**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:

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