Advertisement

Elliptic Functions

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

Abstract

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.

Keywords

Elliptic Function Circular Function Elliptic Integral Addition Theorem Torus Surface 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Copyright information

© Springer Science+Business Media New York 1989

Authors and Affiliations

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

Personalised recommendations