Vandervelde, Sam. (2022). Euler Characteristic Exploration. In T. Busk (Ed.), Math Circle Activity Database. American Institute of Mathematics.

Euler Characteristic Exploration

Math Circles:
The purpose of this activity is to introduce students to elementary concepts in graph theory in a hands-on, accessible manner. Students will create their own graphs, count certain quantities related to their graphs, make conjectures regarding these quantities, and learn how to explain why their conjecture is true. In the process they will discover the Euler characteristic, a powerful tool for understanding planar graphs.

Activity Handouts

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Activity Guide

This guide looks at the activity in detail and goes into the underlying math.