#3 Pythagorean Theorem Proof: Constructing a Square with side "h"

Hi! Today we are going to see another proof on the Pythagorean Theorem. This is the third of a series of videos in which we will be seeing as many proofs as we can on this fundamental and beautiful theorem. The different proofs on this theorem are in the following playlist:

https://youtube.com/playlist?list=PLfYI1HSKgu4kSDWBcwB5j5gOPiJ9UQV81

This proof consists of placing copies of the original triangle in such a way that we create a square with side "h". From then on, the proof is pretty straightforward.

As always, here are the time stamps of the video:

0:00 Introduction
0:14 Statement of the theorem
0:42 Previous results
0:46 1. The angles of a triangle sum 180º
1:18 2. Area of a triangle
1:41 3. Area of a square
1:56 Summary of the previous resultsm we will need
2:10 Proof of the theorem
-Music:

Goldberg Variations, BWV. 988 - Variation 29

https://musopen.org/music/?query=Goldberg&composer=johann-sebastian-bach

-References:

This is a really standard and famous proof, in my case, I found it on the website "Cut the Knot", which has a bout 100 different proofs on this theorem! If you want to see really creative and fun proofs on this theorem I really recommend visiting this website:

https://www.cut-the-knot.org/pythagoras/

Also, to make this video I used the amazing Python library "Manim" that Grant Sanderson, the creator of 3b1b, developed. Thanks to him and other developers making math animations like those in the 3b1b channel is accessible for anyone! If you want to know more about this, check out the following links:

3b1b channel: https://www.youtube.com/channel/UCYO_jab_esuFRV4b17AJtAw

Theorem of Beethoven: https://www.youtube.com/channel/UCxiWCEdx7aY88bSEUgLOC6A

LazyAIZ: https://www.youtube.com/channel/UCkJV9VaWUY-x3zmDaDEz9Zg/community

Manim community: https://www.manim.community/

Manim github:
https://github.com/ManimCommunity/manim
https://github.com/3b1b/manim

For now, I'm still learning how to use Manim, but when I'm more comfortable with it I will also make videos on how to use it, so stay tuned to the channel!

Видео #3 Pythagorean Theorem Proof: Constructing a Square with side "h" канала Sandro’s Space