Estimated π

Interactive simulation for estimating π using the Monte Carlo method. Uniformly distributed points are drawn in a square containing an inscribed circle.

The square has side length $2R$ and area $4R^2$; the inscribed circle has radius $R$ and area $\pi R^2$. For many uniformly drawn points, the ratio of the points inside the circle ($N_{\mathrm{inside}}$) to the total number of points ($N_{\mathrm{total}}$) approaches the ratio of the areas. Therefore, $$\frac{N_{\mathrm{dentro}}}{N_{\mathrm{total}}}\approx\frac{\pi R^2}{4R^2}\quad\Rightarrow\quad\pi\approx4\frac{N_{\mathrm{dentro}}}{N_{\mathrm{total}}}.$$

Use the six buttons in the “Draw points” panel to add 1, 3, 10, 100, 1000, or 10000 points. “Point size” changes the markers' visual radius. “Restart” clears the current draw without changing that size or the graph selection. In the “Graph” menu, choose “π versus points drawn” or remove the graph.

Marco P. M. de Souza