Bibliography & Cited Sources

Primary Klein Editions, Historical Treatises, and GEOMETOR Sister Corpora

This bibliography catalogues 36 primary editions, classical memoirs, and sister-corpus treatises referenced across the dual 4-track Book Codices. Every inline :cite: role resolves directly to its corresponding entry below.

Felix Klein (ausgearbeitet von F. Tägert) — Vorträge über ausgewählte Fragen der Elementargeometrie (1895)

  • Citation Key: klein:1895

  • Publication / Locus: Leipzig: B. G. Teubner (v + 66 S., 10 Fig., 2 lithogr. Tafeln)

  • Context: First German edition; Festschrift prepared for the Elberfeld Oberlehrer gathering from Klein’s Göttingen Easter 1895 holiday course. Public domain.

Felix Klein (trans. W. W. Beman & D. E. Smith) — Famous Problems of Elementary Geometry: The Duplication of the Cube, The Trisection of an Angle, The Quadrature of the Circle (1897)

  • Citation Key: klein:1897

  • Publication / Locus: Boston and London: Ginn & Company (ix + 80 pp.)

  • Context: Authorized first English translation from Teubner’s 1895 German text (unencumbered by Archibald’s 1930 annotations). Public domain.

Felix Klein — Vergleichende Betrachtungen über neuere geometrische Forschungen (1872)

  • Citation Key: klein:1872

  • Publication / Locus: Erlangen: Verlag von Andreas Deichert (48 S.); reprinted in Mathematische Annalen 43 (1893), pp. 63–100

  • Context: Klein’s inaugural Erlangen Program monograph classifying geometries as invariant theories of transformation groups. Public domain (Project Gutenberg #38033).

Felix Klein (trans. M. W. Haskell) — A Comparative Review of Recent Researches in Geometry (1893)

  • Citation Key: klein:1893:erlangen

  • Publication / Locus: Bulletin of the New York Mathematical Society 2 (10), July 1893, pp. 215–249

  • Context: Authorized English translation of the Erlangen Program with Klein’s 1893 Prefatory Note. Public domain (arXiv:0807.3161).

Felix Klein — Über die sogenannte Nicht-Euklidische Geometrie (1871–1873)

  • Citation Key: klein:1871:noneuclid

  • Publication / Locus: Mathematische Annalen 4 (1871), pp. 573–625; 6 (1873), pp. 112–145

  • Context: Established the projective Cayley–Klein models of hyperbolic, elliptic, and parabolic metric geometries; summarized in Erlangen Note V.

Felix Klein — Über Liniengeometrie und metrische Geometrie (1872)

  • Citation Key: klein:1872:linien

  • Publication / Locus: Mathematische Annalen 5, pp. 257–277

  • Context: Connected Plücker’s 4D line quadric in P^5 with Lie’s sphere geometry and non-Euclidean metric transformations (Erlangen §§ 5 & 7).

Carl Friedrich Gauss — Disquisitiones Arithmeticae, Sectio Septima: De aequationibus circuli sectiones definientibus (1801)

  • Citation Key: gauss:1801

  • Publication / Locus: Leipzig: Gerhard Fleischer, §§ 335–366

  • Context: Proved constructibility of regular polygons of Fermat-prime order p = 2^(2^mu) + 1 and gave the explicit period reduction for p = 17.

Pierre Laurent Wantzel — Recherches sur les moyens de reconnaître si un problème de Géométrie peut se résoudre avec la règle et le compas (1837)

  • Citation Key: wantzel:1837

  • Publication / Locus: Journal de Mathématiques Pures et Appliquées (Liouville) 2, pp. 366–372

  • Context: First complete algebraic proof of the degree-2^h necessity criterion, settling Delian duplication, angle trisection, and non-Fermat polygons.

Gotthold Eisenstein — Über die Irreductibilität und einige andere Eigenschaften der Gleichung, von welcher die Theilung der ganzen Lemniscate abhängt (1850)

  • Citation Key: eisenstein:1850

  • Publication / Locus: Journal für die reine und angewandte Mathematik (Crelle) 39, pp. 160–179 (p. 167)

  • Context: Source of Eisenstein’s p-divisibility irreducibility criterion applied by Klein in Famous Problems Part I, Ch. III, §§ 7–8.

Friedrich Julius Richelot — De resolutione algebraica aequationis X^257 = 1, sive de divisione circuli per bisectionem anguli septies repetitam in partes 257 inter se aequales commentatio coronata (1832)

  • Citation Key: richelot:1832

  • Publication / Locus: Journal für die reine und angewandte Mathematik (Crelle) 9, pp. 1–26, 146–161, 209–230, 337–357

  • Context: Explicit cyclotomic resolution of the regular 257-gon (Famous Problems Part I, Ch. III, § 1).

