Event Detail

Event Type: 
Lonseth Lecture
Date/Time: 
Tuesday, May 10, 2016 -
15:30 to 17:00
Location: 
Construction and Engineering Hall, LaSells Stewart Center

Speaker Info

Institution: 
Rice University
Abstract: 

Dr. Richard Tapia, professor in the Department of Computational and Applied Mathematics at Rice University, will present his talk, "The Remarkable Journey of Isoperimetric Problem: From Euler to Steiner to Weierstrass,” an overview of the history of the impactful isoperimetric problem. He will identify three distinct classes of solution approaches that have been used throughout history: the Cartesian coordinate representation approach of Euler, the synthetic geometry approach of Steiner, and the parametric representation approach of Weierstrass. Euler incorrectly believed that he had established sufficiency, when in reality he had not even established the necessity that he has been credited with by mathematical historians. This failure led Steiner in 1838 to propose his approach which gave only necessity and not sufficiency as he believed.The Steiner path was completed by Lawlor in 1998. Euler’s and Steiner’s failures led Weierstrass in 1879 to propose his approach, which did indeed lead to sufficiency but was excessively long. The Weierstrass approach was completed in 1934 by Littlewood, Hardy, and Polya. Prof. Tapia will present a completion of Euler’s approach in a surprisingly elementary proof.