Bibliography & Source Concordance

Primary online reference pages by Dr. Ron Knott (© 1996–2025 Dr. Ron Knott, University of Surrey) and classical/modern mathematical treatises cited across this catalog.

[KnottFibHub] Fibonacci Numbers, the Golden Section and the Golden String

Dr. Ron Knott, Fibonacci Numbers, the Golden Section and the Golden String (University of Surrey, 1996–2025 (fib.html)) — https://r-knott.surrey.ac.uk/Fibonacci/fib.html.

[KnottPhi2D] Phi in 2D Geometry and Trigonometry

Dr. Ron Knott, Phi in 2D Geometry and Trigonometry (University of Surrey, 1996–2025 (phi2DGeomTrig.html)) — https://r-knott.surrey.ac.uk/Fibonacci/phi2DGeomTrig.html.

[KnottSimpleTrig] Exact Trig Values for Simple Angles

Dr. Ron Knott, Exact Trig Values for Simple Angles (University of Surrey, 1996–2025 (simpleTrig.html)) — https://r-knott.surrey.ac.uk/Fibonacci/simpleTrig.html.

[KnottPhi3D] The Golden Geometry of Solids or Phi in 3 Dimensions

Dr. Ron Knott, The Golden Geometry of Solids or Phi in 3 Dimensions (University of Surrey, 1996–2025 (phi3DGeom.html)) — https://r-knott.surrey.ac.uk/Fibonacci/phi3DGeom.html.

[KnottPropsPhi] Phi’s Fascinating Figures

Dr. Ron Knott, Phi’s Fascinating Figures (University of Surrey, 1996–2025 (propsOfPhi.html)) — https://r-knott.surrey.ac.uk/Fibonacci/propsOfPhi.html.

[KnottPhigits] Phigits and the Base Phi System

Dr. Ron Knott, Phigits and the Base Phi System (University of Surrey, 1996–2025 (phigits.html)) — https://r-knott.surrey.ac.uk/Fibonacci/phigits.html.

[KnottGoldenString] The Fibonacci Rabbit Sequence (The Golden String)

Dr. Ron Knott, The Fibonacci Rabbit Sequence (The Golden String) (University of Surrey, 1996–2025 (fibrab.html)) — https://r-knott.surrey.ac.uk/Fibonacci/fibrab.html.

[KnottFibRep] Fibonacci Representations of Numbers

Dr. Ron Knott, Fibonacci Representations of Numbers (University of Surrey, 1996–2025 (fibrep.html)) — https://r-knott.surrey.ac.uk/Fibonacci/fibrep.html.

[KnottFibGen] General Fibonacci Series, Wythoff and Stolarsky Arrays

Dr. Ron Knott, General Fibonacci Series, Wythoff and Stolarsky Arrays (University of Surrey, 1996–2025 (fibGen.html)) — https://r-knott.surrey.ac.uk/Fibonacci/fibGen.html.

[KnottPythag] Pythagorean Triangles and Triples

Dr. Ron Knott, Pythagorean Triangles and Triples (University of Surrey, 1996–2025 (Pythag/pythag.html)) — https://r-knott.surrey.ac.uk/Pythag/pythag.html.

[KnottPuzzles2] Harder Fibonacci Puzzles

Dr. Ron Knott, Harder Fibonacci Puzzles (University of Surrey, 1996–2025 (fibpuzzles2.html)) — https://r-knott.surrey.ac.uk/Fibonacci/fibpuzzles2.html.

[KnottFormulae] Fibonacci and Phi Formulae

Dr. Ron Knott, Fibonacci and Phi Formulae (University of Surrey, 1996–2025 (fibFormulae.html)) — https://r-knott.surrey.ac.uk/Fibonacci/fibFormulae.html.

[KnottFibPi] The Fibonacci Numbers in a Formula for Pi

Dr. Ron Knott, The Fibonacci Numbers in a Formula for Pi (University of Surrey, 1996–2025 (fibpi.html)) — https://r-knott.surrey.ac.uk/Fibonacci/fibpi.html.

[KnottNature] Fibonacci Numbers and Nature

Dr. Ron Knott, Fibonacci Numbers and Nature (University of Surrey, 1996–2025 (fibnat.html)) — https://r-knott.surrey.ac.uk/Fibonacci/fibnat.html.

[EuclidElements] The Thirteen Books of Euclid’s Elements

Euclid (trans. Sir Thomas L. Heath), The Thirteen Books of Euclid’s Elements (Books II.11, IV.10–11, IV.16, VI.def.3, VI.30, XIII.1–18 (Cambridge, 1908)).

