Systematic Bibliography

Primary Editions, Classical Sources & Heuristic Descendants

David Hilbert — Grundlagen der Geometrie

    1. Teubner, Leipzig, 1899.

Axiomatic foundation of geometry and Chapter VII gauge-and-straightedge constructibility criteria (GEOMETOR hilbert).

Euclid (trans. Sir Thomas L. Heath) — The Thirteen Books of Euclid’s Elements

Cambridge University Press, c. 300 BCE / 1908.

Canonical axiomatic foundation of compass-and-straightedge geometry (GEOMETOR euclid & elements).

Felix Klein — Vorträge über ausgewählte Fragen der Elementargeometrie

    1. Teubner, Leipzig (English trans. Famous Problems of Elementary Geometry, 1897), 1895.

Classic synthesis of straightedge-and-compass, compass-only, and transcendental constructibility.

Ferdinand von Lindemann — Über die Zahl pi

Mathematische Annalen 20, 213–225, 1882.

Proved the transcendence of pi three years after Petersen’s remark on p. 101 of the 1879 English edition.

George Pólya — Mathematical Discovery: On Understanding, Learning, and Teaching Problem Solving (Vol. I)

John Wiley & Sons, New York, 1962.

Chapters 1 and 2 build heuristic pedagogy directly around Petersen’s Pattern of Two Loci and Pattern of Similar Figures.

Heinrich Schröter — Die Steinersche Auflösung der Malfattischen Aufgabe

Journal für die reine und angewandte Mathematik (Crelle) 77, 230–244, 1874.

First proof of Steiner’s Malfatti construction via circle inversions, simplified by Petersen in 1879 (pp. 96–97).

Jakob Steiner — Einige geometrische Betrachtungen

Journal für die reine und angewandte Mathematik (Crelle) 1, 161–184, 1826.

Introduces power of a point, radical axes, centres of similitude, and Steiner’s construction of Malfatti’s circles.

Julius Petersen — Methoder og Theorier til Løsning af geometriske Konstruktionsopgaver, anvendte paa ca. 400 Opgaver

Karl Schønbergs Forlag, Kjøbenhavn, 1866.

First Danish edition of Petersen’s treatise on geometric construction heuristics.

Julius Petersen — Om Ligninger, der løses ved Kvadratrod

Kjøbenhavn (Doctoral Dissertation, University of Copenhagen), 1871.

Petersen’s doctoral thesis on algebraic equations solvable by square roots, cited in the Appendix (p. 98).

Julius Petersen — Theorie der algebraischen Gleichungen

Andr. Fred. Høst & Sohn, Kopenhagen, 1878.

German edition of Petersen’s treatise on Galois theory and quadratic constructibility, cited on p. 98.

Julius Petersen — Die Theorie der regulären graphs

Acta Mathematica 15, 193–220, 1891.

Foundational paper of modern graph theory.

Julius Petersen (trans. Sophus Haagensen) — Methods and Theories for the Solution of Problems of Geometrical Constructions, Applied to 410 Problems

Andr. Fred. Høst & Son, Copenhagen / Sampson Low, Marston, Searle & Rivington, London, 1879.

Authorized English edition from the expanded 2nd Danish edition (102 pages, 410 problems).

Nathan Altshiller-Court — College Geometry: An Introduction to the Modern Geometry of the Triangle and the Circle (2nd ed.)

Barnes & Noble, New York, 1952.

Standard modern synthetic geometry treatise directly extending Petersen’s Chapter I–III methods (GEOMETOR altshiller-court).

Pappus of Alexandria — Synagoge (Mathematical Collection), Book VII — Domain of Analysis

ed. F. Hultsch (1877) / A. Jones (1986), c. 340 CE.

Classical formulation of geometric analysis and synthesis, harmonic ranges, and Apollonius’s lost Tangencies and Plane Loci (GEOMETOR pappus).

Pierre Laurent Wantzel — Recherches sur les moyens de reconnaître si un problème de Géométrie peut se résoudre avec la règle et le compas

Journal de Mathématiques Pures et Appliquées 2, 366–372, 1837.

First rigorous proof of the impossibility of trisecting the general angle and duplicating the cube.

Émile Lemoine — Géométrographie, ou Art des constructions géométriques

  1. Naud, Paris (Scientia, no. 18), 1902.

Operational complexity calculus for Euclidean constructions (GEOMETOR lemoine).