Bibliography & Archival Sources

Primary mathematical treatises, peer-reviewed journal articles, and curated archival pages from Alexander Bogomolny’s Interactive Mathematics Miscellany and Puzzles (Cut-the-Knot, © 1996–2018).

Elements (Heath Edition) (c. 300 BCE)

Euclid — Book II Prop. 11; Book IV Prop. 10–11; Book VI Def. 3 & Prop. 30; Book XIII Prop. 1–10. Sir Thomas L. Heath, The Thirteen Books of Euclid’s Elements, Cambridge University Press, 1908 (GEOMETOR Digital Scriptorium edition). URL: https://geometor.github.io/euclid/ Cataloged in: GC-01.01, GC-05.01

Syntaxis Mathematica (Almagest) (c. 150 CE)

Claudius Ptolemy — Book I, Chapter 10. G. J. Toomer (trans.), Ptolemy’s Almagest, Duckworth / Springer, 1984. Cataloged in: GC-05.01

Letter to Michael Mästlin (Tübingen, October 1597) (1597)

Johannes Kepler — Gesammelte Werke, Vol. 13, Nr. 75. First explicit derivation of the right triangle with sides in geometric progression 1 : √φ : φ. Cataloged in: GC-04.02

Rational Recreations (1794)

William Hooper — 4th ed., Vol. 1, Problem XLIII. Early geometric missing-area rectangle dissection later generalized by Sam Loyd, Martin Gardner, and Paul Curry. Cataloged in: GC-07.06

Géométrographie ou Art des constructions géométriques (1902)

Émile Lemoine — Scientia No. 18, C. Naud, Paris. Foundational treatise quantifying operational simplicity of straightedge-and-compass constructions; see also J. Reusch, Planimetrische Konstruktionen in geometrographischer Ausführung (1904). Cataloged in: GC-01.03

The Divine Proportion: A Study in Mathematical Beauty (1970)

H. E. Huntley — Dover Publications, New York. Classic exposition including the angle-bisector circle division in the 3-4-5 right triangle. Cataloged in: GC-01.01, GC-01.02, GC-04.01

Elementary Problem E3007 (1983)

George Odom & H. S. M. Coxeter — American Mathematical Monthly 90(7), p. 482 (solution 93(7), 1986, p. 566). Equilateral-triangle midline extended to the circumcircle yields the golden section. Cataloged in: GC-02.01

A Simple Construction of the Golden Section (2002)

Kurt Hofstetter — Forum Geometricorum 2, pp. 65–66. Five-circle Mascheroni compass-only construction of the golden section. Cataloged in: GC-01.05

5-Step Division of a Segment in the Golden Section (2003)

Kurt Hofstetter — Forum Geometricorum 3, pp. 205–206. Minimal 5-step straightedge-and-compass internal division of a given segment. Cataloged in: GC-01.03

Another 5-Step Division of a Segment in the Golden Section (2004)

Kurt Hofstetter — Forum Geometricorum 4, pp. 21–22. Alternative 5-step straightedge-and-compass division using three circles and two lines. Cataloged in: GC-01.04

Division of a Segment in the Golden Section with Ruler and Rusty Compass (2005)

Kurt Hofstetter — Forum Geometricorum 5, pp. 135–136. Fixed-opening (rusty) compass construction dividing a unit segment in φ. Cataloged in: GC-01.06

Problems in Plane Geometry (2006)

V. V. Prasolov — MCCME, Moscow (5th ed.). Affine equi-area characterization of golden diagonal ratios in irregular convex pentagons. Cataloged in: GC-05.03

Golden Window (2010)

Jerzy Kocik — Mathematics Magazine 83(5), pp. 384–390. Six-circle Apollonian window packing forcing powers of φ, golden rectangles, and Kepler’s triangle. Cataloged in: GC-06.05

Another Simple Construction of the Golden Section (2011)

Michel Bataille — Forum Geometricorum 11, pp. 55–56. Constructs φ from an equilateral triangle and square erected on the same segment. Cataloged in: GC-02.02

Fibonacci Numbers and the Golden Section (1996–2024)

Ron Knott — University of Surrey Mathematical Archive. Companion archive cataloged in sibling GEOMETOR repository geometor/knott. URL: https://r-knott.surrey.ac.uk/Fibonacci/

Cut-the-Knot: Golden Ratio in Geometry (1996–2018)

