In teaching simulation, the Buffon's needle is a popular experiment to use for designing a Monte Carlo simulation to approximate the number  π . Simulating the Buffon's needle experiment is a perfect example for demonstrating the beauty of a Monte Carlo simulation in a classroom. However, there is a common misconception concerning the Buffon's needle simulation. Erroneously, the simulation of the needle drop cannot be used to evaluate  π . We have to simulate the needle's angle from an uniform (0, π/2) distribution. It is self-referential in theory, since it requires the number  π  as the input value to approximate  π . In this study, we propose a new method using the fixed-point iteration to remove the inherent paradox of the Buffon's needle simulation. A new algorithm with Python implementation is proposed. The simulation outputs indicate that our new method is as good as if we use the true  π  value as an input.
['Maximilian J. Wang', 'Jin Wang']
Removing the inherent paradox of the Buffon's needle monte carlo simulation using fixed-point iteration method