Throwback Fact: President Garfield, Mathematician?

President James Garfield
image: commons.wikimedia.org

Several weeks ago, the Throwback Fact of the week focused on the Pythagorean Theorem. But did you know that the United States has a past president with a published work of mathematics? On April 1st, 1876 (yesterday in history!) James A. Garfield, a congressman at the time, published a unique proof of the Pythagorean Theorem in the New England Journal of Education. 


Garfield is most famous for his time in the Oval Office (sworn in January of 1881), which was cut severly short as he was assassinated, passing away only 200 days into his first term. Garfield, according to this source, had intentions of becoming a math teacher, but left academia to join the Union army at the precipice of the Civil War.

The trapezoid used in the Garfield proof
image: commons.wikimedia.org

Find a detailed account of Garfield's proof here. It depends on trapezoids, instead of squares like the famous proof by the Pythagoreans, by calculating the area of a right trapezoid with the trapezoid formula and by adding up the areas of three inscribed right triangles.

If Garfield's time in the office had not been cut so short, perhaps he would have focused his agenda on the education system in the United States.