Elliptic Functions

  • John Stillwell
Part of the Undergraduate Texts in Mathematics book series (UTM)


The story of elliptic functions is one of the most curious in the history of mathematics, beginning with a complicated analytic idea—integrals \(\int {R\left[ {t,\sqrt {p\left( t \right)} } \right]dt}\), where R is a rational function and p is a polynomial of degree 3 or 4—and reaching a climax with a simple geometric idea—the torus surface. Perhaps the best way to understand it is to compare it with a fictitious history of circular functions which begins with the integral \(\int {dt} /\sqrt {1 - t^2 }\) and ends with the discovery of the circle. Unlikely as this fiction is, it was paralleled by the actual development of elliptic functions between the 1650s and the 1850s.


Elliptic Function Circular Function Elliptic Integral Addition Theorem Torus Surface 


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Copyright information

© Springer Science+Business Media New York 1989

Authors and Affiliations

  • John Stillwell
    • 1
  1. 1.Department of MathematicsMonash UniversityClaytonAustralia

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