Estimate π using random sampling
This simulation demonstrates how we can estimate the value of π using random sampling. By generating random points in a square and counting how many fall within an inscribed circle, we can approximate π based on the ratio of areas.
The Monte Carlo method for estimating π is based on the following principle:
• A circle with radius r = 1 has area π
• A square with side length 2 (containing the circle) has area 4
• The ratio of the circle's area to the square's area is π/4
By randomly placing points in the square and counting how many fall inside the circle, we can estimate this ratio. As the number of points increases, our estimate becomes more accurate: π ≈ 4 × (points inside circle) / (total points)