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- New webpage at www.vadimkulikov.org March 24, 2017
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# Monthly Archives: November 2009

## Tic-tac-toe And A Non-Constructive Proof

Usually the game tic-tac-toe is played on an infinite board (i.e. 30 times 40 or something). The two players draw X:s and 0:s to the squares of a notepad paper. Player 1 (beginner) is the X-drawer and the Player 2 … Continue reading

Posted in Combinatorics, Games, Mathematics, Ramsey Theory, Recreation
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## Erdös and the individual property of dimensions 1 and 2.

Some time ago I read a biography of Paul Erdös titled ‘my brain is open’ written by Bruce Schechter. The book contains some popular exposition of math. As a biography the book is good, but much of the mathematics and … Continue reading

Posted in Geometry, Mathematics, Recreation
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## A liar’s paradox

I will hereby argue that I am the Pope. Consider the following sentence: If this sentence is true, then I am the Pope. It is an implication, i.e. a sentence of the form [tex](A\to B)[/tex], where A is “this sentence … Continue reading

Posted in Philosophy, Recreation
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## Continued fractions and strange homeomorphisms.

Usually one thinks of real numbers represented by a sequence (possibly infinite) of numbers between 0 and 9. For example [tex]34,140414\dots[/tex] One can use various bases like binary, hexadesimal, but the most common is decimal, although with the growing trend … Continue reading

Posted in Calculus, Mathematics, Topology
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