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

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

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.

Beautiful presentation of this elegant proof. Thank you!

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

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

Thank you!!! Keep these videos going!!!

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

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

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

awesome explanation guys .Keep up the good work

Really one of the best videos on the topic.

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

Visual in Combination with theory is Awesome.

I've never seen it expressed like this, nice work.

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!

Great video, beautiful explanation. Thanks

Super High Five & Quod Erat Demonstrandum Gorgeous ! Well done Socratica, Please keep up the awesome work. Best Regards, Kenneth.

Nice video. It really helped me a lot. Thank u so much .

Another awesome video, Keep up the great work.

Ur so calm, I love Ur videos. 😻❤ thank u

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

Right-on! Unfortunately I find myself at the end of another Socratica playlist; I’ll have to find another to binge-watch!

thank you soooo much,I was explaining it to my kid and it was so helpful thanks again

Thanks it's very helpful

Well done. Good Explanation

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

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

thanks...that is was very helpful

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.

thank you it helped me a lot

Was really helpful.

Thank you. very simple.

Thank you …. Very well done !!

BRAVÍSIMOOOOOOOOOOOOOOOOOOOOOO!! AWESOME!! Thanks ever so much.

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.

Thank you this helped so much!

THANKS IT HELPED ME VERY MUCH

Excellent video lecture

Nice explanation

Now i understand.i now have an assignment.

THIS ACTUALLY MADE SENSE THIS IS AWESOME

It's nice to see a method that uses algebra and not just rearranging shapes.

This is awesome...

Beautiful.

Thanks for helping me to learn it.

This is a much better way of proving Pythagoras,s theorem rather than just saying that a squared plus b squared equals c squared which is not in don't as can easily be shown but that in it self don't prove that the triangle is a right angled but your method makes this clear .

Could you do a proof for De Gua's theorem?

Nice, thank you.

Thank you so much.

Brilliant!

Good explanation

Try this: 0:22 a²+b²=(a+b)²-2ab Consider: c²+2ab Factoring: c²(1+2(a/c)(b/c))=c²(1+2sinAcosA) The value 2ab/c² is the double angle trig ratio sin2A. Consider: (a+b)²/c² This is equivalent: (sinA+cosA)² Expanding out: sin²A+cos²A+2sinAcosA Subs for 2sinAcosA & due to “†” & “‡” (bottom), this is: 1+sin2A. From “1”, have: c²+2ab=c²(1+sin2A) From “2”, have: (a+b)²/c²=1+sin2A. Therefore: c²=(c²+2ab)/(1+sin2A)=(c²+2ab)/(a+b)²/c² Multiplying by (a+b)²/c² on both sides: (a+b)²=c²+2ab => (a+b)²-2ab=a²+b²=c² …QED 😊. (†)From the compound angle formulas(‡) for sin & cos, you get double angle formulas for those, and from cos2A you get: 1-2sin²A=2cos²A-1=cos2A => 2=2(cos²A+sin²A) Therefore: 1=(cos²A+sin²A) (‡)Proof in this video: “Angle sum identities for sine and cosine” by blackpenredpen

If this had been my Maths teacher, I would have been the best student in my class.

What is a good mathematical journal to present a new proof of the Pythagorean Theorem? I proof it differently and have checked with more than 400 solutions and did not find my solution, so I want to submit it for publication. Can you suggest a journal?

Nice... thanks

What a nice teacher

Very good

Le théorème de Pythagore s’obtient directement à partir d’une propriété du triangle rectangle selon laquelle on engendre deux triangles semblables au triangle d’origine en projetant une droite à partir d’un de ses sommets sur le côté opposé. On montre facilement que le triangle rectangle est le seul à avoir cette caractéristique. L’hypoténuse est alors divisée en deux par cette ligne projetée qui n'est autre que la hauteur partant de l'angle droit. Chaque angle non droit peut alors s’interpréter de deux façons, soit avec l’hypoténuse en entier soit avec une partie seulement, auquel cas c'est l’autre côté qui est cette fois-ci l’hypoténuse du triangle rectangle inscrit. Voilà d’où vient a^2, le côté a est tantôt hypoténuse tantôt non hypoténuse, donc tantôt au numérateur tantôt au dénominateur dans la formulation issue des triangles semblables, les produits en croix donnent a^2. On obtient le même type d'équation avec l’autre angle non droit, l’addition des deux égalités donne le théorème de Pythagore. Bien à vous

2 new orleans high school students is using this same explanation to say they've proven the theorem.

