Initial 28-Principle Rational Trigonometry & Universal Codex¶
Launched geometor.wildberger v0.1.0, synthesizing the foundational and
advanced principles of Norman J. Wildberger’s Divine
Proportions: Rational Trigonometry to Universal Geometry (Wildberger2005)
and Chromogeometry (Wildberger2008) into a 28-Principle executable
codex (W.01 through W.28).
Highlights¶
Exact Symbolic Engine (
geometor.wildberger.invariants): Implemented quadrance, spread, cross, twist, signed turn, Archimedes’ function, quadrea, Triple/Quadruple Quad & Spread functions, Euler’s four-point function, spread and cross polynomials, 6-proportion Taylor conics, 3D dihedral spreads, rational polar coordinates \([s, Q]\), and finite-field \(\mathbb{F}_p\) metric evaluation.18 Multivariate SymPy Proofs (
geometor.wildberger.proofs): Proved the Five Main Laws, Brahmagupta & Ptolemy’s cyclic theorems, Euler line and Nine-Point Circle over arbitrary fields (\(\operatorname{char}\mathbb{F}\ne 2\)), Chromogeometry’s Nine-Point Midpoint Theorem (\(N_B = \tfrac{1}{2}(C_R + C_G)\)), parabolic optical reflection without derivatives, and the cancellation of \(\sqrt{5}\) in all five Platonic solid dihedral spreads (\(8/9, 1, 8/9, 4/9, 4/5\)).28 Interactive Constructions: Built exact
geometor.model.Modeldossiers with zero floating-point shortcuts and interactive dark-canvas SVGs.