In 1876, Garfield displayed his mathematical talent when he developed a trapezoid proof of the Pythagorean theorem. His finding was placed in the New England Journal of Education. Mathematics historian William Dunhamwrote that Garfield's trapezoid work was "really a very clever proof."[119]
Apparently Garfield did come up with an alternate proof. See https://www.maa.org/press/periodica...-a-garfields-proof-of-the-pythagorean-theoremswampwiz said:I'm talking about the Pythagorean Theorem, which seems to have an alternate proof attested to him!
http://jwilson.coe.uga.edu/EMT668/EMT668.Student.Folders/HeadAngela/essay1/Pythagorean.html
Yes, President James A. Garfield did indeed come up with an alternate proof for the Pythagorean Theorem. As a mathematics enthusiast, Garfield was able to come up with a simple and elegant proof for this well-known theorem.
Garfield's alternate proof involves dividing a right triangle into two smaller triangles and rearranging them to form a square. This proof is also known as the "Garfield proof" or "President's proof".
Garfield's inspiration for the proof came from his interest in geometry and his desire to find a simpler proof for the Pythagorean Theorem. He first came up with the idea while a student at Williams College, and later refined it while serving as a U.S. Congressman.
Yes, Garfield's proof is considered to be a valid and accepted proof for the Pythagorean Theorem. It is often used in geometry textbooks as an alternative to the more commonly known proofs.
While Garfield's alternate proof for the Pythagorean Theorem is his most well-known contribution to mathematics, he also made significant contributions in other areas such as Euclidean geometry and the theory of numbers. However, his political career cut short his potential impact on the field.