Monte Carlo Simulation for Calculating Pi

Description
Demonstration of a calculation estimation the value of pi with Monte Carlo simulations in Excel
Monte Carlo methods, or Monte Carlo experiments, are a broad class of computational algorithms that rely on repeated random sampling to obtain numerical results. The underlying concept is to use randomness to solve problems that might be deterministic in principle. They are often used in physical and mathematical problems and are most useful when it is difficult or impossible to use other approaches. Monte Carlo methods are mainly used in three problem classes: optimization, numerical integration, and generating draws from a probability distribution.

In this example we look at a simple approach to demonstrate the viability of using Monte Carlo simulations with the the simple estimation of pie.

Random numbers are generated in excel and used to generate random points on a graph. Then using a quarter circle graph and counting the number of dots that fall within this circle, we can do a simple Monte Carlo simulation to estimate Pi.

This can be updated by pressing F9 to see new random numbers and a new updated estimate of Pi each time. Pi is estimated and then compared to the actual number of pi.

This example could then be used to model other Monte Carlo simulations