Johann Gustav Hermes — Über die Teilung des Kreises in 65537 gleiche Teile (1894)

  • Citation Key: hermes:1894

  • Publication / Locus: Nachrichten von der Kgl. Gesellschaft der Wissenschaften zu Göttingen, Math.-phys. Klasse 1894, Nr. 3, pp. 170–186

  • Context: Summary of Hermes’s ten-year period computation for the regular 65537-gon stored in Göttingen.

Paul Bachmann — Die Lehre von der Kreistheilung und ihre Beziehungen zur Zahlentheorie (1872)

  • Citation Key: bachmann:1872

  • Publication / Locus: Leipzig: B. G. Teubner

  • Context: Standard cyclotomy treatise recommended by Klein in Famous Problems Part I, Ch. III–IV.

Julius Petersen — Methods and Theories for the Solution of Problems of Geometrical Constructions (and Theorie der algebraischen Gleichungen, 1878) (1879)

  • Citation Key: petersen:1879

  • Publication / Locus: Copenhagen: Andr. Fred. Høst & Søn / London: Sampson Low

  • Context: Praised by Klein in Famous Problems Introduction (p. 2) for elementary algebraic proofs of geometric constructibility (geometor/petersen).

Émile Lemoine — Géométrographie, ou Art des constructions géométriques (1902)

  • Citation Key: lemoine:1902

  • Publication / Locus: Paris: C. Naud (Collection Scientia No. 18)

  • Context: Quantitative complexity calculus of compass-and-straightedge constructions complementing Klein’s restricted-instrument hierarchy (geometor/lemoine).

Lorenzo Mascheroni — La Geometria del Compasso (1797)

  • Citation Key: mascheroni:1797

  • Publication / Locus: Pavia: Eredi di Pietro Galeazzi

  • Context: Proved compass-only constructibility of all Euclidean points (Famous Problems Part I, Ch. IV, § 7).

Jean-Victor Poncelet — Traité des propriétés projectives des figures (1822)

  • Citation Key: poncelet:1822

  • Publication / Locus: Paris: Bachelier

  • Context: Foundational treatise on central projection, ideal elements, and single-circle straightedge constructions.

Jakob Steiner — Die geometrischen Konstruktionen, ausgeführt mittelst der geraden Linie und eines festen Kreises (1833)

  • Citation Key: steiner:1833

  • Publication / Locus: Berlin: Ferdinand Dümmler

  • Context: Proved sufficiency of straightedge + one fixed circle with known center for all quadratic constructions.

Karl Georg Christian von Staudt — Construction des regulären Siebzehnecks (1842)

  • Citation Key: staudt:1842

  • Publication / Locus: Journal für die reine und angewandte Mathematik (Crelle) 24, p. 252 (also Geometrie der Lage, 1847)

  • Context: Original single-circle straightedge construction of the regular 17-gon adapted by Schröter and Klein.

Heinrich Schröter — Zur v. Staudtschen Construction des regulären Siebzehnecks (1872)

  • Citation Key: schroeter:1872

  • Publication / Locus: Journal für die reine und angewandte Mathematik (Crelle) 75, pp. 13–24

  • Context: Direct geometric model for Klein’s fixed-circle quadratic period solver in Famous Problems Part I, Ch. IV, §§ 8–9.

T. Sundara Row — Geometrical Exercises in Paper Folding (1893)

  • Citation Key: sundara-row:1893

  • Publication / Locus: Madras: Addison & Co.

  • Context: Cited by Klein in Famous Problems Part I, Ch. V, § 1 on origami constructions.

Georg Cantor — Über eine Eigenschaft des Inbegriffes aller reellen algebraischen Zahlen (and Über eine elementare Frage der Mannigfaltigkeitslehre, 1891) (1874 / 1891)

  • Citation Key: cantor:1874

  • Publication / Locus: Crelle’s Journal 77, pp. 258–262; Jahresbericht der DMV 1, pp. 75–78

  • Context: Countability of algebraic numbers by height N and diagonal proof of uncountability of the continuum (Famous Problems Part II, Ch. I).

Ferdinand Rudio — Archimedes, Huygens, Lambert, Legendre. Vier Abhandlungen über die Kreismessung (1892)

  • Citation Key: rudio:1892

  • Publication / Locus: Leipzig: B. G. Teubner

  • Context: Historical source anthology underlying Famous Problems Part II, Ch. II.

Charles Hermite — Sur la fonction exponentielle (1873)

  • Citation Key: hermite:1873

  • Publication / Locus: Comptes Rendus de l’Académie des Sciences 77, pp. 18–24, 74–79, 226–233, 285–293

  • Context: First proof of the transcendence of Euler’s constant e.

Ferdinand Lindemann — Über die Zahl π (1882)

  • Citation Key: lindemann:1882

  • Publication / Locus: Mathematische Annalen 20, pp. 213–225

  • Context: Proved the transcendence of pi and impossibility of squaring the circle via 1 + e^(i*pi) = 0.

