Why Are There 180 Proofs for Euclid's Theorem? скачать в хорошем качестве

Why Are There 180 Proofs for Euclid's Theorem?

In this video, we investigate the question of why so many mathematical theorems have more than one proof. Often the most famous theorems even have hundreds of different proofs. But why do so many mathematicians “waste” their time reproving the same theorem over and over again? To answer this question, we look into three different proofs of Euclid’s Theorem (i.e. there are infinitely many primes) to see that each proof provides us with new insights and is therefore not just a repetition. 0:00 Intro 1:09 Euclid (Proof) 3:42 Euclid (Beauty) 4:53 Erdős (Proof) 14:37 Erdős (Beauty) 16:37 Furstenberg (Proof) 24:08 Furstenberg (Beauty) 24:55 Conclusion Notes: 15:25 If you want to learn more why the sum is equal to π²/6 then I recommend    • Why is pi here?  And why is it squared?  A...   17:05 There is a technically a difference between a family and a set. However, for this video the difference is not important. If you are interested, I suggest reading the Wikipedia article “family of sets”. 17:55 Usually, we only require that the intersection of two elements in tau is again in tau. However, using induction, it can be shown that this definition is equivalent to the definition used in the video. 21:05 For example, the intersection of N_{3, 1} and N_{5, 2} is equal to N_{15, 2}. Additional Material: M. Aigner, G. M. Ziegler: Proofs from the Book, Spinger (2018), Chapter 1 P. Erdős: Über die Reihe sum 1/p (in German), Mathematica, Zentralblatt (1938) 18,343 Music: Majestous by Blue Dot Sessions https://app.sessions.blue/browse/trac... J. S. Bach “G-Sharp Minor Fugue”, WTK 2 Maisie Dreamer by Blue Dot Sessions https://app.sessions.blue/browse/trac... Spiro's Etude by Blue Dot Sessions https://app.sessions.blue/browse/trac... Warm Fingers by Blue Dot Sessions https://app.sessions.blue/browse/trac... Maisie Dreamer by Blue Dot Sessions https://app.sessions.blue/browse/trac... R. Schumann “Kinderszenen: Scenes from Childhood", Op. 15 Interpreted by Donald Betts Additional Sources: Painting of Euclid by Jusepe de Ribera: https://commons.wikimedia.org/wiki/Fi... Picture of P. Erdős by Unknown: https://sites.math.rutgers.edu/~sg110... Picture of H. Furstenberg by Yosef Adest: https://commons.wikimedia.org/wiki/Fi... Picture of G. H. Hardy by Unknown: https://commons.wikimedia.org/wiki/Fi... Picture of J. H. Conway by Thane Plambeck: https://commons.wikimedia.org/wiki/Fi... Picture of cat “Bonnie” by my mother “Mug and Torus morph” by LucasVB: https://en.wikipedia.org/wiki/File:Mu...