# 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

Theorem (Brouwer’s Fixed Point Theorem, BFPT). Suppose that $$B\subset \mathbb{R}^n$$ is the closed n-dimensional unit ball and $$f\colon B\to B$$ is a continuous function. Then there exists a point $$x\in B$$ such that $$f(x)=x$$. Theorem (Jordan’s Curve Theorem) Let $$f\colon … Continue reading Posted in Combinatorics, Games, Mathematics, Topology | | 2 Comments ## Pinocchio Is Omnipotent Please visit my new website at www.vadimkulikov.org to find more about mathematics, science, cognitive science and art! Posted in Logic, Mathematics, Philosophy, Recreation | 15 Comments ## More Tricks With Triangulations Please comment your solutions, questions and remarks.. I learned this riddle from Sergei Chmutov. It is also a problem concerning triangulation and sharp angled triangles. Suppose we have a triangulated regular polygon with odd number of edges. The vertices of … Continue reading Posted in Geometry, Mathematics, Recreation, Wednesday Problem | Leave a comment ## Stable Marriages Suppose n men and n women survived after a spaceship crush on a planet orbiting Alpha Centauri. They happen all to be heterosexuals and all single (or their partners died in the crush). Each man then ranks women in order … Continue reading Posted in Combinatorics, Mathematics, Recreation | Leave a comment ## Triangulation Please comment your solutions, questions and remarks.. In the last week’s many in one post I explained what is a triangulation. Can you triangulate a square using only sharp angled triangles (i.e. triangles whose all angles are <[tex]\pi/2$$)? For example … Continue reading

Posted in Geometry, Mathematics, Recreation, Wednesday Problem | Leave a comment

## 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

| | 2 Comments