Hall's Conjecture on extremal sets for random triangles

Thumbnail Image

Files

Khan_Hayes.pdf (148.29 KB)

Date

2018-03

Authors

Journal Title

Journal ISSN

Volume Title

Publisher

Research Projects

Organizational Units

Journal Issue

Abstract

This article discusses some recent progress on Hall's conjecture about the distribution of random triangles. We consider the probability that three points chosen uniformly at random, in a bounded convex region of the plane, form an acute triangle. Hall's conjecture is the "isoprobabilistic inequality" which states that this probability should be maximized by the disk.

Description

Mathematical and Physical Sciences: 2nd Place (The Ohio State University Edward F. Hayes Graduate Research Forum)

Keywords

Random Triangles, Hall's Conjecture, Fourier Analysis, Geometric Probability, Correlation theorem

Citation

URI

http://hdl.handle.net/1811/84542

Collections

32nd Hayes Graduate Research Forum (March, 2018)