Tag: area of a trapezoid

A US President’s Proof of the Pythagorean Theorem

High School Mathematics

James Garfield, the 20th president of the United States, came up with an original proof of the Pythagorean Theorem in 1876 when he was still a Congressman. His proof was published in New England Journal of Education.

Pythagorean Theorem proof by President Garfield

Recall that the Pythagorean Theorem states that given a right triangle with sides a, b, and hypotenuse c, the following equation is always satisified:

a^2 + b^2 = c^2.

President Garfield’s proof is quite simple. We can do this in three steps:

  1. Find the area of figure above using the trapezoid
  2. Find the area of the same figure using the three triangles
  3. Equate the results in 1 and 2. » Read more
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