Arrow-chasing in Pascal's triangle -- Visual proofs for summation formulas involving binomial coefficients

TL;DR

This paper introduces an elementary visual method called 'arrow-chasing' to prove binomial coefficient summation formulas using Pascal's triangle, making the proofs accessible to a broad audience.

Contribution

The paper develops and demonstrates a new visual proof technique called 'arrow-chasing' for binomial coefficient identities using Pascal's triangle.

Findings

Arrow-chasing provides clear visual proofs for summation formulas.

The method is simple and accessible to non-experts.

Numerous examples illustrate the technique's effectiveness.

Abstract

This article demonstrates, using numerous examples of varying complexity, how one can visually prove summation formulas involving binomial coefficients by exclusively using the recurrence relation for binomial coefficients and its illustration through arrows in Pascal's triangle. The method developed for this purpose, which we call "arrow-chasing", is elementary and it is accessible to a very broad audience.