Modules

geometor.knott is organized into focused exact-symbolic verification and rendering modules:

  • geometor.knott — Public package interface exporting constants, notation bridges, catalog registries, phigit/Zeckendorf/Wythoff algorithms, and .euclid-graphic SVG serializers.

  • geometor.knott.constants — Exact \(\mathbb{Q}(\sqrt{5})\) definitions of \(\Phi = (1+\sqrt{5})/2\) (PHI), \(\phi = (\sqrt{5}-1)/2\) (phi), and \(\Psi = (1-\sqrt{5})/2\) (PSI), lossless sp.GoldenRatio conversion helpers, pure-integer Beatty floors (floor_linear_phi()), and Rational Trigonometry invariants (quadrance, spread, cross, cross_ratio).

  • geometor.knott.flat_geometry — Collection 1 (KNOTT-1.1 – KNOTT-1.6): exact geometor.model constructions for internal/external golden section divisions, \(\sqrt{5}\) and whirling-square golden rectangles, acute/obtuse golden triangles, pentagon/pentagram/paper-knot geometry, Kepler’s \((1, \sqrt{\Phi}, \Phi)\) right triangle, and Penrose P2/P3 prototiles.

  • geometor.knott.trigonometry — Collection 2 (KNOTT-2.1 – KNOTT-2.2): exact radical sines, cosines, tangents, and spreads for pentagonal angles (\(18^\circ, 36^\circ, 54^\circ, 72^\circ\)), the full 29-angle \(3^\circ k\) constructible lattice, and Gauss’s regular 17-gon cosine \(\cos(\pi / 17)\).

  • geometor.knott.solid_geometry — Collection 3 (KNOTT-3.1 – KNOTT-3.3): exact 3D coordinates, volumes, and rational dihedral spreads for the regular icosahedron and dodecahedron, the compound of five cubes in a dodecahedron, and acute/obtuse golden quasicrystal rhombohedra.

  • geometor.knott.phigits — Collection 4 (KNOTT-4.1 – KNOTT-4.3): integer-power Fibonacci linearization \(\Phi^n = F_n \Phi + F_{n-1}\), the unit-volume Phibonacci brick, continued-fraction convergents \(F_{k+1}/F_k\), and George Bergman’s base-\(\Phi\) (“phigit”) minimal/maximal encoders and multi-form enumerator.

  • geometor.knott.golden_string — Collection 5 (KNOTT-5.1 – KNOTT-5.3): Sturmian Golden String morphism vs. Beatty cutting-line slope \(\phi\), Zeckendorf non-consecutive Fibonacci base representations, and Beatty, Wythoff, and Stolarsky interspersion arrays.

  • geometor.knott.identities — Collection 6 (KNOTT-6.1 – KNOTT-6.5): four-term Fibonacci Pythagorean triple generators, Cassini’s \(64 \leftrightarrow 65\) and \(64 \leftrightarrow 63\) jigsaw dissections, Binet/Lucas/Catalan/d’Ocagne/Honsberger & Fibonomial power recurrences, reciprocal Fibonacci arctangent telescoping series for \(\pi / 4\), and the unimodular Golden Angle parastichy lattice.

  • geometor.knott.catalog — Master registry of the 6 Collections (COLLECTIONS) and 22 Catalog Items (CATALOG_ITEMS), validator runner, and resources/catalog_manifest.json exporter.

  • geometor.knott.svg_renderer — Deterministic theme-adaptive .euclid-graphic SVG serializer with 3-vertex midpoint <path> segments, #geom-tick-1..3 equality markers, and radial collision-free label placement.