Mathematical Sciences Department Seminar - Sergio Chaves, Cornell University
11:00 am to 12:00 pm
Mathematical Sciences Department Seminar
Sergio Chaves, Cornell University
Thursday, January 23
11:00am - 12:00 pm
Stratton 201
Title: Exploring Counting Problems with Topology and Geometry
Do you enjoy soccer? A typical soccer ball is composed of hexagons and pentagons, and if we count carefully, we find that it has exactly 12 pentagons! Mathematically, it can be proven that any spherical structure must contain exactly 12 pentagons. Perhaps you also enjoy board games! A 6-sided die is commonly used in many games due to its regularity and symmetry. Interestingly, there are four other shapes with different numbers of sides that also satisfy these properties, making them useful for games like Dungeons & Dragons. We can also prove that there are exactly five such shapes. In this talk, we will explore how mathematics, particularly Euler's topological formula for polyhedra, can be used to solve counting problems and demonstrate these physical constraints. We will also discuss additional fun applications that extend beyond these concepts.