fundamentals

Foundational Constructive Geometry Codex & The Fred W. Seelig Archive

geometor.fundamentals bridges classical Euclidean synthesis, projective and harmonic geometry, and modern symbolic algebra. It preserves and synthesizes the complete geometrical notebooks (55 topics, 353 manuscript folios) and computational spreadsheets (59 worksheets in Triangles and Circles.ods) compiled by seelig (SeeligNotebooks, SeeligSpreadsheets).

Architecture of the Codex

Every topic (F.1 through F.55) is presented as a 3-Track Book Codex:

  1. Track 1 — Synthesis (index.rst): Formal geometric .. enunciation::, interactive Explorer-styled SVG construction (f-NN.svg) with two-way hover highlighting, constructive .. signature:: block, symbolic SymPy derivations on the canonical \((a, b, c) = (5, 6, 7)\) triangle, collapsible OpenDocument Spreadsheet tables, Graphviz dependency DAG, and cross-links to geometor/euclid, geometor/elements (G.<n>), and geometor/etc (X(n)).

  2. Track 2 — Folios (folios.rst): High-resolution archival scans (0001.jpg–0353.jpg) paired with .. folio:: markers, diplomatic mathematical transcriptions, and editorial notes.

  3. Track 3 — Code (code.rst): Standalone executable Python script (model.py) constructing the exact geometor.model.Model and verifying symbolic invariants.

Thematic Pillars

Pillar

Topics

Core Themes

I. Triangle Centers & Classical Lines

F.4, F.6, F.11, F.19, F.20, F.21, F.28, F.29, F.34, F.36, F.38, F.46, F.50

Centroid \(X(2)\), circumcenter \(X(3)\), incenter \(X(1)\), orthocenter \(X(4)\), nine-point circle \(X(5)\), Fermat point \(X(13)\), orthic triangle, pedal triangle, Carnot's theorem, and Stewart's theorem.

II. Projective & Harmonic Geometry

F.2, F.5, F.7, F.16, F.25, F.26, F.27, F.39, F.48

Ceva's theorem, Menelaus's theorem, harmonic conjugate, inversion, harmonic mean, pole and polar duality, centers of similitude, and Monge–dalembert collinearity.

III. Circle Geometry & Pencils

F.8, F.9, F.10, F.12, F.13, F.15, F.43, F.51

Power of a point, radical axis, coaxial circles, orthogonal circles, Apollonian circles, geometric mean, and cyclic quadrilateral (ptolemy’s theorem).

IV. Algebraic & Coordinate Systems

F.3, F.14, F.31, F.33, F.35, F.42, F.44, F.47, F.52, F.53, F.54, F.55

Homogeneous barycentric coordinates \((u : v : w)\), Conway triangle notation (\(S, S_A, S_B, S_C\)), biquadratic Heron's formula, and Pythagorean triple parametrization.

V. Conics & Analytic Loci

F.1, F.17, F.22, F.37

Optical reflection and focal properties of the parabola and ellipse.

VI. Special Triangles & Sacred Proportions

F.18, F.23, F.24, F.30, F.32, F.40, F.41, F.45, F.49

Vesica piscis, equilateral triangle, Gothic pointed arches, golden triangle, golden ratio \(\phi\), and markowski’s critique.