Alexander Bogomolny — © 1996–2018. Interactive Mathematics Miscellany and Puzzles (cut-the-knot.org), © 1996–2018 Alexander Bogomolny. URL: https://www.cut-the-knot.org/do_you_know/GoldenRatio.shtml Cataloged in: GC-01.01, GC-01.02, GC-01.03, GC-01.07, GC-02.01, GC-02.04, GC-02.05, GC-02.06, GC-02.07, GC-03.01, GC-03.02, GC-03.03, GC-03.04, GC-03.05, GC-03.06, GC-03.07, GC-03.08, GC-04.02, GC-04.03, GC-04.04, GC-05.02, GC-05.03, GC-05.04, GC-05.05, GC-05.06, GC-06.01, GC-06.02, GC-06.03, GC-06.04, GC-06.06, GC-06.07, GC-07.01, GC-07.02, GC-07.03, GC-07.04, GC-07.05, GC-07.06

Cut-the-Knot: Golden Ratio by Compass Only (1996–2018)

Alexander Bogomolny — © 1996–2018. Interactive Mathematics Miscellany and Puzzles (cut-the-knot.org), © 1996–2018 Alexander Bogomolny. URL: https://www.cut-the-knot.org/do_you_know/GoldenRatioByCompass.shtml Cataloged in: GC-01.05

Cut-the-Knot: Golden Ratio with a Rusty Compass (1996–2018)

Alexander Bogomolny — © 1996–2018. Interactive Mathematics Miscellany and Puzzles (cut-the-knot.org), © 1996–2018 Alexander Bogomolny. URL: https://www.cut-the-knot.org/do_you_know/GoldenRatioByRustyCompass.shtml Cataloged in: GC-01.06

Cut-the-Knot: Kurt Hofstetter’s 5-Step Construction of the Golden Section (1996–2018)

Alexander Bogomolny — © 1996–2018. Interactive Mathematics Miscellany and Puzzles (cut-the-knot.org), © 1996–2018 Alexander Bogomolny. URL: https://www.cut-the-knot.org/do_you_know/Hofstetter3.shtml Cataloged in: GC-01.04

Cut-the-Knot: Bùi Quang Tuân’s 5-Step Construction of the Golden Ratio (1996–2018)

Alexander Bogomolny — © 1996–2018. Interactive Mathematics Miscellany and Puzzles (cut-the-knot.org), © 1996–2018 Alexander Bogomolny. URL: https://www.cut-the-knot.org/do_you_know/BuiGoldenRatio5Step.shtml Cataloged in: GC-01.07

Cut-the-Knot: From Equilateral Triangle and Square to Golden Ratio (1996–2018)

Alexander Bogomolny — © 1996–2018. Interactive Mathematics Miscellany and Puzzles (cut-the-knot.org), © 1996–2018 Alexander Bogomolny. URL: https://www.cut-the-knot.org/do_you_know/MBatailleGoldenRatio.shtml Cataloged in: GC-02.02

Cut-the-Knot: Golden Section in Two Equilateral Triangles (1996–2018)

Alexander Bogomolny — © 1996–2018. Interactive Mathematics Miscellany and Puzzles (cut-the-knot.org), © 1996–2018 Alexander Bogomolny. URL: https://www.cut-the-knot.org/do_you_know/GoldenQTB.shtml Cataloged in: GC-02.03

Cut-the-Knot: Golden Section in Two Equilateral Triangles, II (1996–2018)

Alexander Bogomolny — © 1996–2018. Interactive Mathematics Miscellany and Puzzles (cut-the-knot.org), © 1996–2018 Alexander Bogomolny. URL: https://www.cut-the-knot.org/do_you_know/GoldenQTBAnother.shtml Cataloged in: GC-02.03

Cut-the-Knot: Golden Ratio in Reflected Equilateral Triangles (1996–2018)

Alexander Bogomolny — © 1996–2018. Interactive Mathematics Miscellany and Puzzles (cut-the-knot.org), © 1996–2018 Alexander Bogomolny. URL: https://www.cut-the-knot.org/do_you_know/Buratino2.shtml Cataloged in: GC-02.05

Cut-the-Knot: Golden Ratio in Regular Hexagon and Square (1996–2018)

