How this calculation works
Count ways to divide a convex polygon into triangles by noncrossing diagonals.
THE FORMULA
Cₙ₋₂ = binom(2n−4,n−2)/(n−1)A worked example
A convex hexagon has C₄ = 14 triangulations.
Good to know
Vertices are fixed and distinguished by position.
Reference: NIST DLMF, Functions of Number Theory (opens in a new tab) ↗
Read the result
Count ways to divide a convex polygon into triangles by noncrossing diagonals.
The primary result is labeled “Triangulations”. Keep the input definitions in view when comparing this result with another method.
Try a related calculation
Vertices are fixed and distinguished by position.
For a related exercise, try the greatest common divisor.
A few questions, answered
How can I check the default inputs by hand?
A convex hexagon has C₄ = 14 triangulations.
Which rule does this calculator apply?
Cₙ₋₂ = binom(2n−4,n−2)/(n−1)