## 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

#### 2 comments:

1. Problem as stated, can not be solved. It should be modified to say that they should share at least "part of an edge" and not "edge". Then it has a solution, but only one. The video that you have, albeit a nice one, doesn't illustrate the solution at all.

2. It does... and that also with the word 'edge' not the phrase 'part of an edge'; read the statement of the problem again!!! Also there are two solutions and both are in the video... Hope you find it!!!