Garfield’s Pythagorean Proof
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- Опубликовано: 4 окт 2024
- 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.
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This animation is based on a proof due to James A. Garfield. For a static version of this proof, see Roger Nelsen's first "Proof Without Words: Exercises in Visual Thinking" compendium (page 7) : bookstore.ams..... You can also check out Howard Eves' "Great Moments in Mathematics (Before 1650)" page 34-36.
You can also see the original on MAA Convergence: maa.org/press/...
For other proofs of this same fact check out the following playlist:
• Pythagorean Theorem
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![Pythagoras Would Be Proud: High School Students' New Proof of the Pythagorean Theorem [TRIGONOMETRY]](http://i.ytimg.com/vi/p6j2nZKwf20/mqdefault.jpg)
Many people don’t know he also loved lasagna and hated Mondays.
He like does hate Mondays (in the afterlife), because he died on one
Well I hate Thursdays.
@@AINeverDies I could never get the hang of Thursday’s.
It should really go: Monday, Tuesday, Wednesday, Friday, Saturday, Sunday
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
this is the main proof of the pythagorian theorem that our countrys math curriculum used to teach us (till 2024, rip)
never knew that he proofed it!!
it's basically the same as building a big square with 4 triangles and a c^2 inside
Not bad, but doubling it to the square proof is so simple and elegant I solved it in my head (never been run through it before and while I'm decent at maths I haven't studied any post HS maths except intro stats)
Much prettier when it's extended to a full square rather than a trapezoid
Garfield was also ambidextruous and could write in Latin with his left hand and Greek in his right hand, he was brilliant
Garfield, not only Lasagna eater😀
When US presidents actually contributed to society
Edit: Damn 100 likes, would never have expected this to reach that but thanks y’all 🙏
and now we have a guy who doesnt even know which world we in vs a felon running for president. smh
Didn't Garfield die months into his presidency
@@hontemaassassination
This proof is just a poor copy
"actually contributed to society" lol proving pythagorean's theorem is not pushing the frontier of mathematics forward, it was proven by pythagoras >2,000 years ago, it's the mathematical equivalent of michelle obama's vegetable garden.
it's just a fun little project to find a proof that nobody else has done before.
i'm a math major in grad school and i have three friends who have each done this themselves, it's not a big thing, it's one of the easiest theorems for amateur mathematicians to prove in a new way by just being creative with geometry
for this proof it’s a lot easier to double the shape and make it a square instead of a trapezoid.
But then that proof is even older! :)
Double it and give credit to previous person
I don't see what's so great about coming up with a complicated half of a simple proof.
@@rbettsxhow many recent presidents have learned even the most basic level of calculus? Jimmy Carter got an engineering degree from the Naval Academy.
half it and give it to the next person
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.
Yep, the two arrangements of four triangles inside a square of side a+b is a great visual method of proving Pythagoras' theorem that I learnt as a kid, and doesn't require any algebraic manipulation. Abe Garfield's proof is pretty neat too though.
yup, garfields method is just a poor copy
How ironic that the dude who died on monday has the same name as someone who despises mondays
James subsequently proves that he is the GOAT president 🐐🇺🇸
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
Sorry not earlier :)
A nice proof. I like it 🤘
Bro that loop was clean🤣
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.
I clicked because I was hoping it was the other Garfield 😢
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?
Area formula for a trapezoid is easy everyone knows it
Oh this is a way better proof than most
Brilliant, Mr President!!
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.
Isn't force just defined as m*a?
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.
more like garfield's lasagna proof
Elegant!
It is much easier to create four copies of the triangle, thus needing to only find the area of squares and triangles
Wow!!
Nice and simple
Back in the day when Presidents actually used to think.
This is a much simpler approach comparing to others, like it
Yes, but why complicate it. Just use 4 triangles that make up a square.
Nice proof Mr. president! 🦅 🇺🇸
Yes, and the main idea is to prove the trapezoid area formula without using Pythagorean theorem, not obvious
Check my channel for that :)
Garfield was the PRESIDENT??!?!
This guy really love math and convert his imagination into reality 😁
He wasn't even the math professor.
He taught Latin.
You see it is the way it is, because the way it is, is the way that it is. 🎉 Gimme my nobel prize now. 🏅
Isn't this just half of one of the standard proofs where you put four copies round a square of side c? Not really a new proof.
no one dared to tell the president that or else death penalty so we make him the "inventor of this proof"
source: i made it the fuck up
not very different from the square proof, it's act half of it
Garfield was showing off, that's one of the most complex Pythogorean right triangle proofs I've seen , plus it relies on knowing the trapezoid formula which for this to be a proof you'd aldo need to prove
It's really not that complex. It's basically the square proof in less steps. Finding the formula for area of a trapezoid isn't hard either
@@methatis3013 you literally have to prove one formula first in order to use it in a proof for the formula you're trying to prove....I didn't say it was hard I said it was overly complex. With some graph paper and a pair of scissors I can and have presented a proof to young children that is very easy and simple as in not complex
@@izzabelladogalini you don't have to prove the formula for an area of a trapezoid. When it comes to well known formulas and theorems, you don't need to prove them. Unless you're starting from axioms for some reason
@@methatis3013 in which case you don't need to prove a²+b²=c² the Babylonians did that 4000 years ago and I'm pretty sure it was well accepted by the time of Garfield
@@izzabelladogalini man, there's really no arguing with you, is there
Garfield, had he not been the 2nd president to be assasinated, would have been judge the 2 or 3 best president ever. He could write Latin and Greek simultaneously. (1 by each hand)
Lasagna axiom 😂
when Presidents were logical and intelligent but also seeking to contribute positively to the world.
Didnt know a lazy cat proved a triangle therom
I think there's a mistake when you equal the formulas.
Because you get C^2= B^2+ AB + A^2
No, when, you double both sides you get C^2+2AB = B^2+2AB+A^2
I have got my doubt clear
But isn’t the recent college students one being the only proof without trigonometry
Publishing a novel proof of the Pythagorean theorem should be a constitutional requirement to stand for election.
Imagine any US president so far this century being able to do something like this.
Maybe Obama?
I have a lot of respect for President Garfield, but this proof is only half of the classic chinese(?) "proof without words" and it seriously complicated it...
Bro might be a nerd
Most def
Modern US presidents probably can't even do algebra
Try explaining this to the recent US president
Einstein proved it when he was 12
When presidents were actually worthy of their presidency
What the fu-
im just gonna pretend i understood everything...
We have yet to see Trump do 2+2.
ask trump to prove rt2 is irrational
rip president garfield 😢🔫
But u still used the theorem to prove it i mean yeah its noce but it doesn't explain why the theorem works
How did he use the theorem to prove it? He used the area formula for a trapezoid and area formulas for triangle…
He didn't use the theorem in the proof
Very useless 😂
now tryto ask biden half a quarter he would say we support isreal