A senior thesis by Kennedy Burgess, Spring 2021

Abstract: This document is intended to walk the readers through three proofs of the Pythagorean Theorem. The intended audience is younger levels of education, mainly middle school and high school. The Pythagoreans are remembered for two monumental contributions to mathematics. The first was establishing the importance of, and the necessity for, proofs in mathematics: that mathematical statements, especially geometric statements, must be verified by way of rigorous proof. Prior to Pythagoras, the ideas of geometry were generally rules of thumb that were derived empirically, merely from observation and occasionally measurement. Pythagoras also introduced the idea that a great body of mathematics could be derived from a small number of postulates. Clearly Euclid was influenced by the Pythagoras. The second great contribution was a discovery of and proof of the math that not all numbers are commensurate. More precisely, the Greeks prior to Pythagoras believed would be profound and deeply held passion that everything was built on the whole numbers. Fractions arise in a concrete manner: as ratios of the sides of triangles with integer length. Pythagoras proved the result now called the Pythagorean Theorem.