GEOMETOR • klein¶
Dual-Treatise Bilingual Book Codex & Exact Symbolic Engine for Felix Klein (1849–1925)
Critical 4-track bilingual digital Book Codices (English · Deutsch · Summary · Notes), calibrated .euclid-graphic vector figures, exact SymPy / geometor.model constructibility and transformation-group verifiers, and cross-corpus concordance for the two foundational geometric monographs of Felix Klein:
Famous Problems of Elementary Geometry (1895 / 1897) — Klein’s Göttingen Easter 1895 lectures establishing the algebraic degree-$2^h$ criterion for straightedge-and-compass constructibility, the impossibility of duplicating the cube, trisecting a general angle, and constructing the regular heptagon ($n = 7$), the Poncelet–Steiner–von Staudt–Schröter single-circle straightedge construction of Gauss’s regular 17-gon, and Gordan’s algebraic proofs of the transcendence of $e$ (Hermite, 1873) and $\pi$ (Lindemann, 1882).
A Comparative Review of Recent Researches in Geometry ("The Erlangen Program") (1872 / 1893) — Klein’s inaugural Erlangen monograph reorganizing all of geometry as the invariant theory of transformation groups acting on $n$-dimensional manifolds.
Primary Codices (Opera Geometrica)¶
Famous Problems of Elementary Geometry (1895 / 1897)¶
Vorträge über ausgewählte Fragen der Elementargeometrie, ausgearbeitet von F. Tägert (Leipzig: B. G. Teubner, 1895) · Authorized English Translation by W. W. Beman & D. E. Smith (Boston & London: Ginn & Co., 1897).
Synchronized 10-unit, 4-track Book Codex (English · Deutsch · Summary · Notes) verified page-by-page against high-resolution 1895 Teubner and 1897 Ginn folio scans (strictly preserving 100% public-domain witnesses without post-1930 annotations):
Conspectus & Part I (Algebraic Constructibility): Codex TOC · Prefaces & Introduction · Part I, Ch. I: Square-Root Equations (§§ 1–15) · Ch. II: Delian Cube & Angle Trisection (§§ 1–3) · Ch. III: Cyclotomy & Fermat Primes (§§ 1–8) · Ch. IV: Regular 17-Gon & Fixed Circle (§§ 1–9) · Ch. V: Higher Curves & Instruments (§§ 1–5).
Part II (Transcendence of e and π): Part II, Ch. I: Cantor’s Algebraic Countability & Continuum (§§ 1–3) · Ch. II: Historical Survey of π (§§ 1–5) · Ch. III: Hermite’s Theorem on e (§§ 1–3) · Ch. IV–V: Lindemann’s Theorem on π & the Integraph.
The Erlangen Program — Comparative Review of Recent Researches in Geometry (1872 / 1893)¶
Vergleichende Betrachtungen über neuere geometrische Forschungen (Erlangen: A. Deichert, 1872; Math. Annalen 43, 1893) · Authorized English Translation by M. W. Haskell (Bulletin of the New York Mathematical Society 2, July 1893, pp. 215–249).
Synchronized 6-unit, 4-track Book Codex (English · Deutsch · Summary · Notes) presenting Klein’s complete group-theoretic architecture of geometry together with all seven historical and mathematical Notes (Notes I–VII):
Synchronized 4-Track Book Codex: Codex TOC · Prefatory Note & Introduction · §§ 1–2: Principal Group & Adjoined Hierarchy · §§ 3–5: Projective Geometry, Transference & Space-Elements · §§ 6–7: Reciprocal Radii & Lie’s Sphere Geometry · §§ 8–10: Birational, Topological, Contact & Manifold Groups · Notes I–VII (Non-Euclidean Cayley–Klein Metrics).
Cross-Corpus Apparatus & Exact Symbolic Modules¶
Systematic Bibliography (36 Primary & Sister-Corpus Editions) · Prosopographical Index (52 Mathematicians & Philosophers) · Bilingual Technical Glossary (25 Terms)
Exact Symbolic Python API (geometor.klein) —
analyze_constructibility,construct_gauss_17gon_periods(1-circle Poncelet–Steiner model with 0 floats),verify_erlangen_invariants, andverify_cayley_klein_additivity.