We generate triangles randomly by uniformly choosing a subset of three vertices from the vertices of a regular polygon. We determine the expected area and perimeter in terms of the number of sides of the polygon. We use combinatorial methods combined with trigonometric summation formulas arising from complex analysis. We also determine the limit of these equations to compare with a classical result on triangles whose vertices are on a circle.
Darin Stephenson, Department of Mathematics, Hope Collegestephenson@hope.edu
Madras, Anna and KC, Shova
"Randomly Generated Triangles whose Vertices are Vertices of Regular Polygons,"
Rose-Hulman Undergraduate Mathematics Journal: Vol. 7
, Article 12.
Available at: https://scholar.rose-hulman.edu/rhumj/vol7/iss2/12