The Most Beautiful Proof sqrt(2) is Irrational

The irrationality of sqrt(2) was known to the Greeks, and the classic proof of this fact appeared in at least some versions of Euclid's elements. The proof most commonly shown, often attributed to Hippasus, is arithmetical and not geometric whatsoever. But in year 2000 a proof appeared from Tom Apostol, showing the irrationality of the square root of 2 in a beautiful stroke of geometric construction. We discuss the proof, concerning isosceles right angled triangles, today. #mathematics #maths Join Wrath of Math to get exclusive videos, lecture notes, and more: https://www.youtube.com/channel/UCyEKvaxi8mt9FMc62MHcliw/join The Classic Proof that sqrt(2) is Irrational: https://youtu.be/2FlMkP7jqQo More math chats: https://www.youtube.com/playlist?list=PLztBpqftvzxXQDmPmSOwXSU9vOHgty1RO SOURCES https://fermatslibrary.com/s/irrationality-of-the-square-root-of-2-a-geometric-proof https://www-fourier.ujf-grenoble.fr/~marin/une_autre_crypto/articles_et_extraits_livres/irationalite/Apostol_T._irationality...-.pdf ★DONATE★ ◆ Support Wrath of Math on Patreon: https://www.patreon.com/join/wrathofmathlessons ◆ Donate on PayPal: https://www.paypal.me/wrathofmath Follow Wrath of Math on... ● Instagram: https://www.instagram.com/wrathofmathedu ● TikTok: https://www.tiktok.com/@wrathofmathedu ● X: https://x.com/wrathofmathedu 0:00 Intro 3:38 Proof Begins! 5:48 There Exists an Integer Triangle 7:36 Construction! 9:26 The Key Triangle 13:26 Conclusion