Persons

Mathematicians, geometers, astronomers, and physicists connected to Rational Trigonometry and Universal Geometry.

Norman J. Wildberger (b. 1955)

Canadian-Australian mathematician at UNSW Sydney who formulated Rational Trigonometry, Universal Geometry (Divine Proportions, 2005), and Chromogeometry (2008).

Euclid of Alexandria (fl. 300 BCE)

Author of the thirteen books of the Elements, whose synthetic propositions from Books I–IV, VI, and XIII gain field-independent algebraic proofs in Universal Geometry.

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

Ancient Greek philosopher-geometer associated with Law I of Rational Trigonometry (\(Q_1 + Q_2 = Q_3 \iff s_3 = 1\)).

Archimedes of Syracuse (c. 287–c. 212 BCE)

Hellenistic mathematician after whom Wildberger named Archimedes’ function \(\mathcal{A}(Q_1, Q_2, Q_3)\) for collinearity and triangle quadrea.

Apollonius of Perga (c. 240–c. 190 BCE)

Author of Conics, whose median theorem and focal conic reflections become derivative-free polynomial laws in W.13, W.20, and W.21.

Diocles (c. 240–c. 180 BCE)

Greek geometer whose On Burning Mirrors established the focal reflection property of the parabola.

Heron of Alexandria (c. 10–c. 70 CE)

Geometer and engineer whose radical area formula squares cleanly into \(\mathcal{A} = 16 \Delta^2\).

Menelaus of Alexandria (c. 70–140 CE)

Astronomer and geometer whose transversal theorem shares the exact multiplicative quadrance balance of Ceva’s theorem (W.14).

Claudius Ptolemy (c. 100–c. 170 CE)

Author of the Almagest, whose cyclic quadrilateral diagonal theorem becomes \(\mathcal{A}(Q_{12}Q_{34}, Q_{23}Q_{14}, Q_{13}Q_{24}) = 0\) (W.18).

Pappus of Alexandria (c. 290–c. 350 CE)

Author of the Synagoge (Collection), establishing projective cross-ratio invariance (W.22).

Brahmagupta (598–c. 668 CE)

Indian mathematician whose cyclic quadrilateral area formula (Brahmasphutasiddhanta, 628 CE) underpins cyclic quadrea.

Regiomontanus (Johannes Müller von Königsberg, 1436–1476)

Renaissance astronomer and mathematician who posed the 1471 extremal viewing-angle problem solved algebraically in W.24.

Luca Pacioli (c. 1447–1517)

Franciscan mathematician and author of De Divina Proportione (1509, illustrated by Leonardo da Vinci), celebrating \(\phi\) and the five Platonic solids.

Galileo Galilei (1564–1642)

Establisher of parabolic projectile kinematics (Two New Sciences, 1638), reformulated via \(S_2(s)\) in W.26.

Johannes Kepler (1571–1630)

Astronomer and geometer whose Golden Right Triangle has pure golden-power quadrances \((1, \phi, \phi^2)\) and spreads \((1/\phi^2, 1/\phi, 1)\) (W.11).

Willebrord Snellius (1580–1626)

Dutch astronomer and geodesist who pioneered triangulation resection (1615, W.25) and the law of refraction (\(n_1^2 s_1 = n_2^2 s_2\), W.26).

Girard Desargues (1591–1661)

Founder of synthetic projective geometry and harmonic involution theory.

René Descartes (1596–1650)

Founder of analytic coordinate geometry (La Géométrie, 1637) and discoverer of the folium of Descartes (W.28).

Giovanni Ceva (1647–1734)

Italian geometer who proved Ceva’s concurrency theorem (De lineis rectis, 1678, W.14).

Jakob Bernoulli (1655–1705)

Swiss mathematician who introduced the lemniscate (\(Q = a(1 - 2s)\) in rational polar coordinates, W.28).

Brook Taylor (1685–1731)

English mathematician whose polynomial shift expansion defines derivative-free algebraic tangents to conics (W.21).

Leonhard Euler (1707–1783)

Proved the collinearity of triangle centers along the Euler line (W.16) and the four-point planar distance relation (W.18).

Matthew Stewart (1717–1785)

Scottish geometer who published Stewart’s cevian theorem (Some General Theorems, 1746, W.13).

Peter Andreas Hansen (1795–1874)

Danish-German astronomer and geodesist who formulated Hansen’s two-station surveying problem (1841, W.25).

Pafnuty Chebyshev (1821–1894)

Russian mathematician whose orthogonal polynomials \(T_n\) rescale onto Wildberger’s spread polynomials \(S_n(s)\) (W.05).

Hermann Minkowski (1864–1909)

Formulated relativistic spacetime geometry (1908), corresponding to the Red metric \(Q_R = \Delta x^2 - \Delta y^2\) of Chromogeometry (W.23).

John Horton Conway (1937–2020)

Introduced Conway triangle notation (\(S_A, S_B, S_C\)), matching the quadratic Cross Law numerators \((Q_j + Q_k - Q_i)/2\).

Fred Seelig

Compiler of the archival notebooks and spreadsheets preserved in geometor/fundamentals.