Content of type 'collection'
KNOTT-1 — 2D Golden Geometry & Constructions
Planar compass-and-straightedge divisions in extreme and mean ratio, golden and root-5 rectangles with orthogonal gnomonic spiral poles, self-deflating golden triangles and gnomons, pentagonal star progressions and overhand paper-strip knots, Kepler’s geometric-progression right triangle, and Penrose aperiodic P2/P3 prototiles.
KNOTT-2 — Exact Pentagonal & Constructible Trigonometry
Closed-form quadratic radicals and Rational Trigonometry spreads for 18°, 36°, 54°, and 72°, extended by Euclid IV.16 pentagon-equilateral superposition across all 29 constructible multiples of 3° in the first quadrant and contrasted with Gauss’s Fermat-prime regular 17-gon cosine.
KNOTT-3 — 3D Golden Geometry of Solids
Three-dimensional golden coordinates spanning the regular icosahedron and dodecahedron from three mutually orthogonal golden rectangles, Euclid XIII.17’s inscribed cube and five-cube compound, and the acute and obtuse golden rhombohedra of icosahedral quasicrystals.
KNOTT-4 — Algebraic Powers of Φ, Continued Fractions & Base-Φ Phigits
Linearization of all integer powers of Φ into Fibonacci multiples, the unit-volume Phibonacci brick, extremal continued fraction convergents F_{n+1}/F_n and Hurwitz’s √5 irrationality barrier, and George Bergman’s non-adjacent base-Φ (‘phigit’) numeral system.
KNOTT-5 — The Golden String, Zeckendorf Base, & Wythoff / Stolarsky Arrays
The infinite Sturmian Golden String (101101011011…) generated both by morphism substitution and by a lattice-cutting ray of slope φ, Zeckendorf’s canonical non-consecutive Fibonacci base, and the bijective Beatty, Wythoff, and Stolarsky interspersion arrays.
KNOTT-6 — Fibonacci-Lucas Identities, Pythagorean Triples, Jigsaw Paradoxes & π
Four-term Fibonacci generators of Pythagorean right triangles, Cassini’s alternating ±1 determinant realized as 64 ↔ 65 and 64 ↔ 63 four-piece dissections, Binet/Lucas/Catalan/d’Ocagne/Honsberger and Fibonomial power identities, Fibonacci arctangent telescoping series for π, and the Golden Angle parastichy lattice.