Why 2-Dimensional Polygons?

About the lecture

In this mini-lecture we think about why 2-dimensional polygons are worth studying and give the definition of a polygon. In particular, we consider: (i) what motivates our study of 2D polygons; (ii) the difference between something that is continuous and something that is discrete; (iii) how anything continuous can be approximated with near-perfect accuracy by something discrete; (iv) how computer think digitally, in discrete packets; (v) the need for calculus to understand the continuous; (vi) the definition of a polygon: a closed region of the plane, surrounded by a finite collection of line segments that do no intersect; (v) the importance of objects represented by finite data, which permits computers to store and optimise this data; (vi) examples of polygons; (vii) and the definitions of vertices (singular: vertex) and edges (singular: edge).

About the lecturer

Satyan Devadoss is the Fletcher Jones Chair of Applied Mathematics and Professor of Computer Science at the University of San Diego. His research interests are in topology and geometry, with inspiration coming from theoretical physics, phylogenetics, and scientific visualization. He was a professor of mathematics for 15 years at Williams College prior to arriving at the University of San Diego, and has held visiting positions at Ohio State, UC Berkeley, Mathematical Sciences Research Institute, Harvey Mudd, and Stanford.

Professor Devadoss is an inaugural fellow of the American Mathematical Society. He has been awarded three prestigious teaching wards by the Mathematical Association of America: (i) the Henry L Alder National Teaching Award in 2007, to honour young faculty whose teaching has influence beyond their own classrooms; (ii) the Northeastern Sectional Award for Distinguished Teaching in 2014, for teaching that has been extra ordinarily successful; (iii) and the Deborah and Franklin Tepper Haimo National Teaching Award in 2016, to honour teachers who have been widely recognised as extraordinarily successful.

Professor Devadoss is a coauthor of the textbook Discrete and Computational Geometry (2011), and a coauthor of the tradebook Mage Merlin's Unsolved Mathematical Mysteries (2020). In 2017, he led a team at the University of San Diego to receive a $1M grant from the Fletcher Jones Foundation for the renovation of the mathematics department. The centrepiece of this renovation is his Math Studio that serves as a laboratory promoting the physical experience surrounding mathematics research.