Visual Inductive Proof

Overview

A visual representation using Matplotlib to illustrate a proof by induction for the statement: "Prove that for any 2^n by 2^n grid with any one square removed, a number of L-shaped triominoes can be made to cover the entire board."

Impetus

For an assignment for my discrete math class, I was asked to prove the aforementioned statement. After crafting the inductive proof, I realized that it would be fun to write a visualization for it in Python. After writing the script and showing my professor, he asked me to join his research project on Steiner Triple Systems. This introduced me to a field of mathematics with which I had little experience at the time, but I have grown to love.

• Interest in combinatorial mathematics and visual proofs.
• Desire to create an visualization tool for understanding my inductive proof.
• Challenge of translating abstract mathematical concepts into visual representations.

Usage & Output

Running the Python script, the user will be prompted to enter a number for the size of the grid. Then, the user will be prompted to enter the row and column number for the empty block.

• Usage: Run the Python script to generate visual proofs for different values of n, row and column.
• Output: Matplotlib visualization showing the grid generated using my inductive proof, labeled to indicated the order in which the triominoes were placed into the grid.

Skills Developed & Applied

• Python Programming: Enhanced proficiency in Python, particularly with libraries like Matplotlib.
• Mathematical Reasoning: Deepened understanding of inductive proofs and combinatorial mathematics.
• Data Visualization: Improved skills in creating clear and informative visual representations of complex concepts.
• Problem-Solving: Applied logical reasoning to translate mathematical theory into executable code.