Journal for History of Mathematics (한국수학사학회지)

The Korean Society for History of Mathematics (한국수학사학회)
권호 표지
DOI QR코드

DOI QR Code

A History of the Cycloid Curve and Proofs of Its Properties

사이클로이드 곡선의 역사와 그 특성에 대한 증명

  • Received : 2015.01.25
  • Accepted : 2015.02.22
  • Published : 2015.02.28
Download PDF
⟨ Previous Next ⟩

Abstract

The cycloid curve had been studied by many mathematicians in the period from the 16th century to the 18th century. The results of those studies played important roles in the birth and development of Analytic Geometry, Calculus, and Variational Calculus. In this period mathematicians frequently used the cycloid as an example to apply when they presented their new mathematical methods and ideas. This paper overviews the history of mathematics on the cycloid curve and presents proofs of its important properties.

Keywords

References

  1. Kevin Brown, Reflections on Relativity, lulu.com, September 22, 2014.
  2. Hans van den Ende, Huygens's Legacy, The Golden Age of the Pendulum Clock, Fromanteel Ldt., 2004.
  3. Leonhard Euler, Methodus Inveniendi Lineas Curvas Maximi Minive Proprietate Gaudentes, Bousquet, Lausanne & Geneva, 1744.
  4. M. Gardner, The Sixth Book of Mathematical Games from Scientific American, Chicago, IL: University of Chicago Press, 1984.
  5. C. I. Gerhardt, Uber die vier Briefe von Leibniz, die Samuel Konig in dem Appel au public, Leide MDCCLIII, veroffentlicht hat, Sitzungsberichte der Koniglich Preussischen Akademie der Wissenschaften, I, 1898.
  6. N. P. Johnson, The brachistochrone problem, The College Mathematics Journal 35 (2004), 192-197. https://doi.org/10.2307/4146894
  7. V. J. Katz, A History of Mathematics: An Introduction, 2nd ed., Addison Wesley, 1998.
  8. P. L. M. de Maupertuis, Accord de differentes lois de la nature qui avaient jusqu'ici paru incompatibles, Mem. As. Sc. Paris, 1744.
  9. J. P. Phillips, Brachistochrone, Tautochrone, Cycloid-Apple of Discord, Math. Teacher 60 (1967), 506-508.
  10. P. Sanders, Charles de Bovelles's Treatise on the Regular Polyhedra (Paris, 1511), Annals of Science 41 (1984), 513-566. https://doi.org/10.1080/00033798400200401
  11. David Eugene Smith, A Source Book in Mathematics, Dover books, 1984.
  12. D. J. Struik, ed., A Source Book in Mathematics, 1200-1800, Harvard Univ. Press, 1969.
  13. S. Wagon, Mathematica in Action, New York: W. H. Freeman, 1991.
  14. Evelyn Walker, A Study of Roberval's Traite des Indivisibles, Columbia University, 1932.
  15. D. Wells, The Penguin Dictionary of Curious and Interesting Geometry, London: Penguin, 1991.
  16. E. A. Whitman, Some historical notes on the cycloid, The American Mathematical Monthly 50(5) (1943), 309-315. https://doi.org/10.2307/2302830
  17. Wolfgang Yourgrau, Stanley Mandelstam, Variational Principles in Dynamics and Quantum Theory, Courier Corporation, 1979.