2D Polygons

About this Course

About the Course

In this course, Professor Satyan Devadoss (University of San Diego) explores the importance of 2-dimensional polygons, their properties, and their uses. In the first mini-lecture, we define 2D polygons, discuss what motivates us to study them, and differentiate between something that is continuous and something that is discrete. In the second mini-lecture, we explore how a process called diagonalization allows us to break polygons down into triangles until the polygon is composed solely of triangles (triangulation), making triangles the fundamental building blocks of polygons. In the third mini-lecture, we use our understanding of polygons from the previous mini-lectures to help us think about sensors and security systems, looking in particular at the Art Gallery theorem. In the fourth mini-lecture, we discuss polygon congruency and similarity before delving deeper into a new concept called scissors congruency and the 1833 Wallace–Bolyai–Gerwien theorem. In the fifth mini-lecture, we seek to extend our understanding of 2D polygons to 3D polyhedra, where we see that many of the concepts in the world of 2D polygons fail when applied to 3D polyhedra.

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.