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Square root of R^3
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Asking cute questions is great.
Answering such questions is a nice challenge.
An article by Mark Dominus about this topics is here ( EN ).
Cardinality theorem *****
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Two lines proof of the Cantor-Schroeder-Bernstein theorem ( EN ).
Swindle? *****
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YES, you can swindle and prove theorems similar to this:
Swindle can be correctly used in many proofs, e.g.
Irreducibility of the sphere
Cantor–Bernstein–Schröder theorem ( Wiki EN )
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Can you add the next one to the list?
On rare integers between 0 and 1 *****
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Sexy & clean proof that π is irrational on Dror Bar-Natan pages in 5 full stopped sentences written on a CD envelope ( EN ). The shortest & simplest one?
A Streamlined Proof of an Essential Calculus Fact *****
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GREAT NEW PROOF of the Fundamental Theorem of Calculus
Stephen M. Walk: A Streamlined Proof of an Essential Calculus Fact, The American Mathematical Monthly, Vol. 117, No. 9 (November 2010), pp. 832-833.
(JSTOR abstract EN, idea online EN, CZ)
Formalized definitions and proofs **
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Mizar system for such style writing math ( wiki EN, home EN ).
On formal discontinued project QED ( wiki EN ).
Archive of Formal Proofs **
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An alive collection of formal proof materials ( EN ), organized in a way of a scientific journal.
Behold Proof of the Pythagorean Theorem *****
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Bhaskara's (1114 - ca. 1185) Dissection Proof of the Pythagorean Theorem ( animation EN ).
Infinitude of primes using basic topology *****
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Fürstenberg's proof of the infinitude of primes using basic topology ( wiki EN ).
Proofs in Wiki ***
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A categorized list of proofs online ( wiki EN ).