mission

geometor.petersen establishes a rigorous Digital Scriptorium Book Codex and exact symbolic pattern library for Julius Petersen’s Methods and Theories for the Solution of Problems of Geometrical Constructions, Applied to 410 Problems (1866 / 1879) as the methodological and heuristic bridge of the GEOMETOR constructive canon.

Core Objectives

1. Systematizing Geometric Discovery (*Ars Inveniendi*): Where Euclid’s Elements (geometor/euclid, geometor/elements) presents finished deductive proofs, Petersen reveals the analytic engine that discovers constructions: relaxing a single condition to generate Point Loci (a–k), Tangential Line Loci (l–p), or Positional Homothety, and applying invertible Transformations of the Figure (Parallel Translation, Replacing, Axial Reflection, Spiral Revolution, and Circle Inversion) to gather dispersed data into constructible triangles.

2. 100% Exact Symbolic Realization (geometor.model): Every flagship heuristic pattern is accompanied by an exact, float-free SymPy construction in geometor.petersen.constructions—built with Model(..., auto_intersect=False), explicit intersect / subconstruction DAGs, @proposition verification, and Rational Trigonometry invariants (quadrance, line_spread, cross_ratio), while keeping the historical Book Codex tracks strictly free of embedded py_file scripts.

3. Cross-Corpus Lineage: Map Petersen’s 1866/1879 methods backward to Euclid and Pappus (Synagoge Book VII) and forward to Émile Lemoine (Géométrographie, 1902), David Hilbert (Grundlagen der Geometrie Ch. VII, 1899), Nathan Altshiller-Court (College Geometry, 1925/1952), George Pólya (How to Solve It, 1945), and Clark Kimberling’s Encyclopedia of Triangle Centers (geometor/etc).