Only U.S. President to prove a theorem

In 1880, James Garfield contributed a new proof of geometry's most famous right triangle theorem. #shorts #math #maths #mathematics

Mathematical treasure: Garfield's proof
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[WestExplainsBest]

Imagine if presidential elections were determined by math proofs.

[giacomomosele]

wow, that's actually a really cool way to prove pythagorean theorem

[asifurrahman]

Learned it back in 8th grade. Didn't know a US president proved it

[sadeekmuhammadryan]

*"I used the proof to prove the proof" - James A. Garfield* 😎

[jimmykitty]

Geometry has two great treasures; one of them is Theorem of Pythagoras! ❤

[labzioui]

Yes ! Yes !
In 1876, Garfield demonstrated his talents as a mathematician by providing a proof of the Pythagorean theorem. His work was published in the New England Journal of Education. Mathematical historian William Dunham argued that Garfield's proof was "really a very elegant proof."

[ffggddss]

Thank you for posting this! I recall seeing, some decades ago, that he had been a schoolteacher, and had come up with a novel proof of the Pythagorean Theorem.
But the diagram for that, was twice this one. Namely, there was one big square, with another one (here ½ a square that's a rt. isosc. ∆ in white; green in your thumbnail), side=c, inscribed in it, tilted, so that there were 4 congruent right triangles (here in blue), with legs a & b.

Then, areas were equated:

BIG Square = 4 right ∆s + little square
(a + b)² = 4(½ab) + c²
a² + 2ab + b² = 2ab + c²
a² + b² = c²
QED

When done this way, it is perhaps more obvious that the four ∆s are right ∆s, and all congruent; and there's no need to use, or even know, the area of a trapezoid.
Was your version his original, and someone later turned it into what I've described here?

Anyway, I always thought that this was far superior to, and more elegant than, the tangled mess of a proof we were taught in high school geometry class, which may have been straight out of Euclid's _Elements, _ idk.

EDIT: From your link, I see that your trapezoid version was Garfield's original, and that it was published in 1876, not 1880, which was the year he was elected president.

Fred

[fakeit]

just half of the shape used in the original proof

[anonymousanonymous]

Garfield was actually crazy smart. It was said he could write Latin with one hand and Ancient Greek with the other at the same time. He was head of a university in Ohio, and managed to win a surprise victory as president. Then he got shot by a crazy person who joined a sex cult and didn’t get laid (not a joke).

[suponjubobu]

He was not the first to prove this, but he came up with this proof himself.

[nathanderhake]

This has been proven before by Euclid way back in ancient times. It is a nice proof tho.

[harshitgupta]

Hey presh i want you to take a look at this interesting problem-
"Gold is 19 times as heavy as water, and copper is 9 times as heavy as water, the ratio in which these two metals be mixed so that the mixture is 15 times as heavy as water"
A)1:2
B)2:3
C)3:2
D)19:135
The correct answer is C) 3:2
Will you please solve this

[DavidAnimate]

US Presidents in 1880s: smart as heck
US Presidents in 2020s: **snoring**

[nikko]

Bro was named after a cat that ate lasanga 💀

[WahranRai]

in 1880 in the USA, the first to solve this problem became president : James Garfield had won !

[Ed]

Pythagoras already proved that some 550 years BC. though it was known by the babylonians a millennium earlier already

[arnoldbissen]

Instead of making a trapezoid, why not make a square (by linking four abc triangles). That would be easier to understand..

[ARKGAMING]

I've never seen a proof to that with a trapezoid. It's pretty interesting

[rakhuramai]

Wow this is a much more simple proof the Pythagorean Theorem than what I learnt back in high school!

[ScalarYoutube]

Another cool trick, if you mirror the shape created at the end of the video, flip it upside down and attach it onto the existing shape. You will get a square with a smaller inner square. That smaller inner square that is slightly rotated is c^2