Walk through the problem, as on the Konigsberg bridges

Abstract

Abstract “Walk through the problem, as on the Konigsberg bridges” offers an introduction to the mathematical subfield of graph theory, including its origin in Konigsberg, Prussia—now Kaliningrad, Russia. When townspeople were unable to identify a path that started in one place, crossed all seven of their city’s bridges once, and returned to the same place, they enlisted the help of mathematician Leonard Euler. In response, Euler developed a “geometry of position”—now known as “graph theory”—which concerned not distance, measurements, or angles, but arrangement. The discussion is supplemented with numerous hand-drawn sketches and mention of real-life applications of graph theory in technology, disease modeling, neuroscience, and social media. Mathematics students and enthusiasts are encouraged to “walk through” their own problems in mathematics and life. At the chapter’s end, readers may check their understanding by working on a problem. A solution is provided.