Lewis Carroll's Triangle Problem on Lattices

Presenters/Authors(s)

Abbey Summers, Victor Norton

Abstract or Description

In his book, Pillow Problems, Lewis Carroll proposed the following: “Choosing three random points on the infinite plane, what is the probability that the triangle formed is obtuse?” The problem is not well-defined, since there is no uniform probability distribution on the plane. We have therefore explored this problem on rectangular lattices of points, and we will present closed formulae for the number of different types of triangles on several m-by-n lattices. In addition, we present a limiting formula for the probability of forming an obtuse triangle in a lattice with m rows and n columns as n tends towards infinity.