I've been reading Nahin's book Inside Interesting Integrals and got up to the point where he is calculating the probability that a circle $C_2$ is entirely contained in circle $C_1$, given that three points are chosen at random (which are contained in $C_1$) that uniquely determine $C_2$. The analytic proof makes sense, but there is a contradiction between that number and the number achieved using his Matlab Monte Carlo Simulation Code.
Why the discrepancy considering that the code executes this a million times, and no matter how many times I do it, the numbers fluctuate somewhat between 3.9992 and 4.008, all underestimates of 0.418879...?
The math checks out for me, but not so much the code and the way a computer works with these simulations. If any can provide some insight to why this is, that would be very much appreciated.
NOTE: Please check pages 25-30 in the Google Books version here