What is the probability of a needle hitting a line on graph paper?

  • Level: Undergrad 
  • Thread starter Thread starter daniel_i_l
  • Start date Start date
  • Tags Tags
    Needle Variation
Join the discussion
Registration is free. Start your own thread to ask a follow-up.
Sign up Log in
2 replies · 3K views
daniel_i_l
Gold Member
Messages
864
Reaction score
0
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:
3/pi which is about 95%
is that right?
Thanks.
 
Physics news on Phys.org

Discussion

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:
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.