The Pythagorean Theorem - Educational Outreach

4) Pearls of Fun and WonderPearls of ancient mind and wonder,Time will never pillage, plunder,Or give your soul to the worm—Or worse yet, for nerds to keepWith their mental treasures deepWhere secret squares are cut asunder.So, come good fun, have a turn,Bring your gold, build and learn!April 20054.1) Sam Lloyd’s Triangular LakeSam Lloyd was a famous American creator ofpuzzles, tricks and conundrums who produced most of hismasterpieces in the late 1800s. Many of Lloyd’s puzzleshave survived and actually thrived, having found their wayinto modern puzzle collections. Martin Gardner, of ScientificAmerican fame, has been a tremendous preserver of Lloyd’slegacy to recreational mathematics. Recreationalmathematics, one might classify that phrase as anoxymoron. Yet, back in the late 1800s, Lloyd’s heyday,people actually worked puzzles for evening relaxation, muchlike we moderns watch TV or play video games. The need torelax has always been there; how people fulfill the need ismore a function of the era in which we live and the availabletechnology that enables us to recreate.One of Sam Lloyd’s famous creations is hisTriangular Lake. Lloyd subtlety gives his readers twochoices: solution by sweat and brute force, or solution bycleverness and minimal effort. The clever solution requiresuse of the Pythagorean Theorem. What follows is Lloyd’soriginal statement:“The question I ask our puzzlists is to determine how manyacres there would be in that triangular lake, surrounded asshown in Figure 4.1 by square plots of 370, 116 and 74acres.136