# Buffons needle variation

1. Dec 20, 2006

### daniel_i_l

In the "buffons needle" riddle you have a paper with horizontal lines in it all 1 unit apart and you drop a needle 1 unit long - you have to calculate the chance that the needle will hit a line. but i remembered the riddle wrong so instead i tried to solve the same question with both horizontal and vertical lines (graph paper). all of the cells are 1X1 unit. i got that the chance of hitting a line is:
is that right?
Thanks.

2. Dec 20, 2006

### StatusX

I get the same answer. Also, note the result proves pi>3, and since it's obviously pretty likely the needle will hit a line, it shows pi is pretty close to 3. Maybe you can get other approximations for pi using a similar method, which is ironic considering the point of the original problem was to empirically approximate pi.

Last edited: Dec 20, 2006
3. Dec 21, 2006

### daniel_i_l

I wrote a program that simulates a needle falling 10000000 times and counts the times that it hits a line. using that i got that
3/pi = 0.95521 or pi = 3.14067 - ok but i guess that this method of calculating pi doesn't converge very fast.