What's your favorite proof?

	A	B	C	D	E	F	G	H	I
1		The most beautiful, wonderful, inventive proof you know?
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4		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	Additional testaments of love for this proof	...
5	1	@dandersod	Euclid's Proof of Infinte Primes	http://primes.utm.edu/notes/proofs/infinite/euclids.html	Love proof by contradiction. Simple, powerful, easy to understand.	From the book
6	2	@sophgermain	Why square root of 2 is irrational	http://www.homeschoolmath.net/teaching/proof_square_root_2_irrational.php	It's the first proof i show students and it's simple.
7	3	@nik_d_maths	Induction for sum of squares	http://www.proofwiki.org/wiki/sum_of_sequence_of_squares	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?
8	4	@stwwilkinson	Uncountability of the real numbers (Cantor)	http://en.wikipedia.org/wiki/Cantor's_diagonal_argument	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.
9	5	@MrHonner	Midline of a Triangle	http://mrhonner.com/workshop-session-4-summary/	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
10	6	@Moko58	Product of 2 odd number is an odd number	http://www.algebra.com/algebra/homework/word/numbers/Numbers_Word_Problems.faq.question.26812.html	Even beginners can attempt this proof.	this is a great proof.
11	7	@mpershan	Incompleteness of axioms of arithmetic	http://www.logicmatters.net/igt/further-notes/godel-without-tears/	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.
12	8	@mathymcmatherso	Geometric Proof of the Pythagorean Theorem	http://mathandmultimedia.com/2010/02/03/pythagorean-theorem/	Has a visual and algebraic component that go hand-in-hand. Personally: most convincing and direct proof of pythagorean theorem I've ever seen
13	9	@j_lanier	There exists an irrational number that when raised to an irrational power results in a rational number.	http://www.cut-the-knot.org/do_you_know/irrat.shtml#answer	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.
14	10	@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
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