Follow your curiosity

What discovery has been shared with you?

FACTREE gives you something interesting to discover every day — and something worth talking about together.

Start with one fact. Explore it, go deeper, then follow whichever branch catches your imagination.

Choose subjects for a surprise

Exploring any topic

Begin your discovery

Your next discovery is one click away.

Choose one or more subjects above, or leave Any Topic selected and let curiosity decide.

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?