## cannonball approximation to pi

**T**his year, my daughter started writing algorithms in her math class (she is in *seconde*, which could correspond to the 10th grade). The one she had to write down last weekend was Buffon’s neddle and the approximation of π by Monte Carlo (throwing cannon balls was not mentioned!). Here is the short R code I later wrote to show her the outcome (as the class has not yet learned a computer language):

n=10^6 counter=0 #uniforms over the unit square ray=runif(n)^2+runif(n)^2 #proportion within the quarter circle conv=cumsum((ray<1))/(1:n) plot(conv,type="l",col="steelblue",ylim=c(pi/4-2/sqrt(n), pi/4+2/sqrt(n)),xlab="n",ylab="proportion") abline(h=pi/4,col="gold3")

and here is an outcome of the convergence of the approximation to π/4:

October 29, 2011 at 4:25 am

Why is it

?

October 29, 2011 at 7:12 am

– if you mean the occurrence of a < instead of < into the code, thanks, I just corrected this HTML issue;

– if you mean why I only take rays less than 1 it is because my circle has a radius of 1;

– if you mean why I use cumsum, it is to show the convergence of the estimator as n increases…

October 28, 2011 at 5:59 pm

This is cool. For younger kids, there’s a nice activity on determination of the area of a penny by Monte Carlo methods at the Jefferson Nat’l Lab.

http://education.jlab.org/beamsactivity/6thgrade/differentwayofmeasuring/index.html

October 9, 2011 at 12:00 pm

Actually, they started programming their calculator in a sort of Basic. However, the teacher has not addressed this exercise so far, maybe because she does not want to cover graphical commands that early.