Euler's Polygon Division Problem
The problem of finding in how many ways 👁 E_n
a plane convex polygon
of 👁 n
sides can be divided into triangles by diagonals.
Euler first proposed it to Christian Goldbach in 1751, and the solution is the Catalan number 👁 E_n=C_(n-2)
.
See also
Catalan Number, Catalan's Problem, Polygon Diagonal, Regular Polygon Division by DiagonalsExplore with Wolfram|Alpha
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References
Forder, H. G. "Some Problems in Combinatorics." Math. Gaz. 41, 199-201, 1961.Guy, R. K. "Dissecting a Polygon Into Triangles." Bull. Malayan Math. Soc. 5, 57-60, 1958.Referenced on Wolfram|Alpha
Euler's Polygon Division ProblemCite this as:
Weisstein, Eric W. "Euler's Polygon Division Problem." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/EulersPolygonDivisionProblem.html