The Pythagorean Theorem - Educational Outreach

5 : Solve for area using the formulaA 21 ch .A A A 2 1ca b c a c b c b a c b aa b c a c b c b a c b a164 2ca b c 2c a b c 2b a c b 2a c b a22226 : Substitute s [ a b c]/ 2final result.and simplify to obtain theA 2c2b2as s s {s} 2 2 2 A ( s c)(s b)(s a)s A s(s a)(s b)(s c)***Pappus, like Heron, was a prominent mathematicianof the Alexandrian School and contributed much to the fieldof mathematics. There are several ‘Pappus Theorems’ still inuse today. Notable is the Pappus Theorem utilized in multivariablecalculus to determine the volume of a solid ofrevolution via the circular distance traveled by a centroid.In his masterwork, The Mathematical Collection (circa 300ACE), he published the following generalization of thePythagorean Theorem which goes by his name.Pappus’ Theorem: Let ABC be a general triangle withsides AB , AC , and BC . Suppose arbitrary parallelogramsA are fitted to sides AC and BC ashaving areas A1and2shown in Figure 3.10.107