ICM 1998, Berlin, Aug. 18–27

Abstracts of Short Communications and Posters

Section:

19. History of Mathematics

1991 MS Classification: 01, 14 Lipkovski, Aleksandar, University of Belgrade, Yugoslavia Rational curves with elliptic arcs - Serret’s solution of Legendre’s problem In his memoir ”On geometric representation of elliptic and ultra-elliptic functions” in Liouville’s Journal in 1845, J. -A. Serret solved Legendre’s problem to find curves whose arc length is expressed by elliptic integrals of the first kind, such as the lemniscate. He found all such rational curves. Serret’s curves were rediscovered in 1995 and their properties studied by Solovyev and the author. With the help of G. Betsch (Tübingen), author analysed the original Serret’s work. Prasolov V., Solovyev Yu. : Elliptic Functions and Elliptic Integrals, Transl. AMS, vol. 170, 1997 Lipkovski A. : Serret’s curves. Topology and applications, Moscow, Phasis, 1996, p. 191-192