Like this blog?- New webpage at www.vadimkulikov.org March 24, 2017
- (Ir)rational Behavior of Calculation October 18, 2011
- The Product of Topological Spaces Does Not Obey Cancellation October 12, 2011
- Wild Embeddings October 11, 2011
- Progress October 4, 2011
- Class-metric August 24, 2011
- Intellectual Lazyness August 22, 2011
- Time Limit: One Minute! August 17, 2011
- Douglas Hofstadter: I Am a Strange Loop. August 15, 2011
- 0.999999……=1? (continuation) July 10, 2011
- Walks on Planets July 5, 2011
- 0.999999….. = 1? July 3, 2011
- Prisoners’ problem 6 June 29, 2011
- I am back! June 28, 2011
- A non-associative “group” March 21, 2011
- Why I haven’t blogged March 21, 2011
- Doodling with Fractals and Persistent Worms. January 2, 2011
- Five groups November 23, 2010
- Splitting A Rectangle November 17, 2010
- Sphere November 10, 2010
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
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[/tex])? 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
Posted in Combinatorics, Mathematics, Topology, Wednesday Problem
Tagged Brouwer's Fixed Point Theorem
2 Comments