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A Combinatorial Proof for the Geometric Series, Binomial Theorem, and the Square of a Polynomial with Tiling

CSEF · 2016 Mathematics & Computer Science

Jimin Kim · Jeffrey Trail Middle School, Irvine, Orange County

Overview

Objectives/Goals Provide a visual proof for complex mathematical identities. Methods/Materials Paper and pencil. Results The three formulas I proved using a visual method called tiling helped me understand the combinatorial concept behind these mathematical identities. Conclusions/Discussion I proved the formulas for the geometric series, binomial theorem, and the square of a polynomial with an inductive and combinatorial approach. To do so, I used a method called tiling. This allows many visual learners to understand proofs more easily.

Summary statement

I visually proved the formula for the geometric series, binomial theorem, and square of a polynomial using a method called tiling.

Help received

After I had done quite some research on tiling, I stumbled upon a concept within tiling, so I reached out to the UCI Math Department and received help from a PhD, Hayan Nam.

Competition history

  • CSEF 2016 Mathematics & Computer Science · Entry J1414

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