Mission — Mathematical Cataloging & Source Respect

A GEOMETOR Mathematical Catalog indexes the mathematical facts, constructions, sequences, and theorems curated in a copyrighted modern reference without reproducing its copyrighted prose or illustrations—pairing direct attribution and section-level deep links with 100% original symbolic proofs and synthesized .euclid-graphic diagrams.

Why a Mathematical Catalog?

Since 1996, Dr. Ron Knott (formerly of the Department of Mathematics at the University of Surrey) has authored and continuously expanded Fibonacci Numbers, the Golden Section and the Golden String (KnottFibHub), one of the richest and clearest mathematical web compendia ever created. Across dozens of interconnected pages, Dr. Knott gathers Euclidean and modern compass-and-straightedge constructions of \(\Phi\), exact radical trigonometric tables, three-dimensional polyhedral coordinates, George Bergman’s irrational base-\(\Phi\) (“phigit”) arithmetic, the recursive Rabbit / Golden String sequence, Édouard Zeckendorf <zeckendorf>’s Fibonacci base, Willem Wythoff’s and Kenneth Stolarsky’s interspersion arrays, Fibonacci Pythagorean triples, Giovanni Domenico Cassini’s area jigsaw paradoxes, and reciprocal Fibonacci arctangent series for \(\pi\).

In the GEOMETOR initiative, historical public-domain treatises—such as Euclid’s Elements (EuclidElements), Luca Pacioli <pacioli>’s De Divina Proportione (Pacioli1509), and D'Arcy Wentworth Thompson’s On Growth and Form (Thompson1917)—are published as full Digital Scriptorium Editions derived from archival folios. For living, copyrighted modern works (© 1996–2025 Dr. Ron Knott, University of Surrey), full-text reproduction is neither appropriate nor desired. Instead, GEOMETOR constructs a Mathematical Catalog:

  1. Zero Copyrighted Text or Media Reproduction: Not a single prose sentence, HTML markup block, or GIF/PNG diagram is copied from r-knott.surrey.ac.uk. Mathematical theorems, sequences, and geometric relations are universal facts; Dr. Knott’s pedagogical writing and figures belong exclusively to him, and readers are encouraged to visit his cited pages directly.

  2. Exact Section-Level Attribution: Every catalog entry (KNOTT-1.1 through KNOTT-6.5) records the exact page title, full clickable URL + #anchor, and copyright credit to Dr. Ron Knott, University of Surrey.

  3. 100% Exact Symbolic Verification: Every cataloged construction and identity is modeled in geometor.knott over \(\mathbb{Q}\), \(\mathbb{Q}(\sqrt{5})\), \(\mathbb{Q}(\sqrt{\Phi})\), or explicit cyclotomic radical towers with zero float or sp.Float approximations, verified via Rational Trigonometry invariants (quadrance, spread, cross-ratio) and polynomial reductions.

  4. Original Interactive ``.euclid-graphic`` SVGs: Every entry renders a clean, theme-adaptive vector diagram synthesized directly from its geometor.model.Model instance and wired to inline :g: and :eq: prose highlights.

  5. Cross-Corpus GEOMETOR Concordance: Every entry connects Dr. Knott’s hub to geometor/euclid, geometor/elements, geometor/pacioli, geometor/wildberger, geometor/divine, geometor/etc, geometor/phyllotaxis, and geometor/trees.