What is the average distance between points in a square?

In my family we love riddles, puzzles and mathematical challenges and it’s not unusual that we share weird problems via our whatsapp group. A couple weeks ago, we received the following question from my brother Alvaro: “what is the average distance between two points in a square?”

Solving this problem mathematically with integrals exceeds my current level of skill, but I realised it would be rather easy to solve this for a discrete amount of points in a square NxN matrix. I could solve it for a matrix of 10×10, 20×20 and see whether the solution converged to a number.

With my raspberry pi, connected via ssh from my iphone, from the comfort of my sofa I wrote the following program in c that iterated with increasing sizes of square matrixes

When reaching a 216×216 matrix, the number of combinations was 2 thousand million at which some variable must have exceeded the maximum size of a double type because I started getting negative results.


The result is that the mean distance between any two points in a square is 0.5214 times the length of the side. I have no clue what this ratio means mathematically.

Do you know what 0.5214 represents in a square of side 1? đŸ™‚

Advertisements

Leave a Reply

Fill in your details below or click an icon to log in:

WordPress.com Logo

You are commenting using your WordPress.com account. Log Out /  Change )

Google+ photo

You are commenting using your Google+ account. Log Out /  Change )

Twitter picture

You are commenting using your Twitter account. Log Out /  Change )

Facebook photo

You are commenting using your Facebook account. Log Out /  Change )

Connecting to %s