Paul Gordan — Transcendenz von e und π (1893)

  • Citation Key: gordan:1893

  • Publication / Locus: Mathematische Annalen 43, pp. 222–224 ( alongside Hilbert pp. 216–219 & Hurwitz pp. 220–221)

  • Context: Purely algebraic operator proof (h^r = r!) of Hermite’s and Lindemann’s theorems presented in Famous Problems Part II, Chs. III–IV.

Bruno Abdank-Abakanowicz (trans. Emil Bitterli) — Die Integraphen: Die Integralkurve und ihre Anwendungen (1889)

  • Citation Key: abakanowicz:1889

  • Publication / Locus: Leipzig: B. G. Teubner (French original: Paris, Gauthier-Villars, 1886)

  • Context: Mechanical continuous-motion quadrature of the circle analyzed in Famous Problems Part II, Ch. V / Anhang.

Arthur Cayley — A Sixth Memoir upon Quantics (1859)

  • Citation Key: cayley:1859

  • Publication / Locus: Philosophical Transactions of the Royal Society of London 149, pp. 61–90

  • Context: Subsumed metrical geometry under projective invariants relative to the Absolute quadric (Erlangen §§ 1–2, § 10, Note V).

Bernhard Riemann — Über die Hypothesen, welche der Geometrie zu Grunde liegen (1854 (pub. 1867))

  • Citation Key: riemann:1854

  • Publication / Locus: Abhandlungen der Kgl. Gesellschaft der Wissenschaften zu Göttingen 13

  • Context: Introduced n-dimensional manifolds and constant-curvature metrics contrasted and unified with projective group theory in Erlangen § 10 & Notes IV–VI.

Sophus Lie — Über Complexe, insbesondere Linien- und Kugel-Complexe, mit Anwendung auf die Theorie partieller Differential-Gleichungen (and Theorie der Transformationsgruppen, 1888–1893) (1872)

  • Citation Key: lie:1872

  • Publication / Locus: Mathematische Annalen 5, pp. 145–256

  • Context: Lie’s contact transformations and line-to-sphere correspondence featured in §§ 7 & 9 of the Erlangen Program.

Euclid (trans. Sir Thomas L. Heath) — The Thirteen Books of Euclid’s Elements (c. 300 BC / 1908)

  • Citation Key: euclid:elements

  • Publication / Locus: Cambridge University Press, Books I & IV

  • Context: Classical straightedge-and-compass postulates and regular polygon constructions (geometor/euclid, geometor/elements).

Johannes Kepler — Harmonices Mundi, Liber I: De figuris regularibus harmonicis (1619)

  • Citation Key: kepler:1619

  • Publication / Locus: Linz: Johann Planck (Props. XLV–XLVII)

  • Context: Philosophico-geometric analysis of constructible (‘knowable’) vs. non-constructible (‘unknowable’) regular polygons including the heptagon (geometor/kepler).

David Hilbert — Grundlagen der Geometrie (1899 / 1902)

  • Citation Key: hilbert:1899

  • Publication / Locus: Leipzig: B. G. Teubner (Ch. VII, §§ 36–39)

  • Context: Axiomatic characterization of problems solvable with straightedge and segment-transferrer (Eichmass) over Pythagorean vs. Euclidean fields (geometor/hilbert).

Bertrand Russell — An Essay on the Foundations of Geometry (and The Principles of Mathematics, 1903) (1897 / 1903)

  • Citation Key: russell:1897

  • Publication / Locus: Cambridge University Press

  • Context: Philosophical and logicist reception of Klein’s Cayley–Klein metageometry and Erlangen hierarchy (geometor/bertrand-russell).

Petrus H. J. Hoenen, S.J. — De Noetica Geometriae: Origine Theoriae Cognitionis (1954)

  • Citation Key: hoenen:1954

  • Publication / Locus: Analecta Gregoriana Vol. LXIII, Rome: Pontificia Universitas Gregoriana

  • Context: Epistemological examination of Klein’s group-theoretic structuralism and non-Euclidean models (geometor/hoenen).

Pappus of Alexandria — Synagoge (Collection), Books III, IV & VII (c. 340 AD)

  • Citation Key: pappus:collection

  • Publication / Locus: Hultsch ed. (1876–1878)

  • Context: Ancient classification of plane, solid, and linear constructions and projective cross-ratio invariance (geometor/pappus).

Norman J. Wildberger — Divine Proportions: Rational Trigonometry to Universal Geometry (2005)

  • Citation Key: wildberger:2005

  • Publication / Locus: Sydney: Wild Egg Books

  • Context: Algebraic invariant formulation of Euclidean and Cayley–Klein geometries via quadrance and spread (geometor/wildberger).