Garfield's proof of the Pythagorean theorem | Geometry | Khan Academy

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James Garfield's proof of the Pythagorean Theorem.
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[@nickbarton3191]

Just goes to show how boring political meetings are that he had to resort to trig for entertainment.

[@marcoskano4437]

Trig is fun even more when you start with cálculos

[@saturn21207]

When you think you're eating lasag but you accidentally solve quantum physics

[@zombieslayer2225]

Garfield:*Doodles in a meeting. Garfield:*Constructs a trapezoid using three triangles. Garfield:*Solves the equation. Garfield:*Realizes that he just prove the Pythagorean theroem. Garfield: :O

[@AlexandrBorschchev]

just imagine garfield's face when he found the proof. *EUREKA*

[@Xclann]

Search for "Electron Configuration". That's where the 1s 1s^2 2p^6 3s^2... etc. is explained by Khanacademy (Khan himself).

[@parthibhayat]

Ok?

[@JamesMac-fd7dx]

2s orbital remains unfilled as a result of shielding

[@4gate]

beautiful. so simple

[@smyleylily]

this is a lot easier than the proof in the book. thumbs up

[@Bobyfototube]

Thank u Mr president

[@VanBurenOfficial]

James A. Garfield was a great man.

[@callumvanheerden1530]

Is it just me or is this easier than the other methods

[@mausam6101]

it is/.

[@marcoskano4437]

You have seen the square method ? It is much easier than this but this is more fun

[@viki2133]

Huh... That's quite simple and it's actually using just geometry for the 7th grade.

[@viki2133]

Shane Yaw ?

[@myrus5722]

Dylan Atwater It is a pretty arbitrary to think to create a trapezoid like that, and the solve for the area in two ways. It makes sense why no one would have thought to do that.

[@javipdr19]

i've always wondered how a mathematician (amateur or profesional) feels when he finds a proof for something! It must be great, even i got excited watching this video.

[@Bakmoon]

Thank you so much for posting this. This is one of my favorite proofs of the Pythagorean theorem along with the Bhasakra proof and the Chinese proof.

[@JoeBrenn]

Very cool, I'll admit I wished that I'd seen the end proof coming a little sooner than I did, but it was very interesting nonetheless. Done perfectly to keep peoples' attention too!

[@Spawnwarrior007]

Thanks Sal you're the best bro!

[@longhorn4500]

But there are still things that need to be proved such as the sum of the angles of a triangle is 180 and the area of a trapezoid is h * (a + b)/2 :)

[@sidyom5068]

A little bit easier of a way to look at it would be to continue the triangle construction all the way around to make a square of side length (a+b) then noting that the crooked square made by the hypotenuses with side length c has area of c^2. Then you can note that [(a+b)^2 - c^2]/4 = ab/2 which leads very naturally into the pythagorean theorem!

[@thewirelessbrain9331]

Now THAT is a true masterpiece.

[@Funney14096]

Can Obama do this too?

[@dalawhether6079]

Funney14096 and Trump?😂😂😂

[@Burgundian_accel]

call Mr Donald Trump to attempt for 1 proof.😃

[@davidgould9431]

Trump: "Pythagermmm Theorem - FAKE NEWS"

[@jcc777777]

In this instance: B1 = a , B2 = b and H = a+b

[@ducameana]

all the color changing would have been awesome on paper with one of those multicolor clicky pens.

[@javed00]

brilliant explanation

[@ubrax8161]

Thanks

[@alizaadnan1367]

why do u multiply both sides with 2 at 6:56 ???

[@dataspace8869]

To cancel out those "1/2", which makes clearer the proof

[@thedt7746]

To get rid of the fraction

[@jaywaijy]

excellent proof, much more convincing!! Hahaha! I feel like a nerd.

