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Pythagorean Theorem Before and After Pythagoras

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Following the footpaths of Lakshmikantham, et. al. [15], and succeeding by Agarwal et. al. [3], in this article a sincere effort has been made to report the origin of the Pythagorean Theorem. Out of about 500 known different proofs of this theorem, we select five which have historical importance. We also discuss several generalizations of this theorem, and list some antique enduring problems. We genuinely hope students and teachers of mathematics will appreciate this article.

Abstract

Following the footpaths of Lakshmikantham, et. al. [15], and succeeding by Agarwal et. al. [3], in this article a sincere effort has been made to report the origin of the Pythagorean Theorem. Out of about 500 known different proofs of this theorem, we select five which have historical importance. We also discuss several generalizations of this theorem, and list some antique enduring problems. We genuinely hope students and teachers of mathematics will appreciate this article.

참고문헌 (26)

  1. R.P. Agarwal, "Ordinary and Partial Differential Equa-tions with Special Functions, Fourier Series and Boundary Value Problems" (2009), Springer-Verlag
  2. R.P. Agarwal, "Birth, Growth and Computation of Pi to ten trillion digits", Advances in Difference Equations, 100, pp.59~ (2013)[DOI]
  3. R.P. Agarwal, "Creators of Mathematical and Computational Sciences" (2014), Springer-Verlag
  4. R.P. Agarwal, "An Introduction to Linear Algebra" (2017), CRC Press
  5. "Note on an n-dimensional Pythagorean theorem" (2018)[URL]
  6. E. Atzema, "Beynd’s Monge’s theorem", Mathematics Magazine, 73, pp.293~296 (2000)
  7. S. Casey, "The converse of the theorem of Pythagoras", Mathematical Gazette, 92, pp.309~313 (2008)
  8. T.L. Chow, "Mathematical Methods for Physicists: A Concise Introduction" (2000), Cambridge University Press
  9. D.R. Conant, "Generalized Pythagorean theorem", The American Mathematical Monthly, 81, pp.262~265 (1974)
  10. "On the theorem of Pythagoras" (2010)[URL]
  11. "The full Pythagorean theorem" (2010)[URL]
  12. J. Gilman, "Hyperbolic Triangles: Two-generator Discrete Subgroups of PSL(2,R)" (1995), American Mathematical Society Bookstore
  13. "De Gua and the Pythagoreans" (2017)[URL]
  14. T.L. Heath, "The Thirteen Books of Euclid’s Elements, 3 Vols" (1956), Dover
  15. V. Lakshmikantham, "The Origin and History of Mathematics" (2005), Cambridge Scientific Publishers
  16. E.S. Loomis, "The Pythagorean Proposition" (1968), National Council of Teachers of Mathematics
  17. Eli Maor, "The Pythagorean Theorem: A 4000-Year History" (2007), Princeton Uni-versity Press
  18. W. B.Macro, "Pythagoras’s theorem and its extension", Mathematical Gazette, 57, pp.339~340 (1973)
  19. D.W. Mitchell, "Feedback on 92.47", Mathematical Gazette, 93, pp.156~
  20. R.B. Nelsen, "Proofs without Words II: More Exercises in Visual Thinking" (2000), Mathematical Association of America
  21. J.F. Putz, "On generalizing the Pythagorean theorem", The College Mathematical Journal, 34, pp.291~295 (2003)
  22. M.K. Siu, "The Pythagorean theorem again? Anything new,?", CuboMatem´atica Educacional, 3, pp.1~9 (2001)
  23. M.K. Siu, "Mathematics = Proof? (translated by P.Y.H. Pang)", Mathematical Medley, 27, pp.3~14 (2000)
  24. D. Veljan, "The 2500-year-old Pythagorean theorem", Mathematics Magazine, 73, pp.259~272 (2000)
  25. "A generalized N-dimensional Pythagorean theorem" (2002)[URL]

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