# Followup to Favorite Proof

Results to Favorite Proof:

What's your name/twitter? Name of proof Link to proof somewhere online... Why do you like this proof? Additional testaments of love for this proof Additional testaments of love for this proof ...
@dandersod Euclid's Proof of Infinte Primes link Love proof by contradiction. Simple, powerful, easy to understand. From the book
@sophgermain Why square root of 2 is irrational link It's the first proof i show students and it's simple.
@nik_d_maths Induction for sum of squares link Proof by induction is fun, and this involves enough algebra for students to feel they have done something, while being short enough to use early on I love induction?
@stwwilkinson Uncountability of the real numbers (Cantor) link very simple to explain, yet challenges a lot of intuitive notions about infinity The set up for this proof -- the countability of the rational numbers -- is also mind blowing.
@MrHonner Midline of a Triangle link Elementary, but powerful idea in geometry; several different ways to think about why it's true Great way to demonstrate the power of coordinate geometry for proof Leads to beautiful results like Varignon's Theorem
@Moko58 Product of 2 odd number is an odd number link Even beginners can attempt this proof. this is a great proof.
@mpershan Incompleteness of axioms of arithmetic link It's problably the hardest mathematical idea that I even sort of understand, which is definitely part of why I like it, but the self-referential sentence is brilliant and all sorts of cool things follo wform it.
@mathymcmatherso Geometric Proof of the Pythagorean Theorem link Has a visual and algebraic component that go hand-in-hand. Personally: most convincing and direct proof of pythagorean theorem I've ever seen
@j_lanier There exists an irrational number that when raised to an irrational power results in a rational number. link I like this proof because it is simple; it yields a positive result, rather than a "there exists no..."; and it's concrete but so delightfully non-constructive--we find out that there exists such a thing without having a single example of it! So cheeky. I can't promise that it's my favorite ever, but it's a dang neat proof.
@DanielPearcy Can't pick between irrationality of root(2), infinitely many primes, uncountability of reals Looks like I'm a sucker for proof by contradiction. Funnily enough I don't know many recent (last 100 years) proofs

A pretty common theme: Simplicity in presentation or Visual Component.

<snark>Note: No 2 column geometry proofs are found in this list.</snark>

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