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.

Author Bio

Anna Madras recently graduated from Drury University in Springfield, Missouri with a degree in mathematics and secondary education along with minors in Global Studies and Spanish. I am currently teaching mathematics at Parkview High School in Springfield, Missouri, but my future plans include getting my master's degree in mathematics. I enjoy outdoor activities such as canoeing and hiking along with watching movies with my friends and playing board games.

Shova KC is a senior at Hope College where she hopes to major in economics and mathematics. Currently, Shova is participating in an internship at ICPRS at the University of Michigan in Ann Arbor, Michigan. After college, Shova plans to attend graduate school most likely studying economics. She enjoys traveling, especially to visit her family in Nepal, eating exotic foods, and also reading books.