about

Historical, philological, and symbolic-verification provenance for geometor.klein.

Primary Public-Domain Witnesses

  • 1895 German Editio Princeps of Famous Problems (B. G. Teubner, Leipzig): Vorträge über ausgewählte Fragen der Elementargeometrie, ausgearbeitet von F. Tägert, eine Festschrift zu der Pfingsten 1895 in Göttingen stattfindenden dritten Versammlung des Vereins zur Förderung des mathematischen und naturwissenschaftlichen Unterrichts (v + 66 S., mit 10 in den Text gedruckten Figuren und 2 lithographierten Tafeln). Transcribed and verified by page-by-page 300-DPI multimodal scan inspection.

  • 1897 Authorized English Edition of Famous Problems (Ginn & Company, Boston & London): Famous Problems of Elementary Geometry: The Duplication of the Cube, The Trisection of an Angle, The Quadrature of the Circle, translated by Wooster Woodruff Beman and David Eugene Smith (ix + 80 pp.). Verified page-by-page against the 1897 Ginn folio scans. (Rights note: R. C. Archibald’s 1930/1956 supplementary bibliographic notes are strictly excluded; only the pure 1895/1897 public-domain treatises are included.)

  • 1872 German Editio Princeps of the Erlangen Program (Andreas Deichert, Erlangen): Vergleichende Betrachtungen über neuere geometrische Forschungen: Programm zum Eintritt in die philosophische Facultät und den Senat der k. Friedrich-Alexanders-Universität zu Erlangen (1872; reprinted with minor authorial note in Mathematische Annalen 43, 1893, pp. 63–100; Project Gutenberg #38033).

  • 1893 Authorized English Edition of the Erlangen Program (NYMS Bulletin): A Comparative Review of Recent Researches in Geometry, translated by Mellen Woodman Haskell with Klein’s 1893 Prefatory Note (Bulletin of the New York Mathematical Society 2, July 1893, pp. 215–249; arXiv:0807.3161).

Content / Code Separation & Exact Symbolic Verification

In accordance with GEOMETOR Digital Scriptorium standards, zero executable Python scripts are embedded inside resources/. All exact symbolic algebra and geometric constructions reside in src/geometor/klein/ and demos/:

  • geometor.klein.constructibility — Exact SymPy Gauss–Wantzel polygon classifier, irreducible polynomial degree-$2^h$ & quartic cubic-resolvent Galois test, and Hermite–Lindemann transcendence diagnostics.

  • geometor.klein.heptadecagon — Exact cyclotomic field canonicalizer over $K_{16} = K_8(\sin\frac{2\pi}{17})$ and Klein’s von Staudt–Schröter single-circle straightedge construction of all 17 exact vertices V0..``V16`` inside geometor.model.Model (len(model.circles) == 1, 0 floating-point coordinates).

  • geometor.klein.erlangen — Exact rational verification of invariants preserved and broken across the Principal Similarity Group, Affine Shear Group, Projective Homography Group, and Möbius Reciprocal-Radii Inversion Group, together with Cayley–Klein logarithmic cross-ratio additivity.