Mathematical  Culture and Thought

Mathematical Culture and Thought

Plato's Academy and Euclid's Elements

Document Type : Original

Author
Department of Mathematical Sciences‎, ‎Sharif University of Technology‎, ‎Iran
Abstract
‎The millennium of classical Greek mathematics may be divided into three periods‎: ‎The First Period encompasses the 6th and 5th centuries B.C‎. ‎and the Second Period consists mainly of the 4th century B.C‎. ‎up to early 3rd century‎. ‎The end of this period coincides with the transfer of the focus of mathematics research from Plato’s Academy to Alexandria and the appearance of Euclid’s Elements‎. ‎The mathematics of this period and its paradigmatic style of presentation in the Elements will be the subject of the present article‎. ‎The long Third Period‎, ‎which will not be discussed here‎, ‎witnessed great advances in mathematics‎, ‎but followed the general philosophical framework of the Second Period‎. ‎The present manuscript is the expanded version of the talks given by the author in Esfahan Mathematics House and Tarbiat Modarres University‎, ‎on 15 and 20 May‎, ‎2025‎, ‎respectively‎.
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[1]افلاطون، دوره آثار افلاطون، ترجمه محمدحسن لطفی و رضا کاویانی، انتشارات خوارزمی، تهران، ۱۳۶۵
[2]  اقلیدس، اصول اقلیدس (سیزده مقاله)، ترجمه محمدهادی شفیعیها، مرکز نشر دانشگاهی، تهران، ۱۳۸۸
[3]  فان آتن، مارک، فلسفه براوئر، ترجمه محمد اردشیر، هرمس، تهران، ۱۳۸۷
[4]  گرینبرگ، ماروین جی، هندسه‌های اقلیدسی و نااقلیدسی و بسط آن، ترجمه محمدهادی شفیعیها، مرکز نشر دانشگاهی، تهران، ۱۳۹۵.
   [5] Bishop, E., Bridges, D., Constructive Analysis, Springer-Verlag, Berlin, 1985.
   [6] Borsuk, K., Szmielew, W., Foundations of Geometry, North-Holland, Amsterdam 1960.
   [7] Browder, F., ed., Mathematical Developments Arising from Hilbert Problems, Part 1, American Mathematical Society Providence, 1976.
   [8] Dedekind, R., Essays on the Theory of Numbers, Dover, New York, 1963.
   [9] Descartes, R., The Geometry of, Dover, New York, 1954.
   [10] Ebbinghaus, H.-D., et al, eds., Numbers, Springer-Verlag, Berlin, 1991.
   [11] Fowler, D., The Mathematics of Plato's Academy, 2nd ed., Clarendon Press, Oxford, 1999.
   [12] Hamilton, E., Cairns, H., eds., The Collected Dialogues of Plato, PUP, Princeton, 1961.
   [13] Hartshorne, R., Geometry, Euclid and Beyond, Springer-Verlag, Berlin, 2000.
   [14] Khinchin, A., Continued Fractions, University of Chicago Press, Chicago, 1964.
   [15] Knorr, W., The Evolution of the Euclidean Elements, D. Reidel, Dordrecht, 1975.
   [16] Knorr, W., La Croix des Mathematiciens: The Euclidean theory of irrational lines, Bull. Amer. Math. Soc., 9 (1983), no.1.
   [17] Landry, E. Plato Was Not a Mathematical Platonist, CUB, Cambridge, 2023.
   [18] McKeon, R., ed., The Basic Works of Aristotle, The Modern Library, New York, 2001.
   [19] Netz, R., The Transformation of Mathematics in Early Mediterranean World: From Proofs to Equations, CUB, Cambridge, 2004.
   [20] Rashed, R., Vahabzadeh, B., Omar Khayyam, the Mathematician, Bibliotheca Persica, New York, 2000.
   [21] Wedberg, A., Plato's Philosophy of Mathematics, Almqvist and Wiksell, Stockholm, 1955.

  • Receive Date 18 October 2025
  • Accept Date 01 December 2025
  • Publish Date 23 September 2025