[@MCPickaxe]

i thought garfield was lasagna guy

[@chaitanyanaik641]

Wow😍 too simple

[@danieltambunan5409]

Where did you get 2ab on the left side

[@4ltrz555]

(a+b)^2 = a^2 + b^3 + 2ab

[@beru58]

“In the course of my law-reading I constantly came upon the word ‘demonstrate.’ I thought, at first, that I understood its meaning, but soon became satisfied that I did not…. At last I said, ‘Lincoln, you can never make a lawyer if you do not understand what demonstrate means’; and I left my situation in Springfield, went home to my father’s house, and stayed there till I could give any propositions in the six books of Euclid at sight.” That was Abe Lincoln on Euclid's Elements. Many important politicians and leaders understood the importance of mathematics. Napoleon is famous for his method to find the centre of a circle with a compass ONLY. NOT compass and straight edge. No wonder the Declaration of Independence is layed out in many respects as the Elements.

[@rozerincagli4021]

He was maths teacher before his political career

[@rahimeozsoy4244]

Lie

[@kafumbla]

Lol no he uses a drawing tablet (a Wacom Bamboo tablet). You can find his set-up and gear somewhere on his site

[@nurlatifahmohdnor8939]

Page 450 WILLIAM HENRY HARRISON and BENJAMIN HARRISON (grandfather and grandson).

[@DrEnginerd1]

this makes me realize that we arent 1/10 th the man these guys were, cut from a different cloth i guess. kind of sad really

[@Klazyo]

sooo awesome

[@morgengabe1]

Favourite US President.

[@LiamInviteMelonTeee]

This reminds me of that clever visual proof on Wikipedia

[@trymore123]

hello there, i am thinking if i could use a little bit of your help.. i am a constant user of khanacademy website.. i use it a lot but i cant seem to find the video(under chemistry) where you've explained aufbau's principle... am basically having a problem understanding the configuration and how use those 1s 1s^2 2p^6 and others... if you could just help me find the particular video or any related ones... it would be great!! thanks!

[@StevenEncarnacion]

awesome...good job Mr Garfield!

[@qszwax57]

Do you have a video on the difference between theorems and laws?

[@WiseSquash]

this is so beautiful I almost cried :')

[@sofiagonzalez-nolde9974]

beautifully simple i love it lol

[@astroboomboy]

Yeah, I was wondering about that, thanks for answering, I'll check it out. Would be neat to use it in lectures!

[@tmjcbs]

This is rather similar to the proof with the square with sides a+b

[@charlessmyth]

James Garfield,: Showing that the House of Representatives is sometimes good for something :-)

[@MonstersSeeMeToo]

WHAAAT PYTHAGORAS WASN'T REAL EITHER!!! Whats next? Plato never lived in a cave?

[@alexgold133]

i am so confused

[@theimmux3034]

Wonder if he was just playing around with some geometry and stumbled upon this

[@FrankEgan]

Garfield discovered a new proof for The Pythagorean Theorem while fiddling around as a member of The House of Representatives. Too bad most members of the current House of Representatives are too bussy doing another kind of fiddling around…

[@adityaaysola9708]

Often times in life , I ask the question "why?" a lot. And, I would like to apply my philosophy to this problem as well. Why did you construct the trapazoid?

[@staticchimera44]

He had a feeling in his bones.

[@thecosmos7671]

No, it's just that we construct something which we know about, because in a two triangles like this he could not create a square,he could have if it were 4 triangles. So ,he just joined the triangles with a line and found it to resemble a trapezoid,as we know one pair opposite sides are parallel in a regular trapezoid so the corresponding sides of the triangles will be the parallel sides and the sum of the bases of the right triangles will be the height of the trapezoid . Since we know the formula of area of a trapezoid i.e 1/2(sum of parallel sides*height) We just have to equate the area of the trapezoid tp the sum of areas of three triangles ,the two which we already had and the third we constructed which is an isosceles right triangle with the two equal side lengths to be c ,and when finding out the area We have( 1/2)ab+(1/2 )ab 1/2(c^2)=1/2(a+b)(a+b) [ the third triangle has base and height both as 6] Simplifying, we get the result!👍

[@kerch00]

The way to find the area of a trapezoid using its height and bases is proven, so you can build a proof about the bases and height - which are a, b and c here - in a way which can describe their relation, this ends up with the relationship between a, b and c being a^2 + b^2 = c^2

[@GlorifiedTruth]

I read somewhere that Garfield ripped this proof off from Rutherford B. Hayes.

