In the nineteenth century many people tried to seek a value for the most famous irrational number, [pi], by means of an experiment known as Buffon's needle, consisting of throwing randomly a needle onto a surface ruled with straight parallel lines. Here we propose to extend this experiment in order to evaluate other irrational numbers, such as [square root]2, [square root]3, and the golden ratio, [phi]=(1+[square root]5)/2, by simply replacing the needle by a suitable regular polygon and then calculating the probability that a line intersects two consecutive sides of the polygon. A computer simulation of the experiment by means of Monte Carlo methods is reported. (Contains 3 figures.)