Page 614 - 8th European Congress of Mathematics ∙ 20-26 June 2021 ∙ Portorož, Slovenia ∙ Book of Abstracts
P. 614
ALGEBRAIC AND COMPLEX GEOMETRY
About new examples of Serret’s curves
Aleksandar Lipkovski, acal@matf.bg.ac.rs
University of Belgrade - Faculty of Mathematics, Serbia
Coauthor: Theodore Popelensky
Abel’s theorem claims that the lemniscate can be divided into n equal arcs by ruler and compass
iff n = 2kp1...pm, where pj are pairwise distinct Fermat primes. The proof relies on the fact that
the lemniscate can be parametrised by rational functions and the arc length is an elliptic integral
of the first kind of the parameter. In 1845, Serret proposed a method to describe all such curves.
He found a series of such curves and described its important properties. Since then, no new
examples of curves with rational parametrisation, such that arc length is an elliptic integral of
the first kind of the parameter are known. In this note we describe anew example of such curve.
612
About new examples of Serret’s curves
Aleksandar Lipkovski, acal@matf.bg.ac.rs
University of Belgrade - Faculty of Mathematics, Serbia
Coauthor: Theodore Popelensky
Abel’s theorem claims that the lemniscate can be divided into n equal arcs by ruler and compass
iff n = 2kp1...pm, where pj are pairwise distinct Fermat primes. The proof relies on the fact that
the lemniscate can be parametrised by rational functions and the arc length is an elliptic integral
of the first kind of the parameter. In 1845, Serret proposed a method to describe all such curves.
He found a series of such curves and described its important properties. Since then, no new
examples of curves with rational parametrisation, such that arc length is an elliptic integral of
the first kind of the parameter are known. In this note we describe anew example of such curve.
612