[@Funney14096]

Thanks again!

[@jacksawhavoc]

There is a proof like this where the two trapezoids form a larger square so (a+b)^2 = 4(ab/2) + c^2 . Is Garfield considered to be responsible for this as well?

[@PillSmasher]

Any possible way you could elaborate further on this proof by extending the top (a) to be equal to the bottom (b), thus creating a rectangle, then solving for the 4th triangle? From this proof, I've came to the conclusion that theta is equal to 30, and that 90 minus theta equals 60, making the a,b triangles 30,60,90 triangles, and the c triangle is a 45, 45, 90 triangle.

[@trevorstevenson5814]

I still do not understand why those certain positions of triangles have anything to do with the relationship of side measurements in a right triangle.

[@doctorcrazydude]

I just sat there watching the video, not expection anything impressing, but when he just solved the misterious angle I was like: HOLY SH**! I know that sounds nerdy, but it really blew my mind :D Thanks Sal!

[@64diamonds99]

My math teacher sucks at teaching, so I came here.

[@SuperExodus13]

Apparently he did this when he was bored.

[@miken5771]

Genius President.

[@dsb1763]

Garfield was probably as board sitting Congress then as we are now watching CSPAN. Nothing has changed!

[@R4G3QUI7]

how can he write so clean with mouse ?

[@oriraykai3610]

Did he run on this platform and win?

[@lost50]

you could also use opposite reciprocal slopes, i.e. b/a and -a/b, to show that's a 90 degree angle

[@JoshuaIfidi]

James Garfield's proof of the pythagorean theorem was the 5th proof not the first

[@Nickuncle]

Honestly, just because you said "mean" for .5(A+B) for the trapezoid I'll actually remember the rule...finally. Thank you.

[@cobyup10]

*one-halves lying around

[@chezbgone-alpha]

If anyone notices, this is just half of bhaskara's proof. :)

[@kremitlol5556]

Garfield funny lasagne cat

[@zaixhadouken]

I didn't know Garfield did this. Excellent. +1 for Cats

[@kelvincheng1833]

i just noticed that most of the time, he uses red for side a, blue for side b and yellow for side c in his videos

[@morgengabe1]

MS Paint. Use the slanted brushes, not the solid circular ones.

[@Ensign_Cthulhu]

That is the neatest and easiest Pythagorean proof I've yet seen.

[@chitranshnigam4796]

I just got to know this and this is so cleverrrr

[@RealisticCookingIRL]

Does he like lasagna?

[@andrewreed5743]

What about using this area for a trapezoid (B1+B2)•H/2

[@islulison]

i like this one the most, no moving or anything

[@daedricwomack7843]

I thought dis was gonna be Garfield im an idiot

[@XagonogaX]

Could we have a video that proves e=mc squared?

[@studytravels2270]

Thanks

[@maevei-j4798]

what software do you use to draw and speak at the same time !?!?

[@bobsagget823]

nice

[@klesstwo]

he's using a pen with a tablet :)

[@astroboomboy]

Do you draw with a mouse?

[@ShadowCloud143]

I did not know that.

[@montrast0705]

what program are you using for drawing?

[@ereklo]

5:12 fuck

[@Gravegore]

You are a wizard sir.

[@elbay2]

Yet ANOTHER proof... cool stuff !!

[@rakib567]

Garfield the cat?

[@Linqua2112]

i second more electronics and quantum physics!

[@paul1964uk]

Nice proof.

[@gptrefback]

nice and easy (:

[@cajunmane82]

Your first time hearing about James Garfield is it?

[@rauffant]

Amazing proof.

[@groundhogjugglers]

Nice!

[@esmeraldahernandez1709]

Thanks Helped me out ! :)

[@Mintchocolator]

So interesting!!

[@danieltambunan5409]

Oh i know

[@christophersedlak1147]

Thanks!

[@Puddlewhite1]

Not that your statement is bad but... its just so mundane,,,

[@philz96]

he´s using a pen tablet