Pythagorean Theorem Proof (Geometry)

The Pythagorean Theorem says that for any right triangle, a^2+b^2=c^2. In this video we prove that this is true. There are many different proofs, but we chose one that gives a delightful visual explanation for why the Pythagorean Theorem works.

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Geometer: Louise McCartney
Artwork: Kelly Vivanco
Written by Michael Harrison
Directed & Produced by Kimberly Hatch Harrison & Michael Harrison

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[thetruthfulchannel]

People should be taught this in school instead of just being given the formula and told to memorize it.

[lonelywuffy]

After finishing my Engineering degree, where I use the right angle triangle a million times, I finally found out WHY we can do this haha

[liliacfury]

3:24 if you confused by what happened here, (a+b) squared is basically (a+b)(a+b) and if you distribute that, a times a is a squared, + a times b which is ab, + b times b which is b squared, plus b times a which is ba, or ab. So now we have the terms a squared. b squared. ab. and ab. Since were trying to add them all together ab plus ab is just 2 times ab. 2ab. So now its 2ab + b squared + a squared. Or in her case using associative property of addition she moved around the terms. That's how she got that equation.

[learnerlearns]

Beautiful presentation of this elegant proof. Thank you!

[lakshayyadav]

GOOD EXPLANATION WITH BEAUTIFUL DIAGRAMS, SPEECH AND EXPRESSIONS
...

[learnphilosophy]

Aw I love this proof. So simple but the fact you can visualise it is nice

[felipesdam]

This class, it's so completed. I've learned more about it that has showed the foundation of this theorem. Thanks ...

[learnphilosophy]

It's just as good as Euclid's proof that there are infinitely many primes. Proofs are the best thing in mathematics.

[learnphilosophy]

They never showed you these proofs in school but i loved to go look them up and i loved being able to understand for the first time

[lucyhendry]

Oh my gosh this helped so much! I had math homework that asked me to prove Pythagoras theorem and it made no sense to me at all. I watched other videos but they didn't really help at all! I used this and it totally made it so much easier for me to understand! Thank you!

[firedancerdk]

Beautifully done! The shortest most elegant and precise proof of the Pythagorean Theorem. I am almost sad that summerhollidays are coming... :D :D

[ashutoshsuman]

Visual in Combination with theory is Awesome.

[josephwilles]

Your aesthetics equal your timbre and your articulate way you explain this proof.

[kenlezzy]

Super High Five & Quod Erat Demonstrandum Gorgeous !

Well done Socratica, Please keep up the awesome work.

Best Regards,
Kenneth.

[Coolblueocean]

Really one of the best videos on the topic.

[tekharthazenyatta]

As The Truthful Channel noted, this proof should be taught in all high school geometry classes. First, it's not difficult to understand once the trick is laid out for you as in this video. Second, a simple proof like this demystifies the theorem and gives the students the feeling they're not expected to be passive robots tasked with memorizing formulas of dubious utility. Third, the proof gives insight into mathematical ingenuity. An instructor can instill the feeling that every single student in the class could have come up with this proof with just a little perseverance and willingness to think. You only need to know a bit of algebra and the area formulas for squares and triangles. Such an approach, which avoids the subtle implication that students are intellectually incapable or too disinterested to understand the origin of famous results, can provide an early trigger to a mathematically talented students who otherwise might never have considered studying the subject seriously.

[krish]

Elegant! - with the least assumptions and using the very basics of algebra and Geometry.

[stormplayzop]

Great video, beautiful explanation. Thanks

[danmichael]

Good video, best I have seen. Here is an important tip. The Pythagorean Theorem works in 3 dimensional space. So, consider x, y, and z (elevation coordinates). Then x squared + y squared + z squared = length squared... So for example. imagine a squared off room. What is the length from a corner to a spot on the ceiling somewhere in the room? I you know its x, y and z coordinates...use the Pythagorean theorem. I use this in machining, outside measurements, etc.

[randellporter]

I love her explanation.   It's very under understandable.