English

Counting Triangles in Triangles

Combinatorics 2024-10-28 v2

Abstract

We give a formula for counting the triangles in a picture consisting of the three sides of a triangle and some cevians. This lets us prove statements that are claimed without proof in the Online Encyclopedia of Integer Sequences and some popular YouTube videos, and also prove some new results. We also give formulas that apply when the cevians cut each side into equal-length pieces.

Keywords

Cite

@article{arxiv.2409.17117,
  title  = {Counting Triangles in Triangles},
  author = {Jim Propp and Adam Propp-Gubin},
  journal= {arXiv preprint arXiv:2409.17117},
  year   = {2024}
}

Comments

11 pages. To appear in the Pi Mu Epsilon Journal in 2025

R2 v1 2026-06-28T18:56:56.844Z