Reasoning and Sense Making with Pythagoras

In 1996, a new proof of the Pythagorean theorem appeared in the "College Mathematics Journal" (Burk 1996). The occurrence is, perhaps, not especially notable given the fact that proofs of the Pythagorean theorem are numerous in the study of mathematics. Elisha S. Loomis in his treatise on the subject, "The Pythagorean Proposition" (1968), presents more than 350 unique proofs. What is notable about Burk's discovery is that his proof provides mathematics students who have not been exposed to the theorem opportunities to make connections among a rich set of mathematical topics that all precede the presentation of the Pythagorean theorem in the Common Core State Standards (2010). The intent of this article is to demonstrate the connections that Burk's approach to the Pythagorean theorem offers and to make a case for its consideration as a new vehicle for students to arrive at a deep understanding of this venerable theorem.