The Pythagorean Theorem - Educational Outreach

2.12) A Challenge for All AgesAs shown in this chapter, proving the PythagoreanTheorem has provided many opportunities for mathematicaldiscovery for nearly 4000 years. Moreover, the PythagoreanTheorem does not cease in its ability to attract newgenerations of amateurs and professionals who want to addyet another proof to the long list of existing proofs. Proofscan be of many types and at many levels. Some are suitablefor children in elementary school such as the visual proofattributed to Pythagoras himself—super effective if madeinto a plastic or wood hand-manipulative set. Other proofsonly require background in formal geometry such as theshearing proof in Section 2.11. Still others requirebackground in both algebra and geometry. The CauliflowerProof requires a background in calculus. Thus, one can saythere is a proof for all ages as, indeed, there have beenproofs throughout the ages. The Pythagorean Crown Jewelnever ceases to awe and inspire!Type Example CommentVisualDissectionPythagoras Elementary SchoolAdvancedVisualLiu Hui Middle SchoolDissectionAlgebraicDissectionBhaskara Middle SchoolConstruction Euclid Early High SchoolTransformer Kurrah Middle SchoolSimilarity Legendre High SchoolTiling Perigal Early High SchoolCalculus ‘Cauliflower’ Early CollegeShearing Section 2.11 Early High SchoolTable 2.3: Categories of Pythagorean Proofs86