–72°–36° triangle and regular pentagon/15-gon (IV.10–16), and the icosahedron/dodecahedron (Book XIII).

Leonardo Pisano (Fibonacci) (c. 1170 – c. 1240–1250)

Pisan mathematician whose Liber Abaci (1202) introduced Hindu-Arabic numerals to Europe and posed the monthly rabbit problem generating 1, 1, 2, 3, 5, 8, 13, …

Luca Pacioli (c. 1447 – 1517)

Franciscan friar and mathematician; authored De Divina Proportione (1509, illustrated by Leonardo da Vinci) cataloging thirteen geometric effects of the Golden Ratio across plane and solid figures.

Johannes Kepler (1571 – 1630)

Astronomer and geometer; discovered the (1, √Φ, Φ) right triangle (1597 letter to Mästlin), observed F_{n+1}/F_n → Φ (1608), and studied the rhombic triacontahedron.

Claudius Ptolemy (c. 100 – c. 170 CE)

Alexandrian astronomer-mathematician whose Almagest chord theorem (Book I.10) yields the pentagonal diagonal-to-side identity d = Φ s and exact trigonometric tables.

Pythagoras of Samos (c. 570 – c. 495 BCE)

Founder of the Pythagorean school; associated with the pentagram badge (ὑγίεια) and right-triangle quadrance additivity.

Giovanni Domenico Cassini (1625 – 1712)

Italian-French astronomer and mathematician who presented F_{n-1} F_{n+1} - F_n^2 = (-1)^n to the Royal Academy of Sciences in 1680.

Leonhard Euler (1707 – 1783)

Swiss mathematician whose Machin-type rational arctangent decompositions underpin the reciprocal Fibonacci telescoping series for π/4.

Carl Friedrich Gauss (1777 – 1855)

Proved at age 18 (30 March 1796; Disquisitiones Arithmeticae, 1801) that the regular 17-gon is constructible by straightedge and compass via nested quadratic radicals.

Jacques Philippe Marie Binet (1786 – 1856)

French mathematician who published (1843) the closed-form power formula F_n = (Φ^n - (-φ)^n)/√5 previously known to Euler, Daniel Bernoulli, and de Moivre.

Eugène Charles Catalan (1814 – 1894)

Belgian-French mathematician who generalized Cassini’s identity to F_n^2 - F_{n-r} F_{n+r} = (-1)^{n-r} F_r^2 (1879).

Édouard Lucas (1842 – 1891)

French number theorist who named the Fibonacci sequence, introduced the companion Lucas sequence L_n = Φ^n + (-φ)^n, and developed Fibonomial coefficients.

Sam Loyd & Sam Loyd Jr. (1841 – 1911 / 1873 – 1934)

American puzzle pioneers who popularized both the 64 = 65 vanishing-square dissection and the 64 = 63 notched-rectangle dissection.

Henry Ernest Dudeney (1857 – 1930)

English mathematical puzzle creator who analyzed generalized Fibonacci chessboard dissections for both +1 gap and -1 overlap paradoxes.

Adolf Hurwitz (1859 – 1919)

German mathematician who proved (1891) that \(|\alpha - p/q| < 1/(\sqrt{5}\, q^2)\) has infinitely many rational solutions for every irrational α, with √5 optimal specifically because of Φ.

D’Arcy Wentworth Thompson (1860 – 1948)

Scottish biologist, mathematician, and classicist whose On Growth and Form (1917) analyzed Fibonacci phyllotaxis and gnomonic biological growth.

Willem Abraham Wythoff (1865 – 1939)

Dutch mathematician who characterized cold positions of Wythoff’s Nim (1907) as the complementary Beatty pairs (⌊nΦ⌋, ⌊nΦ^2⌋).

Édouard Zeckendorf (1901 – 1983)

Belgian physician, army officer, and amateur mathematician who published the canonical non-consecutive Fibonacci representation theorem (1972, discovered c. 1939).

Derrick Henry Lehmer (1905 – 1991)

American number theorist who posed (1936) the reciprocal Fibonacci arctangent series π/4 = ∑_{k=1}^∞ arctan(1/F_{2k+1}).

Harold Scott MacDonald Coxeter (1907 – 2003)

Geometer whose Regular Polytopes and Introduction to Geometry unified 3D golden polyhedra, 5-cube compounds, and cylindrical phyllotaxis lattices.

Roger Penrose (b. 1931)

Mathematical physicist and geometer who discovered the five-fold aperiodic P2 (kite & dart) and P3 (thick & thin golden rhomb) tilings in 1973–1974.

John Horton Conway (1937 – 2020)

Mathematician who named Penrose’s ‘kite’ and ‘dart’ prototiles and connected Fibonacci shift operations with Wythoff’s array.

Kenneth B. Stolarsky (b. 1942)

Number theorist who constructed the Stolarsky interspersion array (1977) via nearest-integer Golden Ratio rounding.

Clark Kimberling (b. 1942)

Mathematician who formalized interspersion and dispersion arrays generalizing the Wythoff and Stolarsky arrays, and curated the Encyclopedia of Triangle Centers (ETC).

George M. Bergman (b. 1943)

Mathematician who discovered and published the base-Φ (‘phigit’) positional numeral system in 1957 at age 14.

Norman J. Wildberger (b. 1955)

Creator of Rational Trigonometry (Divine Proportions, 2005), replacing transcendental distance and angle with exact algebraic quadrance and spread.