The Pythagorean Theorem - Educational Outreach

In Table 2.3, we briefly summarize the categories of existingproofs with an example for each. Not all proofs neatly tuckinto one category or another, but rather combine variouselements of several categories. A prime example isLegendre’s similarity proof. In Chapter 3, Diamonds of theSame Mind, we will explore a sampling of major mathematical‘spin offs’ attributed to the Pythagorean Theorem. In doingso, we will get a glimpse of how our Crown Jewel haspermeated many aspects of today’s mathematics and, bydoing so, underpinned many of our modern technologicalmarvels and discoveries.Euclid’s Beauty RevisitedNever did Euclid, as Newton ‘, discernAreas between an edge and a curveWhere ancient precisions of straight deferTo infinitesimal addends of turn,Precisely tallied in order to learnThose planes that Euclid could only observeAs beauty…then barren of quadratureAnd numbers for which Fair Order did yearn.Thus beauty of worth meant beauty in square,Or, those simple forms that covered the same.And, though, Archimedes reckoned with careArcs of exhaustion no purist would claim,Yet, his were the means for Newton to bareTrue Beauty posed…in Principia’s frame.October 200687