Monte Carlo Pi

1. Enter the number of points to generate using the input field.

2. (optional) Select the simulation mode.

• Simulate: generate points one by one
• Instant: generate everything at once
• Automatic: choose for me

3. Click the Start button to start the simulation.

The Monte Carlo method is a statistical method that uses random sampling to estimate numerical results.

In this simulation, a circle is inscribed in a quadrant. The ratio between the area of the circle and the area of the square is$$\frac{\pi r^2}{(2r)^2} = \frac{\pi}{4}$$This means we can approximate pi by generating random points in the quadrant and calculating the ratio of points inside the circle to the total number of points.$$\frac{\pi}{4} \approx \frac{r}{n}$$$$r = \text{points inside circle}$$$$n = \text{total points}$$