Garfield’s Pythagorean Proof

This is a short, animated visual proof of the Pythagorean theorem (the right triangle theorem) using the trapezoid that is now attributed to President James Garfield. This theorem states the square of the hypotenuse of a right triangle is equal to the sum of squares of the two other side lengths.

Thanks!

For other proofs of this same fact check out the following playlist:

#mathshorts #mathvideo #math #pythagoreantheorem #pythagorean #triangle #manim #animation #theorem #pww #proofwithoutwords #visualproof #proof

To learn more about animating with manim, check out:

[spherence]

Many people don’t know he also loved lasagna and hated Mondays.

[RetroGamer]

I have never heard this proof. Beautifully explained and an elegant proof all around. It's robust enough that you could actually prove it to 9th graders. Most high schoolers can't prove it normally. I wonder why even through college I never saw this. That's awesome. Definitely a great way to start the morning

[LinusE]

Garfield was also ambidextruous and could write in Latin with his left hand and Greek in his right hand, he was brilliant

[Scubadooper]

Much prettier when it's extended to a full square rather than a trapezoid

[Unbaguettable]

for this proof it’s a lot easier to double the shape and make it a square instead of a trapezoid.

[renren]

When US presidents actually contributed to society




Edit: Damn 100 likes, would never have expected this to reach that but thanks y’all 🙏

[yahyagd]

How ironic that the dude who died on monday has the same name as someone who despises mondays

[GaurangAgrawal]

There is also another very similar version of the proof, where you rotate and make 4 copies of the same triangle, and join them by creating a larger square of side a + b.

Then we draw another version of the same square, this time making 2 rectangles of side a and a +b, and b and a + b, inside the larger square

We then notice by areas that a² + b² = c².

tho, it's a very good visual proof, I never really got that. But the trapezoid proof shown here is very easy to understand.

[silasmobhall]

That's actually crazy, i was preparing for a test in my math class on Sunday, and one of the questions were about this proof. I did not understand this proof at all, and behold 13 hours after i finished studying, and 3 hours after i had my test, this video.

Thankfuly at least i understand it now

[General_Blockz-Iminpain]

Didn’t know lasagna-lover Garfield was into math. I thought he was lazy.

[miscellaneousrat]

I’ve always seen this done with a full square, bot a trapezoid.

[colinjava]

Small variation of the 4 triangles in a big square proof.

There was a neat proof that proved it by scaling triangles, something like ka^2 + kb^2 = kc^2, but I don't remember it.

[ccbgaming]

James subsequently proves that he is the GOAT president 🐐🇺🇸

[CountArtha]

He wasn't even the math professor.

He taught Latin.

[AndrewPurnell-ty]

Math proofs are always fascinating to me when explained properly. You can just accept F=ma. Or, you can mathematically prove it and that’s cool.

[londonalicante]

There was no need to gloss over the algebra at the end. Just multiply both sides by 2 to get rid of the halves, and it becomes obvious that you have a 2ab on both sides that cancels.

[HaldaneSmith]

Mr. President, inflation is running at 70%, and there are Indian uprisings in Oklahoma, Arizona, and New Mexico!
Garfield: Er, you wouldn't happen to remember the area formula for a trapezoid would you?

[imstudying]

Yes, and the main idea is to prove the trapezoid area formula without using Pythagorean theorem, not obvious

[zackbuildit]

Oh this is a way better proof than most

[Avighna]

It is much easier to create four copies of the triangle, thus needing to only find the area of squares and triangles