Maths With R.Khan

(20th President of U.S ) who Proved .

James A. Garfield (1831-1881) was the twentieth president of the United States. After he graduated from Williams College in 1856, he taught Greek, Latin, mathematics, history, philosophy, and rhetoric at Western Reserve Eclectic Institute, now Hiram College, in Hiram, Ohio, a private liberal arts institute. In addition to teaching, he also practiced law, was a brigadier general in the Civil War, served as Western Reserve’s president, and was elected to the U.S. Congress.

Garfield contributed an original proof of the Pythagorean Theorem to the hundreds that have been recorded over the centuries. For a repository of original proofs of the Pythagorean Theorem, see Elisha Loomis’ The Pythagorean Proposition. Garfield developed his proof in 1876 while a member of Congress; that was the year Alexander Graham Bell developed the telephone. This “very pretty proof of the Pythagorean Theorem,” as Howard Eves described it, was published in the April 1, 1876 issue of the New-England Journal of Education. Evidently the editor of the journal erroneously (or perhaps in political jest) called the theorem Pons Asinorum or “Bridge of Asses,” actually a nickname for the isosceles triangle theorem (Euclid's Elements, Book I, Proposition 5). The latter theorem may have earned its name because many medieval students had difficulty understanding the proof, for which the diagram somewhat resembles a bridge, and therefore could not cross over the bridge to subsequent proofs in Euclid's Elements.
Garfield's proof of the Pythagorean Theorem essentially consists of a diagram of a trapezoid with bases a and b and height a+b. He looked at the area of the diagram in two different ways: as that of a trapezoid and as that of three right triangles, two of which are congruent.