The Pythagorean Theorem - Educational Outreach

2.9) President Garfield’s Ingenious TrapezoidThe Ohioan James A. Garfield (1831-1881) was the20 th president of the United States. Tragically, Garfield’sfirst term in office was cut short by an assassin’s bullet:inaugurated on 4 March 1881, shot on 2 July 1881, anddied of complications on 19 Sept 1881. Garfield came frommodest Midwestern roots. However, per hard work he wasable to save enough extra money in order to attendWilliam’s College in Massachusetts. He graduated withhonors in 1856 with a degree in classical studies. After ameteoric stint as a classics professor and (within two years)President of Hiram College in Ohio, Garfield was elected tothe Ohio Senate in 1859 as a Republican. He fought in theearly years of the Civil War and in 1862 obtained the rankof Brigadier General at age 31 (achieving a final rank ofMajor General in 1864). However, Lincoln had other plansfor the bright young Garfield and urged him to run for theU.S. Congress. Garfield did just that and served from 1862to 1880 as a Republican Congressman from Ohio,eventually rising to leading House Republican.While serving in the U.S. Congress, Garfieldfabricated one of the most amazing and simplistic proofs ofthe Pythagorean Theorem ever devised—a dissection proofthat looks back to the original diagram attributed toPythagoras himself yet reduces the number of playingpieces from five to three.cbaFigure 2.32: President Garfield’s Trapezoid66