mission

geometor.poincare unites a verbatim, philologically verified bilingual Book Codex of Henri Poincaré’s La Science et l’Hypothèse (Science and Hypothesis, 1902 / 1905) with 100% exact symbolic constructions of the Poincaré Conformal Hyperbolic Disk inside geometor.model.

Core Pillars

1. Verbatim Bilingual Primary Sources: Pair Ernest Flammarion’s 1902 Paris French text (including Poincaré’s critical section Les Géométries de Hilbert, omitted from the 1905 London translation) with W. J. Greenstreet’s 1905 London translation and G. B. Halsted’s 1905 New York translation across a synchronized 4-track reader (English · French (1902) · Summary · Notes).

2. Poincaré’s Translation Dictionary in Exact Algebra: Realize Poincaré’s profound insight—that every theorem of Bolyai–Lobachevsky hyperbolic geometry translates into an exact theorem of Euclidean circle inversion and orthogonal circles inside geometor.model—using exact SymPy rationals and quadratic radicals with zero floating-point approximation.

3. Noetic & Axiomatic Dialogue Across GEOMETOR: Situate Poincaré’s geometric conventionalism (les axiomes ne sont que des définitions déguisées) directly alongside Euclid (Elements Postulate V), Hilbert (Grundlagen der Geometrie), Bertrand Russell (An Essay on the Foundations of Geometry & the 1898–1900 Revue de Métaphysique et de Morale debate), Peter Hoenen S.J. (De Noetica Geometriae, 1954), Felix Klein (Erlanger Programm), Pappus (cross-ratio invariance), John Casey (orthogonal circles), Émile Lemoine (Géométrographie), and Norman Wildberger (Universal Hyperbolic Geometry).