Mario Pieri's axiomatization of geometry

Document Type : Review Paper

Author

‎School of Mathematics‎, ‎Statistics and Computer Science‎, ‎College of Science‎, ‎University of Tehran‎, ‎Tehran. Iran

Abstract

In this paper, we discuss the method of the Italian mathematician, Mario Pieri, for axiomatization of geometry, which is based only on two undefined terms, point and motion. We examine the postulates proposed by him, definitions of various geometrical concepts and some important theorems arising from those postulates.

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References

[1] G. D. Birkhoff, A set of postulates for plane geometry, based on scale and protractor, Ann. Math., 33 (1932) 329–345.
[2] J. M. Lee, Axiomatic Geometry, American Mathematical Society, Providence, 2013.
[3] E. A. Marchisotto and J.T. Smith, The Legacy of Mario Pieri in Geometry and Arithmetic, Birkhäuser, Boston, 2007.
[4] E. A. Marchisotto, F. R. Consuegra and J. T. Smith, The Legacy of Mario Pieri in Foundations and Philosophy of Mathematics, Birkhäuser, New York, 2021.
[5] E. E. Moise, Elementary Geometry from an Advanced Standpoint, Addison-Wesley, Reading, Mass., 1990.
[6] M. Pasch, Vorlesungen über Neuere Geometrie , Teubner, Leipzig, 1882.
[7] G. Peano, I Principii di Geometria Logicamente Esposti , Fratelli Bocca Editore, Torino, 1889.
[8] G. Peano, Sui fondamenti della geometria, Rivista di matematica, 4 (1894) 51–90.
[9] M. Pieri, Della geometria elementare come sistema ipotetico deduttivo: Monografia del punto e delmoto, Memorie della Reale Accademia delle Scienze di Torino (series 2) , 49 (1900) 173–222.

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History

  • Receive Date: 20 July 1402
  • Revise Date: 08 November 1402
  • Accept Date: 14 November 1402
  • Publish Date: 07 March 1403

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