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- New webpage at www.vadimkulikov.org March 24, 2017
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# Monthly Archives: February 2010

## Sorry I Am Late

Please comment your solutions, questions and remarks.. How many of the statements below the line are true? 2/5 ———— This post was not published on Wednesday 24. February 2010 There are at least 2 true statements in this post (after … Continue reading

Posted in Logic, Recreation, Wednesday Problem
3 Comments

## Games in Topology (Another Proof of Brouwer’s Fixed Point Theorem)

Theorem (Brouwer’s Fixed Point Theorem, BFPT). Suppose that [tex]B\subset \mathbb{R}^n[/tex] is the closed n-dimensional unit ball and [tex]f\colon B\to B[/tex] is a continuous function. Then there exists a point [tex]x\in B[/tex] such that [tex]f(x)=x[/tex]. Theorem (Jordan’s Curve Theorem) Let [tex]f\colon … Continue reading

Posted in Combinatorics, Games, Mathematics, Topology
Tagged Brouwer's Fixed Point Theorem
2 Comments

## Pinocchio Is Omnipotent

Please visit my new website at www.vadimkulikov.org to find more about mathematics, science, cognitive science and art!

Posted in Logic, Mathematics, Philosophy, Recreation
15 Comments

## More Tricks With Triangulations

Please comment your solutions, questions and remarks.. I learned this riddle from Sergei Chmutov. It is also a problem concerning triangulation and sharp angled triangles. Suppose we have a triangulated regular polygon with odd number of edges. The vertices of … Continue reading

Posted in Geometry, Mathematics, Recreation, Wednesday Problem
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## Stable Marriages

Suppose n men and n women survived after a spaceship crush on a planet orbiting Alpha Centauri. They happen all to be heterosexuals and all single (or their partners died in the crush). Each man then ranks women in order … Continue reading

Posted in Combinatorics, Mathematics, Recreation
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## Triangulation

Please comment your solutions, questions and remarks.. In the last week’s many in one post I explained what is a triangulation. Can you triangulate a square using only sharp angled triangles (i.e. triangles whose all angles are <[tex]\pi/2[/tex])? For example … Continue reading

Posted in Geometry, Mathematics, Recreation, Wednesday Problem
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## Brouwer’s Fixed Point Theorem: Many in One Post

In this post I will (1) give a simple proof of Brouwer Fixed Point Theorem (2) fulfill the promise given here (3) present the Wednesday Problem in the form fill in the details in the below text Theorem (Brouwer’s Fixed … Continue reading

Posted in Combinatorics, Mathematics, Topology, Wednesday Problem
Tagged Brouwer's Fixed Point Theorem
2 Comments