Triangle Inscribed-Triangle Picking

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Acknowledgments

I thank Dr. Patterson from The University of Texas at San Antonio for supervising the progress of this research. Additionally, Dr. Patterson encouraged, and outlined the direction for the derivation of the probability and cumulative density functions. I am grateful to A. K. Cline, R. A. van de Geijn, and D. Klyve for their words of encouragement. Finally, I am thankful to the reviewers for their corrections and suggestions.

Summary

Given a triangle, we derive the probability distribution function and the moments of the area of an inscribed triangle whose vertices are uniformly, and independently distributed on different sides of the given triangle. The theoretical results are confirmed by a Monte Carlo simulation and explored using a computer algebra system.

Additional information

Notes on contributors

Arman Maesumi

Arman Maesumi ([email protected]) is a junior at the University of Texas at Austin. He is studying computer science and also has interests in mathematics. In his spare time he writes software, and creates digital renderings of physics simulations. His plan is to pursue a PhD in computer science after his undergraduate studies. Arman became interested in the minimal enclosing circle problem, and his attempt at studying random sets of points led to this article.