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
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.
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.
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!
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.
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!
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!
“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.
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!
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?
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?
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!👍
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
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…
![Pythagoras Would Be Proud: High School Students' New Proof of the Pythagorean Theorem [TRIGONOMETRY]](http://i.ytimg.com/vi/p6j2nZKwf20/mqdefault.jpg)
![Pythagoras Would Be Proud: High School Students' New Proof of the Pythagorean Theorem [TRIGONOMETRY]](/img/tr.png)
Just goes to show how boring political meetings are that he had to resort to trig for entertainment.
Trig is fun even more when you start with cálculos
When you think you're eating lasag but you accidentally solve quantum physics
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
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.
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.
James A. Garfield was a great man.
Search for "Electron Configuration". That's where the 1s 1s^2 2p^6 3s^2... etc. is explained by Khanacademy (Khan himself).
Ok?
2s orbital remains unfilled as a result of shielding
Thank u Mr president
beautiful. so simple
just imagine garfield's face when he found the proof.
*EUREKA*
Is it just me or is this easier than the other methods
it is/.
You have seen the square method ? It is much easier than this but this is more fun
Now THAT is a true masterpiece.
this is a lot easier than the proof in the book. thumbs up
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 :)
Yeah, I was wondering about that, thanks for answering, I'll check it out. Would be neat to use it in lectures!
Huh... That's quite simple and it's actually using just geometry for the 7th grade.
Shane Yaw ?
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.
awesome...good job Mr Garfield!
Do you have a video on the difference between theorems and laws?
Thanks Sal you're the best bro!
this is so beautiful I almost cried :')
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!
That is the neatest and easiest Pythagorean proof I've yet seen.
you could also use opposite reciprocal slopes, i.e. b/a and -a/b, to show that's a 90 degree angle
Thanks again!
Honestly, just because you said "mean" for .5(A+B) for the trapezoid I'll actually remember the rule...finally. Thank you.
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.
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!
In this instance: B1 = a , B2 = b and H = a+b
i like this one the most, no moving or anything
I just got to know this and this is so cleverrrr
You are a wizard sir.
beautifully simple i love it lol
What about using this area for a trapezoid (B1+B2)•H/2
Can Obama do this too?
Funney14096 and Trump?😂😂😂
call Mr Donald Trump to attempt for 1 proof.😃
Trump: "Pythagermmm Theorem - FAKE NEWS"
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!
all the color changing would have been awesome on paper with one of those multicolor clicky pens.
Yet ANOTHER proof... cool stuff !!
brilliant explanation
why do u multiply both sides with 2 at 6:56 ???
To cancel out those "1/2", which makes clearer the proof
To get rid of the fraction
Wow😍 too simple
Thanks Helped me out ! :)
Could we have a video that proves e=mc squared?
what software do you use to draw and speak at the same time !?!?
i thought garfield was lasagna guy
Where did you get 2ab on the left side
(a+b)^2 = a^2 + b^3 + 2ab
So interesting!!
Thanks!
WHAAAT PYTHAGORAS WASN'T REAL EITHER!!! Whats next? Plato never lived in a cave?
what program are you using for drawing?
I didn't know Garfield did this. Excellent. +1 for Cats
nice
Page 450
WILLIAM HENRY HARRISON and BENJAMIN HARRISON (grandfather and grandson).
“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.
My math teacher sucks at teaching, so I came here.
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!
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
This reminds me of that clever visual proof on Wikipedia
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?
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.
Thanks
Garfield funny lasagne cat
Amazing proof.
James Garfield,: Showing that the House of Representatives is sometimes good for something :-)
Nice proof.
Nice!
Garfield was probably as board sitting Congress then as we are now watching CSPAN. Nothing has changed!
Genius President.
This is rather similar to the proof with the square with sides a+b
He was maths teacher before his political career
Lie
Wonder if he was just playing around with some geometry and stumbled upon this
excellent proof, much more convincing!! Hahaha! I feel like a nerd.
how can he write so clean with mouse ?
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?
He had a feeling in his bones.
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!👍
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
MS Paint. Use the slanted brushes, not the solid circular ones.
Lol no he uses a drawing tablet (a Wacom Bamboo tablet). You can find his set-up and gear somewhere on his site
Apparently he did this when he was bored.
I read somewhere that Garfield ripped this proof off from Rutherford B. Hayes.
If anyone notices, this is just half of bhaskara's proof. :)
sooo awesome
5:10 "now, how can we also fuc- figure out the area?" :P
Favourite US President.
nice and easy (:
James Garfield's proof of the pythagorean theorem was the 5th proof not the first
Amazingly WoW !
Thanks for this ...
Did he run on this platform and win?
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…
Do you draw with a mouse?
i second more electronics and quantum physics!
I did not know that.
Your first time hearing about James Garfield is it?
I thought dis was gonna be Garfield im an idiot
i am so confused
*one-halves lying around
Garfield the cat?
Oh i know
this is actually the easiest of the three proofs ..... pretty interesting
he's using a pen with a tablet :)
he´s using a pen tablet
Does he like lasagna?
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