PSU Mark
Eberly College of Science Mathematics Department

Meeting Details

For more information about this meeting, contact Sergei Tabachnikov, Flossie Dunlop.

Title:A short look at the long history of the lemniscate of Bernoulli
Seminar:MASS Colloquium
Speaker:Joel Langer, Case Western Reserve University
Abstract:
Could a beautiful plane curve launch a thousand propositions? To make the case for the lemniscate, this talk will romp through hundreds (ok thousands!) of years of history: From the spiric sections of Perseus, to the planetary orbits of Cassini, to mechanical linkages of Watt and others; not to mention the ``Enigma of Viviani's Temple" and the early investigations on the theory of elasticity by Bernoulli himself. But above all, the lemniscate is tied to the birth of elliptic functions and their connections to the theory of equations and numbers through the discoveries of Count Fagnano, Euler, Gauss and Abel. All of this predates the fuller view of the lemniscate as a Riemann surface of genus zero--i.e., a sphere--sitting in the complex projective plane. In this setting, the ever-elegant lemniscate turns out to have octahedral symmetry. In fact, with the help of pictures, this talk will attempt to provide some impression of the lemniscate as a disdyakis dodecahedron.

Room Reservation Information

Room Number:MB113
Date:11 / 15 / 2012
Time:02:30pm - 03:30pm