[Pacioli1509] De Divina Proportione

Luca Pacioli (illus. Leonardo da Vinci), De Divina Proportione (Venice: Paganino Paganini, 1509).

[Hambidge1920] Dynamic Symmetry: The Greek Vase

Jay Hambidge, Dynamic Symmetry: The Greek Vase (Yale University Press, 1920).

[Wildberger2005] Divine Proportions: Rational Trigonometry to Universal Geometry

Norman J. Wildberger, Divine Proportions: Rational Trigonometry to Universal Geometry (Wild Egg Books, Sydney, 2005).

[Penrose1974] The Role of Aesthetics in Pure and Applied Mathematical Research

Roger Penrose, The Role of Aesthetics in Pure and Applied Mathematical Research (Bulletin of the Institute of Mathematics and Its Applications 10 (1974), 266–271).

[Gardner1977] Extraordinary Nonperiodic Tilings That Enrich the Theory of Tiles

Martin Gardner, Extraordinary Nonperiodic Tilings That Enrich the Theory of Tiles (Scientific American 236(1), January 1977, 110–121).

[Gauss1801] Disquisitiones Arithmeticae

Carl Friedrich Gauss, Disquisitiones Arithmeticae (Section VII, arts. 365–366 (Leipzig, 1801)).

[Coxeter1973] Regular Polytopes (3rd ed.) & Introduction to Geometry

H. S. M. Coxeter, Regular Polytopes (3rd ed.) & Introduction to Geometry (Dover, 1973; Wiley, 1969 (Ch. 11: The Golden Section and Phyllotaxis)).

[Vajda1989] Fibonacci and Lucas Numbers, and the Golden Section: Theory and Applications

Steven Vajda, Fibonacci and Lucas Numbers, and the Golden Section: Theory and Applications (Ellis Horwood, Chichester, 1989).

[Hurwitz1891] Ueber die angenäherte Darstellung der Irrationalzahlen durch rationale Brüche

Adolf Hurwitz, Ueber die angenäherte Darstellung der Irrationalzahlen durch rationale Brüche (Mathematische Annalen 39 (1891), 279–284).

[Bergman1957] A Number System with an Irrational Base

George M. Bergman, A Number System with an Irrational Base (Mathematics Magazine 31(2), Nov.–Dec. 1957, 98–110).

[Zeckendorf1972] Représentation des nombres naturels par une somme de nombres de Fibonacci ou de nombres de Lucas

Édouard Zeckendorf, Représentation des nombres naturels par une somme de nombres de Fibonacci ou de nombres de Lucas (Bull. Soc. Roy. Sci. Liège 41 (1972), 179–182).

[Wythoff1907] A Modification of the Game of Nim

Willem Abraham Wythoff, A Modification of the Game of Nim (Nieuw Archief voor Wiskunde (2) 7 (1907), 199–202).

[Stolarsky1977] A Set of Generalized Fibonacci Sequences Such That Each Natural Number Belongs to Exactly One

Kenneth B. Stolarsky, A Set of Generalized Fibonacci Sequences Such That Each Natural Number Belongs to Exactly One (Fibonacci Quarterly 15(3), 1977, 224).

[Morrison1980] A Stolarsky Array of Wythoff Pairs

David R. Morrison, A Stolarsky Array of Wythoff Pairs (A Collection of Manuscripts Related to the Fibonacci Sequence, Fibonacci Assoc., 1980, 134–136).

[Horadam1961] Fibonacci Number Triples

Alwyn F. Horadam, Fibonacci Number Triples (American Mathematical Monthly 68(8), 1961, 751–753).

[Gardner1956] Mathematics, Magic and Mystery

Martin Gardner, Mathematics, Magic and Mystery (Dover Publications, New York, 1956 (Ch. 7: Geometrical Vanishes)).

[Horadam1962] Fibonacci Sequences and a Geometrical Paradox

Alwyn F. Horadam, Fibonacci Sequences and a Geometrical Paradox (Mathematics Magazine 35(1), 1962, 1–11).

[Honsberger1985] Mathematical Gems III

Ross Honsberger, Mathematical Gems III (Mathematical Association of America, 1985 (Ch. 8: A Second Look at the Fibonacci and Lucas Numbers)).

[Lehmer1936] Problem 3801 (Reciprocal Fibonacci Arctangent Identity)

Derrick Henry Lehmer, Problem 3801 (Reciprocal Fibonacci Arctangent Identity) (American Mathematical Monthly 43 (1936), 580; solution 45 (1938), 636–637).

[Thompson1917] On Growth and Form

D’Arcy Wentworth Thompson, On Growth and Form (Cambridge University Press, 1917 (Ch. XIV: On Leaf-Arrangement, or Phyllotaxis)).