The Pythagorean Theorem - Educational Outreach

Euclid’s proof of the Pythagorean Theorem (Book 1,Proposition 47) is commonly known as the Windmill Proofdue to the stylized windmill appearance of the associatedintricate geometric diagram, Figure 2.8.Note: I think of it as more Art Deco.There is some uncertainty whether or not Euclid wasthe actual originator of the Windmill Proof, but that is reallyof secondary importance. The important thing is that Euclidcaptured it in all of elegant step-by-step logical elegance viaThe Elements. The Windmill Proof is best characterized as aconstruction proof as apposed to a dissection proof. InFigure 2.8, the six ‘extra’ lines—five dashed and one solid—are inserted to generate additional key geometric objectswithin the diagram needed to prove the result. Not allgeometric objects generated by the intersecting lines areneeded to actualize the proof. Hence, to characterize theassociated proof as a DRXX (the reader is invited to verifythis last statement) is a bit unfair.How and when the Windmill Proof first came intobeing is a topic for historical speculation. Figure 2.9reflects my personal view on how this might have happened.Figure 2.9: Pondering Squares and Rectangles37