GEOMETOR Knott Mathematical Catalog¶
“Nature uses as little as possible of anything.”
—Johannes Kepler, on the Golden Ratio and Fibonacci numbers
GEOMETOR Knott (geometor-knott) is an exact symbolic Mathematical
Catalog of the planar and solid Golden Ratio constructions, constructible
pentagonal and \(3^\circ\) trigonometry, base-\(\Phi\) (“phigit”)
numeral systems, Sturmian Golden String morphisms, Zeckendorf representations,
Wythoff and Stolarsky interspersion arrays, and Fibonacci–Lucas–\(\pi\)
identities curated by Dr. Ron Knott in his landmark online
reference:
Curated Source: Fibonacci Numbers, the Golden Section and the Golden String — https://r-knott.surrey.ac.uk/Fibonacci/fib.html (© 1996–2025 Dr. Ron Knott, University of Surrey).
Unlike GEOMETOR’s public-domain Digital Scriptorium Editions (such as
geometor/euclid or geometor/pacioli), GEOMETOR builds Mathematical
Catalogs for copyrighted modern works: zero prose paragraphs or graphic
files are copied from Dr. Knott’s site. Instead, each of the 22 catalog
entries (KNOTT-1.1 – KNOTT-6.5) across 6 thematic collections
formulates an independent GEOMETOR mathematical enunciation, cites Dr. Knott’s
exact URL and #anchor so readers explore his rich exposition directly,
proves every geometric and algebraic invariant from scratch in 100% exact
SymPy and geometor.model (0 sp.Float atoms), renders an original
interactive .euclid-graphic SVG, and links every result across the wider
GEOMETOR ecosystem.