The Pythagorean Theorem - Educational Outreach

In Figure 2.28, we update the annotations used by Henryand provide some key geometric information on his overallconstruction.Master righttriangle a, b, cECFBb 2ADbacGThis is the center ofthe ‘a’ square. Thetwo cross lines runparallel to thecorresponding sidesof the ‘c’ square.b 2IAll eightconstructedquadrilaterals arecongruentHEach line segment isconstructed from themidpoint of a sideand runs parallel tothe correspondingside of the ‘b’ square.Figure 2.28: Annotated Perigal DiagramWe are going to leave the proof to the reader as a challenge.Central to the Perigal argument is the fact that all eight ofthe constructed quadrilaterals are congruent. Thisimmediately leads to fact that the middle square embeddedin the ‘c’ square is identical to the ‘a’ square from which2 2 2a b c can be established.Perigal’s proof has since been cited as one of themost ingenious examples of a proof associated with aphenomenon that modern mathematicians call aPythagorean Tiling.62