Applied Mathematics Seminar
Speaker: Dr. Richard Tapia
Professor in Engineering and Director of the Center for Excellence & Equity in Education at Rice University
Host: Professor Steven Zucker
Title: The Final Step in the Remarkable Journey of the Isoperimetric Problem: The Completion of Euler’s Approach
Abstract:
In this presentation, we give a brief overview of the remarkable life of the impactful isoperimetric problem. We 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. We say that one of our three classes of approaches has been completed when an appropriately short sufficiency proof for the isoperimetric problem has been constructed that belongs to this class of proofs. In a legendary work from 1744, Euler presented his contribution, establishing neither necessity nor sufficiency for this problem. This failure led Steiner in 1838 to propose his approach that 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 required a somewhat elaborate theory. The Weierstrass approach was completed in 1934 by Littlewood, Hardy, and Polya. The major contribution in this presentation is our completion of Euler’s approach. Our proof uses elementary tools.
Bio:
Richard Tapia was born in Los Angeles, California to parents who immigrated from Mexico. In 2011 he was awarded the National Medal of Science, the highest honor bestowed by the United States government on scientists and engineers. This award spotlighted the distinguished contributions he has made to the mathematical frontiers of optimization theory and numerical analysis, but it also brought attention to another achievement: his long-time work in inspiring underrepresented minority and female students in science and math. He is a mathematician in Rice University’s Computational and Applied Mathematics Department and holds the rank of University Professor, the university’s highest academic title awarded to only seven individuals in the university’s history. Among his numerous other honors is the National Science Board’s Vannevar Bush Award and election to the National Academy of Engineering, the first Hispanic to receive these honors. He holds seven honorary doctorates and has given commencement addresses at six major universities. Two professional conferences have been named in his honor: the Richard Tapia Celebration of Diversity in Computing Conference and the Blackwell-Tapia Mathematics Conference. Tapia served on the National Science Board from 1996-2002. Because of his leadership, Rice University is recognized as a national leader in the preparation of women and underrepresented minority doctoral degree recipients in science, engineering, and mathematics.
Please visit the Center for Teaching and Learning website (https://ctl.yale.edu/DivEdRichardTapia) for other events planned for Dr. Tapia’s visit to Yale.