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
Category Archives: Geometry
Time Limit: One Minute!
I found this lovely geometrical riddle in Martin Gardner’s book “My Best Mathematical and Logic Puzzles”. The most lovely thing about it is that Gardner gives a time limit: one minute! So, now draw out your stopwatch and read the … Continue reading
Posted in Geometry, Mathematics, Popular, Recreation, Wednesday Problem
11 Comments
Walks on Planets
My gps-equipped radiowave controllable robot Lori is somewhere on the surface of Earth. I order her to drive 100 miles South and she obeys. Then I order her to drive 100 miles West and she obeys. Then I order her … Continue reading
Posted in Geometry, Mathematics, Popular, Recreation, Wednesday Problem
7 Comments
Doodling with Fractals and Persistent Worms.
Suppose we have a rubber line of length 1 m and a worm at the other end. The worm moves 10 cm in a minute and its goal is to reach the other end moving along the rubber line. However … Continue reading
Posted in Combinatorics, Geometry, Mathematics, Recreation
1 Comment
Splitting A Rectangle
Find all ways to cut a rectangle into two connected pieces of equal area so that they can be rearranged to get a new rectangle with different dimensions (side lengths) than the orgininal one. I already know countably many ways. … Continue reading
Posted in Geometry, Mathematics, Recreation, Wednesday Problem
2 Comments
Sphere
Pick randomly three points on the unit sphere. The geodesic triangle with these points as vertices divides the sphere into two parts. What is the probability that the north pole is contained in the smaller of these parts? For instance … Continue reading
Posted in Geometry, Mathematics, Probability, Wednesday Problem
Leave a comment
Map Colouring Problem And Compactness
Suppose G is a planar graph embedded into the plane. The graph divides the plane into regions. Let us say that two regions are adjoint if they have a common edge. Question: (Q) Is it possible to colour the regions … Continue reading
Posted in Combinatorics, Geometry, Logic, Mathematics, Topology
Leave a comment
Irrational Rectangles
Please comment your solutions, questions and remarks.. This riddle is not easy. I solved it only after I got a hint. I got the hint without wanting it though, and I was already thinking in the right direction; so with … Continue reading
Posted in Geometry, Mathematics, Wednesday Problem
9 Comments
How To Find Your Way Out of Woods
Please comment your solutions, questions and remarks.. A lumberjack got lost in a forest. He knows that the area of the forest is S and that there are no meadows in the forest. Show that he can get out from … Continue reading
Posted in Geometry, Mathematics, Recreation, Wednesday Problem
3 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
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
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