Ten Epic Pythagorean Proofs Without Words

This video is a compilation of ten shorter videos I have created showing various visual proofs without words of the famous right triangle theorem (usually referred to as the Pythagorean theorem). To see the original videos (in shorter form and sometimes with words/explanations), check the links below. Of course there are many other visual proofs of this amazing fact, but these are my favorite ten.
Let me know your favorite in the comments!
If you like this video, consider subscribing to the channel or consider buying me a coffee: www.buymeacoffee.com/VisualPr.... Thanks!
Here are the original series videos (along with attribution; for more detailed attribution, see the original videos):
0:00 Introduction
0:07 Hexagon Areas Proof : • Pythagorean Theorem V ... (attribution: Leonardo da Vinci)
1:01 Behold! Proof : • Pythagorean Theorem VI... (attribution: Bhāskara)
1:52 Trapezoid Proof: • Pythagorean Theorem IV... (attribution: James Garfield)
2:37 Adaptation of Euclid's Area Preserving Transformation : • Pythagorean Theorem VI... (attribution : Euclid; Eves/Nelsen)
3:21 Triangle in a Circle Proof : • Pythagorean Theorem II... (attribution: Michael Hardy)
3:59 Scaling Proof : • Pythagorean Theorem I ... (attribution: Frank Burk)
4:40 Hinged Dissection : • Pythagorean Theorem IX... (attribution: Bogomolny's cut-the-knot site)
5:25 Dudeney's Dissection: • Pythagorean Theorem XI... (attribution: Henry Dudeney)
6:10 Pythagoras with Height Lemma : • Pythagorean Theorem VI... (attribution: Roger B. Nelsen and Claudi Alsina)
7:06 Sliding Rectangles Proof : • Pythagorean Theorem II... (attribution: adapted from the Chou pei suan ching)
7:52 Ending citation
If you like the right triangle theorem, you can check out my playlist of proofs and other videos that utilize the theorem:
• Pythagorean Theorem
#math #manim #pythagoreantheorem #pythagorean #triangle #animation #theorem #pww #proofwithoutwords #visualproof #proof #mathshorts #mathvideo
To learn more about animating with manim, check out:
manim.community

[@quay6292]

Triangles similarity is possibly my favourite one up there.

[@MathVisualProofs]

Definitely one of my faves too!

[@matematicke_morce]

The transition into a square at 5:03 is really satisfying!

[@MathVisualProofs]

😀👍

[@avyakthaachar2.718]

Amazing video! Thank you so much 🙏

[@MathVisualProofs]

Thanks for checking it out! Share it with math friends :)

[@RaymondBarbour]

In Dudeney's Dissection it was the one where I couldn't confirm that the yellow square would fit. It must fit but I couldn't see why.

[@MathVisualProofs]

That one takes thought. I have a short in my shorts feed that shows a bit more detail, and there are commenters who fill in the details.

[@asr2009]

it fits because of pythogoras theorem(sarcasm)

[@JavaScripting64]

9 of these are unhinged

[@MathOrient]

Amazing job. Thanks :)

[@MathVisualProofs]

Thank you!

[@philippepujol2806]

Abonné. Liké et partagé. Merci pour ces brillants visuels.

[@anushreemittal6359]

Nice animation 👍
Thanks for taking efforts for this video.
It enriched our creativity while solving problems . This video is surely benefial for maths lovers like me

[@MathVisualProofs]

Thank you so much 😀 Glad you liked it!

[@LittlePaimon]

谢谢！

[@LauraEdgar-xv1bs]

So good!

[@MathVisualProofs]

Thanks! 🎉

[@milonjyotibarman9421]

This was just amazing😮. Mathematics is really fun

[@MathVisualProofs]

Glad you liked it. Thanks for watching ! 😀

[@sanilkumar4082]

Great video.

[@MathVisualProofs]

Thanks!

[@alinayfeh4961]

Thanks 😊

[@MathVisualProofs]

👍😀

[@juliancamiloromerovaron5297]

Hi! that's so interesting, i am learning manim and i would like if you could give us your manim code, thank you man!

[@MathVisualProofs]

I don't have many of my animations publicly (and they could be challenging to parse as I am not very good at commenting my code), but I do have some code available: github.com/Tom-Edgar/MVPS

[@full_legit191]

What property are we using to have the equality in the micheal hardy please ?

[@MathVisualProofs]

First we use Thales triangle to deduce that the triangle with hypotenuse given by diameter is right triangle. That means the two triangles it decomposes into are similar (they are both right triangles and upper angles are complementary). So we use the similarity of those triangles.

[@full_legit191]

Thanks, that is clearer now. It is terrible, I'm in a pretty good university in France, and we don't learn anything about geometry in first and 2nd year of college. I don't know if it is the same everywhere else

[@bigbadbith8422]

This channel is 😊

[@MathVisualProofs]

Thanks!

[@SeanSkyhawk]

I take it that the "waffle cone" proof isn't exactly an intuitive visual one

[@MathVisualProofs]

I would like to animate it. But I want to see it better first.

[@wyattstevens8574]

Trapezoid proof for me!

[@MathVisualProofs]

President Garfield’s!

[@wyattstevens8574]

​@@MathVisualProofsWho were the rest? Just curious.

[@MathVisualProofs]

@@wyattstevens8574the description has attributions listed. There are also links to standalone animations and those descriptions usually have links to original static diagram.