Uploaded May 2025 | Updated September 2026, 2 weeks ago
There are so many proofs of the Pythagorean theorem, and often we learn Euclid's proof from Book I of the elements in school, or we learn some other cute variation involving a dissection and translation of rigid pieces. But there is a very simple proof which only requires to draw one altitude then make some basic similarity arguments. I'll show you this simplest proof of the Pythagorean theorem today and explain why Euclid might not have used it, and why it might not show up during class lectures. #geometry #maths
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More Math Chats: youtube.com/playlist?list=PLztBpqftvzxXQDmPmSOwXSU9vOHgty1RO
Outro music: youtube.com/shorts/tfifiSdTZRg
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SOURCES
The Pythagorean Theorem: A 4,000 Year History by Eli Maor: amzn.to/4kBtBg6
cd1.edb.hkedcity.net/cd/maths/en/ref_res/material/mss_e/exemp21.pdf
cut-the-knot.org/pythagoras
http://aleph0.clarku.edu/~djoyce/elements/
en.wikipedia.org/wiki/Pythagorean_theorem#Other_proofs_of_the_theorem
0:00 Intro
0:54 Euclid's Elements
2:34 The Simplest Proof
6:58 Trig?
8:20 Why Didn't Euclid Use It
11:16 Greek Perspective
12:31 Arthur Quote
13:05 Mathshion
13:26 Conclusion
There are so many proofs of the Pythagorean theorem, and often we learn Euclid's proof from Book I of the elements in school, or we learn some other cute variation involving a dissection and translation of rigid pieces. But there is a very simple proof which only requires to draw one altitude then make some basic similarity arguments. I'll show you this simplest proof of the Pythagorean theorem today and explain why Euclid might not have used it, and why it might not show up during class lectures. #geometry #maths
Join Wrath of Math to get exclusive videos, lecture notes, and more:
youtube.com/channel/UCyEKvaxi8mt9FMc62MHcliw/join
Check out the coolest math clothes in the world: mathshion.com
More Math Chats: youtube.com/playlist?list=PLztBpqftvzxXQDmPmSOwXSU9vOHgty1RO
Outro music: youtube.com/shorts/tfifiSdTZRg
Follow Wrath of Math on...
● Instagram: instagram.com/wrathofmathedu
● TikTok: tiktok.com/@wrathofmathedu
● X: https://x.com/wrathofmathedu
SOURCES
The Pythagorean Theorem: A 4,000 Year History by Eli Maor: amzn.to/4kBtBg6
cd1.edb.hkedcity.net/cd/maths/en/ref_res/material/mss_e/exemp21.pdf
cut-the-knot.org/pythagoras
http://aleph0.clarku.edu/~djoyce/elements/
en.wikipedia.org/wiki/Pythagorean_theorem#Other_proofs_of_the_theorem
0:00 Intro
0:54 Euclid's Elements
2:34 The Simplest Proof
6:58 Trig?
8:20 Why Didn't Euclid Use It
11:16 Greek Perspective
12:31 Arthur Quote
13:05 Mathshion
13:26 Conclusion
