Pythagorean Theorem - Behold!

This is a short, animated visual proof of the Pythagorean theorem (the right triangle theorem) following essentially Bhāskara's proof (Behold!). 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.

This animation is based on a proof due to Bhāskara. For a static version of this proof, see Roger Nelsen's first "Proof Without Words: Exercises in Visual Thinking" compendium (page 4). You can also check out Howard Eves' "Great Moments in Mathematics (Before 1650)" page 29-32.

For other proofs of this same fact check out:

#math #manim #pythagoreantheorem #pythagorean #triangle #animation #theorem #pww #proofwithoutwords #visualproof #proof #mathshorts #mathvideo

To learn more about animating with manim, check out:

[GusBatista]

Is this theorem the most proven thing ever?

[misaelarvizu]

The Mathematical Symmetricalness of that Proof is Insane... how it concluded to c^2 = a^2 + b^2

[IceMaster-si]

Wouldnt it be b-a square?

Edit: mb I thought shorter side was a

[Jason-os]

Cheer~~~relating to or characteristic of the Greek philosopher Pythagoras or his ideas.😊

[xjuhox]

Lovely, again. But we always need to use an equivalent fact: the sum of the angles in a triangle is 180 degrees.

[retinadothegamer]

hurray for neww math, newhewhew math, so simple, so very simple, that only a child can do it!

[Jayman]

Bro said in a more complicated way than my colleagues' math teacher

[RobG]

That c by c square was included in Edward Tufte's book The Visual Display of Quantitative Information which is recommended reading for anyone interested in maths.

[rajeevkhanna]

Thanks for the visual proof.
The moment you proved that the central square has a side length of a-b, it can be simplified to:
c^2 = (a-b)^2 + 4 (a*b/2)
which straightaway simplified to a^2 + b^2

[willy_larry]

πa^2+πb^2=πc^2 is my favorite. If your asking what a line is in a different dimension, just pick one and use it ... The fact 90 degrees is already a circular term brings home the rotated perspective and any triangle can be skewed into this perspective of a 90 degree triangle, calculated and skewed back to its original obtuse and still know the length of the line... Just use circles... Quit with the squares and trying to visually prove it. Its just measures of circles or cones or whatever shape you put to the number to define an area of its line because the area of the circle and the area of the square created by the math from that line are not the same for every shape yet if you stay in circular math or square math its still the area + the area = the area.

[aweirdguy]

I've been reminded of the torture i have to go through with this in school.

[timothyennis]

C by C square, Nah
Roblox logo, Yeah

[GaurangAgrawal]

funny how a few years ago, I thought we can't prove Pythagorean theorem and now, I know a lot of different ways to prove this theorem.

[doomsdaylamb]

Schools trying to credit any mathematician east of Greece challenge (impossible)