Three Random Intercepts of a Segment

TL;DR

This paper explores different models for constructing random triangles from line segments in the plane, comparing their appropriateness and aiming to involve a broader audience in understanding the underlying assumptions.

Contribution

It examines two competing models of uniform sampling for random triangles, clarifying their differences and implications in geometric probability.

Findings

Comparison of two models for uniform sampling

Discussion on the appropriateness of each model

Engagement of broader audience in geometric probability questions

Abstract

We construct random triangles via uniform sampling of certain families of lines in the plane. Two examples are given. The word "uniform" turns out to be vague; two competing models are examined. Everything we write is well-known to experts. Which model is more appropriate? Our hope is to engage a larger audience in answering this question.