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 ).


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Cardinality theorem *****

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Two lines proof of the Cantor-Schroeder-Bernstein theorem ( EN ).



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Swindle? *****

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YES, you can swindle Wink 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 )


Can you add the next one to the list?

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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 ENCZ)



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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 ).