Triangulating an Octagon
A convex octagon is to be divided into triangles by drawing diagonals that do not cross in the interior. (Any such triangulation uses exactly 5 diagonals.) Different sets of diagonals count as different triangulations, even if one is a rotation of another. How many triangulations are there? Give an integer.
Related problems & prerequisites
Worth solving first
- Chords Without Crossing 4.0/10
- Dominoes and Big Squares 4.0/10
- The Ballot Problem 2.4/10
Source: Euler's polygon-division problem (1751), solved via Segner's recurrence. Statement written for AxiomIQ.