Meditation in Mathematics - PHP, Bose Olympiad, Gravity in Mars

Dear students, 

Let the world engage in rat race. We will focus on deep and beautiful learning. 

Here is a beautiful problem that we worked on this week.

Suppose there are 5 points spread in 1 by 1 square field. The points can be at the corners, on the edges or inside the square. Show that the two nearest points are 1/rt 2 or less distance apart.

Can you try this problem? It uses the Pigeon Hole Principle (PHP) which says:

If you want to put n+1 pigeons in n boxes then there is at least one box with more than one pigeon in it. 

Do not be fooled by the simplicity of PHP. Using it we can do some really challenging problems. 

Another interesting idea that came up in the Physics Olympiad Program.

This is the velocity versus time graph of a particle moving in straight line. Can you draw the graph of its acceleration (versus time)? 

In the Physics Virtual Lab a few kids are simulating gravity of Mars. They hope to create projects leading up to Google Science Fair.

We want kids to break free from rote-learning and formula-cramming. Mathematical Science, be it Mathematics, Physics, or Informatics should be fun and problem-focussed. Moreover the problems should inivite curiosity and imagination. 

One such book, that a few of our Bose Olympiad Awardees received is One two three.. infinity by Gammow. If you like the wonderful world of mathematics, you will surely fall in love with this book. 

The Bose Spring Olympiad is coming up in April. If you want to do some real fun problems in teams (and individually), you may try it here: 

All the best!

Dr. Ashani Dasgupta

Cheenta 
Passion for Mathematics