Alexander Bogomolny — © 1996–2018. Interactive Mathematics Miscellany and Puzzles (cut-the-knot.org), © 1996–2018 Alexander Bogomolny. URL: https://www.cut-the-knot.org/do_you_know/Buratino3.shtml Cataloged in: GC-02.06

Cut-the-Knot: Golden Ratio in Equilateral Triangle and Incircle (1996–2018)

Alexander Bogomolny — © 1996–2018. Interactive Mathematics Miscellany and Puzzles (cut-the-knot.org), © 1996–2018 Alexander Bogomolny. URL: https://www.cut-the-knot.org/do_you_know/TranQuangHung2015.shtml Cataloged in: GC-02.04

Cut-the-Knot: Golden Ratio Astride Equilateral Triangle (1996–2018)

Alexander Bogomolny — © 1996–2018. Interactive Mathematics Miscellany and Puzzles (cut-the-knot.org), © 1996–2018 Alexander Bogomolny. URL: https://www.cut-the-knot.org/do_you_know/GoldenRatioAstrideEquilateralTriangle.shtml Cataloged in: GC-02.07

Cut-the-Knot: Golden Ratio in Square and Circle (1996–2018)

Alexander Bogomolny — © 1996–2018. Interactive Mathematics Miscellany and Puzzles (cut-the-knot.org), © 1996–2018 Alexander Bogomolny. URL: https://www.cut-the-knot.org/do_you_know/GoldenRatioInRectangles.shtml Cataloged in: GC-03.01

Cut-the-Knot: Golden Ratio in Square (1996–2018)

Alexander Bogomolny — © 1996–2018. Interactive Mathematics Miscellany and Puzzles (cut-the-knot.org), © 1996–2018 Alexander Bogomolny. URL: https://www.cut-the-knot.org/do_you_know/Buratino1.shtml Cataloged in: GC-03.02

Cut-the-Knot: Golden Ratio in 2×2 Square (1996–2018)

Alexander Bogomolny — © 1996–2018. Interactive Mathematics Miscellany and Puzzles (cut-the-knot.org), © 1996–2018 Alexander Bogomolny. URL: https://www.cut-the-knot.org/do_you_know/2x2GoldenRatio.shtml Cataloged in: GC-03.03

Cut-the-Knot: Golden Ratio in 3×3 Square (1996–2018)

Alexander Bogomolny — © 1996–2018. Interactive Mathematics Miscellany and Puzzles (cut-the-knot.org), © 1996–2018 Alexander Bogomolny. URL: https://www.cut-the-knot.org/do_you_know/3x3GoldenRatio.shtml Cataloged in: GC-03.04

Cut-the-Knot: Another Golden Ratio in 3×3 Square (1996–2018)

Alexander Bogomolny — © 1996–2018. Interactive Mathematics Miscellany and Puzzles (cut-the-knot.org), © 1996–2018 Alexander Bogomolny. URL: https://www.cut-the-knot.org/do_you_know/3x3GoldenRatio2.shtml Cataloged in: GC-03.05

Cut-the-Knot: Golden Ratio via Two Incircles in a Square (1996–2018)

Alexander Bogomolny — © 1996–2018. Interactive Mathematics Miscellany and Puzzles (cut-the-knot.org), © 1996–2018 Alexander Bogomolny. URL: https://www.cut-the-knot.org/do_you_know/GoldenRatioInSquare.shtml Cataloged in: GC-03.06

Cut-the-Knot: Golden Cross and Golden Square (1996–2018)

Alexander Bogomolny — © 1996–2018. Interactive Mathematics Miscellany and Puzzles (cut-the-knot.org), © 1996–2018 Alexander Bogomolny. URL: https://www.cut-the-knot.org/do_you_know/GoldenCross.shtml Cataloged in: GC-03.07

Cut-the-Knot: Golden Ratio by Rotating a Square (1996–2018)

Alexander Bogomolny — © 1996–2018. Interactive Mathematics Miscellany and Puzzles (cut-the-knot.org), © 1996–2018 Alexander Bogomolny. URL: https://www.cut-the-knot.org/do_you_know/JohnArioni.shtml Cataloged in: GC-03.08

Cut-the-Knot: Golden Ratio and the Egyptian 3-4-5 Triangle (1996–2018)

Alexander Bogomolny — © 1996–2018. Interactive Mathematics Miscellany and Puzzles (cut-the-knot.org), © 1996–2018 Alexander Bogomolny. URL: https://www.cut-the-knot.org/do_you_know/GoldenRatio345.shtml Cataloged in: GC-04.01

