# 80-110: The Nature of Mathematical Reasoning

## Carnegie Mellon University

## Spring 2015

## Homework 1

At http://www.cut-the-knot.org/pythagoras/, there are 104 different proofs of the Pythagorean theorem.

Look them over, and pick your favorite! In *your own words*, explain the proof to me. This doesn't have to be a detailed proof like we've discussed, referring to axioms and inference rules; tell me, in natural language, how the proof works to establish the truth of the Pythagorean theorem. Then, in a few sentences each, answer the following two questions:
- To what extent is your proof
*algebraic*? That is, does it use variables like x, y, etc. to represent numbers? Does it use algebraic techniques like factoring, or (a+b)*c = a*c + b*c?
- How hard would it be to explain your proof to somebody without using pictures? Are the pictures essential to the proof, or do they just help make it easy to follow?