Analyzing π through Monte Carlo Simulations

A Comparative Study with Experimental Approaches


  • Sanjay B Kulkarni Hope Foundationa's Finolex Academy of Management and Technology, University of Mumbai



Random Number, Triplets, Non-parametric Tests, Friedman’s Test, Chi-square Test


This study investigates the estimation of π using the Monte Carlo Simulation Method, comparing the results with experimental values. To determine π's experimental value, a unit circle (z=1) centered at the origin within a square bounded by points (0,0), (1,0), (1,1), and (0,1) is considered, where an infinite number of points exist within both the circle and the square. Points with z≤1 are within or on the circle's arc, and those with z>1 are outside the arc but within the square. By selecting hundreds or thousands of random number pairs, their positions relative to the arc and square are determined. With N representing the total number of points considered and n the number of points within or on the arc, the experimental value of π is calculated as π=4n/N. This formula indicates that a larger sample size, N, results in a π value closer to its true value. Furthermore, non-parametric hypothesis testing, such as Friedman's Test, is applied to a Monte Carlo Simulation distribution of 20 triplets of random numbers to evaluate their distribution on a semicircle, followed by a Chi-Square Test for goodness of fit. This comprehensive methodology elucidates various insights into the distribution and impact of random number triplets and their conformity to the expected goodness of fit.



How to Cite

S. B. Kulkarni, “Analyzing π through Monte Carlo Simulations: A Comparative Study with Experimental Approaches”, J. Comput. Mech. Manag, vol. 3, no. 1, Feb. 2024.



Original Articles


Received 2023-09-02
Accepted 2023-12-16
Published 2024-02-29