Cut-the-Knot: Another Golden Ratio in the 3-4-5 Triangle (1996–2018)

Alexander Bogomolny — © 1996–2018. Interactive Mathematics Miscellany and Puzzles (cut-the-knot.org), © 1996–2018 Alexander Bogomolny. URL: https://www.cut-the-knot.org/do_you_know/3-4-5-GoldenRatio.shtml Cataloged in: GC-04.01

Cut-the-Knot: Golden Ratio and Midpoints (Jo Niemeyer) (1996–2018)

Alexander Bogomolny — © 1996–2018. Interactive Mathematics Miscellany and Puzzles (cut-the-knot.org), © 1996–2018 Alexander Bogomolny. URL: https://www.cut-the-knot.org/do_you_know/GoldenJo.shtml Cataloged in: GC-04.03

Cut-the-Knot: Golden Ratio in Right Isosceles Triangle (1996–2018)

Alexander Bogomolny — © 1996–2018. Interactive Mathematics Miscellany and Puzzles (cut-the-knot.org), © 1996–2018 Alexander Bogomolny. URL: https://www.cut-the-knot.org/do_you_know/BuiGoldenRatio3.shtml Cataloged in: GC-04.04

Cut-the-Knot: Regular Pentagon and Golden Ratio (1996–2018)

Alexander Bogomolny — © 1996–2018. Interactive Mathematics Miscellany and Puzzles (cut-the-knot.org), © 1996–2018 Alexander Bogomolny. URL: https://www.cut-the-knot.org/pythagoras/pentagon.shtml Cataloged in: GC-05.01

Cut-the-Knot: Golden Ratio in Regular Pentagon (1996–2018)

Alexander Bogomolny — © 1996–2018. Interactive Mathematics Miscellany and Puzzles (cut-the-knot.org), © 1996–2018 Alexander Bogomolny. URL: https://www.cut-the-knot.org/do_you_know/GoldenRatioInRegularPentagon.shtml Cataloged in: GC-05.02

Cut-the-Knot: Another Golden Ratio in Regular Pentagon (1996–2018)

Alexander Bogomolny — © 1996–2018. Interactive Mathematics Miscellany and Puzzles (cut-the-knot.org), © 1996–2018 Alexander Bogomolny. URL: https://www.cut-the-knot.org/do_you_know/AnotherGoldenRatioInRegularPentagon.shtml Cataloged in: GC-05.02

Cut-the-Knot: Golden Ratio in an Irregular Pentagon (1996–2018)

Alexander Bogomolny — © 1996–2018. Interactive Mathematics Miscellany and Puzzles (cut-the-knot.org), © 1996–2018 Alexander Bogomolny. URL: https://www.cut-the-knot.org/do_you_know/NoRegularPentagon.shtml Cataloged in: GC-05.03

Cut-the-Knot: Golden Ratio in Pentagon and Hexagon (1996–2018)

Alexander Bogomolny — © 1996–2018. Interactive Mathematics Miscellany and Puzzles (cut-the-knot.org), © 1996–2018 Alexander Bogomolny. URL: https://www.cut-the-knot.org/do_you_know/5-6-GoldenRatioIn.shtml Cataloged in: GC-05.04

Cut-the-Knot: Star, Six Pentagons and Golden Ratio (1996–2018)

Alexander Bogomolny — © 1996–2018. Interactive Mathematics Miscellany and Puzzles (cut-the-knot.org), © 1996–2018 Alexander Bogomolny. URL: https://www.cut-the-knot.org/do_you_know/StarSixPentagonsGoldenRatio.shtml Cataloged in: GC-05.05

Cut-the-Knot: Golden Ratio in Wu Xing (1996–2018)

Alexander Bogomolny — © 1996–2018. Interactive Mathematics Miscellany and Puzzles (cut-the-knot.org), © 1996–2018 Alexander Bogomolny. URL: https://www.cut-the-knot.org/do_you_know/GoldenRatioInWuXing.shtml Cataloged in: GC-05.06

Cut-the-Knot: Golden Ratio in Circle — in Droves (1996–2018)

Alexander Bogomolny — © 1996–2018. Interactive Mathematics Miscellany and Puzzles (cut-the-knot.org), © 1996–2018 Alexander Bogomolny. URL: https://www.cut-the-knot.org/do_you_know/BuiGoldenRatioGeneral.shtml Cataloged in: GC-06.01

