Mathematics
Eulerian Paths and Circuits: Conditions for Traversable Graphs
Quick fact
A connected graph has an Eulerian circuit exactly when every vertex has an even degree, and an Eulerian trail exactly when exactly two vertices have odd degree—this is Euler's theorem, the foundation of graph theory.
Why this is interesting
Imagine trying to trace a shape without lifting your pen, crossing each line exactly once. Some figures are impossible—how can you know just by looking at the corners?