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 | Leave a comment

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 | Leave a comment

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 | Leave a comment

Wednesday Problem

I shall start a tradition of a Wednesday Problem. Thus every Wednesday I shall (try to) post a mathematical puzzle or an exercise. I will try to indicate the level of the problem on the scale 1-5, 1=simple, 5=advanced. High … Continue reading

Posted in Meta, Wednesday Problem | 8 Comments

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 | 8 Comments

The First Step

This is a new blog. Its title is White Math [upd: later changed to Walks On Math] and the description says “Mathematics for millions of people”. My idea is to start blogging once or twice a week on some interesting … Continue reading

Posted in Meta | 4 Comments

Not yet a blog, but already [tex]\LaTeX[/tex]

Posted in Meta | 3 Comments