Cut-the-Knot: Golden Ratio in Circle (1996–2018)

Alexander Bogomolny — © 1996–2018. Interactive Mathematics Miscellany and Puzzles (cut-the-knot.org), © 1996–2018 Alexander Bogomolny. URL: https://www.cut-the-knot.org/do_you_know/BuiGoldenRatio.shtml Cataloged in: GC-06.01

Cut-the-Knot: Golden Ratio in Two Equal Circles (1996–2018)

Alexander Bogomolny — © 1996–2018. Interactive Mathematics Miscellany and Puzzles (cut-the-knot.org), © 1996–2018 Alexander Bogomolny. URL: https://www.cut-the-knot.org/do_you_know/ElliotMcGucken1.shtml Cataloged in: GC-06.02

Cut-the-Knot: Golden Ratio in Two Tangent Circles (1996–2018)

Alexander Bogomolny — © 1996–2018. Interactive Mathematics Miscellany and Puzzles (cut-the-knot.org), © 1996–2018 Alexander Bogomolny. URL: https://www.cut-the-knot.org/do_you_know/GoldenRatioInCircles.shtml Cataloged in: GC-06.02

Cut-the-Knot: Four Golden Circles (1996–2018)

Alexander Bogomolny — © 1996–2018. Interactive Mathematics Miscellany and Puzzles (cut-the-knot.org), © 1996–2018 Alexander Bogomolny. URL: https://www.cut-the-knot.org/do_you_know/FourGoldenCircles.shtml Cataloged in: GC-06.03

Cut-the-Knot: Golden Ratio in Three Tangent Circles (1996–2018)

Alexander Bogomolny — © 1996–2018. Interactive Mathematics Miscellany and Puzzles (cut-the-knot.org), © 1996–2018 Alexander Bogomolny. URL: https://www.cut-the-knot.org/do_you_know/3TangentCirclesGoldenRatio.shtml Cataloged in: GC-06.04

Cut-the-Knot: Golden Window (1996–2018)

Alexander Bogomolny — © 1996–2018. Interactive Mathematics Miscellany and Puzzles (cut-the-knot.org), © 1996–2018 Alexander Bogomolny. URL: https://www.cut-the-knot.org/do_you_know/GoldenWindow.shtml Cataloged in: GC-06.05

Cut-the-Knot: Golden Ratio in Yin-Yang (1996–2018)

Alexander Bogomolny — © 1996–2018. Interactive Mathematics Miscellany and Puzzles (cut-the-knot.org), © 1996–2018 Alexander Bogomolny. URL: https://www.cut-the-knot.org/do_you_know/GoldenRatioInYinYang.shtml Cataloged in: GC-06.06

Cut-the-Knot: Golden Ratio in Rhombus (1996–2018)

Alexander Bogomolny — © 1996–2018. Interactive Mathematics Miscellany and Puzzles (cut-the-knot.org), © 1996–2018 Alexander Bogomolny. URL: https://www.cut-the-knot.org/do_you_know/Buratino8.shtml Cataloged in: GC-07.01

Cut-the-Knot: Golden Ratio via Golden Rhombus (1996–2018)

Alexander Bogomolny — © 1996–2018. Interactive Mathematics Miscellany and Puzzles (cut-the-knot.org), © 1996–2018 Alexander Bogomolny. URL: https://www.cut-the-knot.org/do_you_know/GoldenRatioMolokach.shtml Cataloged in: GC-07.02

Cut-the-Knot: Golden Ratio in Isosceles Trapezoid (1996–2018)

Alexander Bogomolny — © 1996–2018. Interactive Mathematics Miscellany and Puzzles (cut-the-knot.org), © 1996–2018 Alexander Bogomolny. URL: https://www.cut-the-knot.org/do_you_know/TQHGoldenRatio.shtml Cataloged in: GC-07.04

Cut-the-Knot: Golden Ratio in Mixtilinear Circles (1996–2018)

Alexander Bogomolny — © 1996–2018. Interactive Mathematics Miscellany and Puzzles (cut-the-knot.org), © 1996–2018 Alexander Bogomolny. URL: https://www.cut-the-knot.org/do_you_know/GoldenMixtilinear.shtml Cataloged in: GC-07.05