Is there a name for this proof? Also, it would be nice if you could explain why the proof fails when the triangle is not a right triangle. Presumably because you cannot form a square when you align them?

We had to learn this for our exams, I spent about 2 hours last night trying to remember it and all I got was a bunch of ultimately useless truths about a right triangle by using sin cos and tan of two triangles made using H as an adjacent line to the hypotenuse through the 90deg angle of the original right triangle. Gave up once I got an equation that boiled down to 0 = 0

This woman is a stunner....

Oh my god, how do people think of so good constructions, I can't even think a Little.

thank you :)

We'll done!

i love this.

Please answer me if you can: Do we know why the circle has 360 degrees and why is 1 degree the foundation of common angle measurements? Because in all these gemotric theorums etc. we use these as the base, unless the ancients proved them in some other fashion.

Great!..

Thank you :)

Thanks

That's a really intuitive proof. I always see people draw squares just on the sides of the triangle and summing their area together and the areas being the same. Thats just a circular argument though and it bothered me.

I've noticed that all of the people your channel feature are beautiful.

Great video but how do you multiply out the (a+b)² to get a²+2ab+b² ?

I'm going to fail

Amazing

The Pythagorean Theorem is not only a famous theorem, but the hardest to pronounce.

To be a bit more creative.... rather then just using areas... a^2 + b^2 = c^2 rearrange a^2 = c^2 - b^2 = (c + b)(c- b) a*a = (c + b)(c- b)...... intersecting chords a/(c- b) = (c + b)/a ....... similar triangles

Wow m a student nd its helpfull for me

nice 1

I have a disability that makes difficult to remember things. So the way solve this problem is by understanding. And this an prime example.

fortunately the most beautiful proof of Pythagorean theorem and the female speaker too.

Wow very simple.

En cuanto al Triángulo rectángulo, donde se aplica el "Teorema de Pitágoras", tengo un nuevo concepto sobre este "Teorema" voy a llamar "Teorema de Sidney Silva" sigue mi relato; Condición de Existencia de un Triángulo; para construir un triángulo no podemos utilizar ninguna medida, tiene que seguir la condición de existencia: Para construir un triángulo es necesario que la medida de cualquiera de los lados sea menor que la suma de las medidas de los otros dos y mayor que el valor absoluto de la diferencia entre estas medidas, esto está relacionado en el Teorema de Pitágoras, ya en el "Teorema de Sidney Silva" podemos sí utilizar cualquier medida, siguiendo la condición de existencia; donde puedo construir un Triángulo que la necesidad de la medida de cualquiera de los lados sea mayor que la división de las medidas del lado más pequeño del valor absoluto (fórmula a ^ 2 = b ^ 2: c ^ 2 o b ^ 2: c ^ 2 En el caso de la hipotenusa será menor que los catetos, y siempre los catetos serán mayores que la Hipotenusa, donde los números 5,4,3 ya están obsoletos, cuando cambien de números, será aproximado , redondeado y simplificado, ya por mi "Teorema de Sidney Silva" siempre será exacto con 100% exactos .. !!!!, Sr Sidney Silva.

perfect

Pls ma a full video on Pythagoras rule from the beginning to the end pls a video ma pls reply I need it aloy

Oh Its great...why dont the teachers teach like this instead of giving the formula directly...thank u so much..Raj from India

Nice

this helps a lot as an Indian student

thanks beyb

awesome

Peace😊 Love from India🙏

nice

My mind is blown 🤯🤯

i love u teacher 😍

never ever took interest in the proof........... thanks a lot very interesting .........

👏👏👏

Tq mam

1:02 Not random; arbitrary!

Does anyone know the name of this proof?