Garfield's Proof of the Pythagorean Theorem
This Demonstration shows President James Garfield's elegant proof of the Pythagorean theorem.[more]
The area of the trapezoid (step 5) can be calculated in two ways: as a trapezoid with base and heights and , or as the sum of the areas of three triangles:
Multiply through by 2 and expand the left-hand side to get
which simplifies to
James Abram Garfield (1831–1881), the twentieth president of the United States, published this proof in the New England Journal of Education.
 S. Klebe, "Garfield, the Pythagorean Theorem, and the Fight for Universal Education," Executive Intelligence Review, 22(9), 1995 pp. 50–51. www.larouchepub.com/eiw/public/1995/eirv22n09-19950224/eirv22n09-19950224_050-garfield_the_pythagorean_theorem.pdf.