Pi Experiments Calculator
Estimating Pi (Ï€)
Pi (Ï€) is a mathematical constant representing the ratio of a circle's circumference to its diameter, approximately equal to 3.14159. This calculator explores different methods to estimate its value.
Monte Carlo Method: Random points are plotted in a square. A circle is inscribed in the square. The ratio of points inside the circle to the total points is used to estimate π.
\[ \pi \approx 4 \times \frac{\text{points in circle}}{\text{total points}} \]
Leibniz Formula: A slow-converging infinite series.
\[ \frac{\pi}{4} = \sum_{n=0}^{\infty} \frac{(-1)^n}{2n+1} = 1 - \frac{1}{3} + \frac{1}{5} - \frac{1}{7} + \cdots \]
Nilakantha Series: A much faster-converging infinite series.
\[ \pi = 3 + \sum_{n=1}^{\infty} \frac{4(-1)^{n+1}}{2n(2n+1)(2n+2)} \]
Disclaimer: These methods are approximations. The accuracy depends on the number of iterations or points. This tool is for educational purposes to demonstrate mathematical concepts.
Visually estimate π by randomly plotting points in a square.
Estimate π using the Leibniz infinite series.
Estimate π using the faster-converging Nilakantha series.
Powered by: Calco