Sunday, June 20, 2010

How Many Triangles?

Here’s a question: Take an equilateral triangle ( △) and make 4 (and only 4; 5 or more should be impossible!) triangles out of it by drawing a few lines in its interior such that at least one edge is common to each pair of  these 4 triangles!

This problem has two solutions: One has a trick to it and the other one is straightforward. The tricky one is easy to find but finding the straightforward one requires thinking out of the box as one of my friends put it!

Here’s the thought process that leads to both of these solutions:

This video is ‘inspired’ by this video titled Metamorphosis of the Cube.

During the making of my ‘trigon’ video, I started thinking about 3D rotations and found a very concise (and hence, beautiful!) solution to a problem. A ‘problem’ which I had encountered while going through the chapter ‘Spinors’ in Misner, Thorne & Wheeler’s Gravitation about 3 years back! That chapter does have the solution but somewhy I never got comfortable with it! To get to know the problem and the solution, head to the post on my Physics’ blog:

3D Rotations