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

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

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

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

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

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 <$$\pi/2$$)? For example … Continue reading