Then, Proposition I.47, the Pythagorean theorem, is proven, followed by Proposition I.48, its converse. It then lists and explains some of the earlier propositions, which are needed to complete the later proofs. Next, the paper establishes some foundational principles for Euclid’s proofs: definitions, postulates, and common notions. The paper begins with an introduction of Elements and its history. This paper seeks to prove a significant theorem from Euclid’s Elements: Euclid’s proof of the Pythagorean theorem. Her paper is a stand-alone, mathematically easy to follow (for those with some experience reading proofs), and logical progression of Euclid’s proof of the Pythagorean Theorem. She correctly uses terminology and notation throughout her paper (which is heavy on notation). She uses complex and refined mathematical reasoning. Her explanations show complete understanding of the mathematical concepts and are detailed and clear. She worked to understand the material and then presented it logically and mathematically. Katherine tackled the proof with no prior undergraduate work in geometry. This proof is not seen very often outside an undergraduate Geometry course. Katherine’s paper is a very thorough exposition of Euclid’s proof of the Pythagorean Theorem. Euclid’s Proof of the Pythagorean Theorem By Katherine Lowe '18
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