Monte Carlo Pi Estimation

About This Experiment

The Monte Carlo method is a statistical technique that uses random sampling to solve problems that might be deterministic in principle. In this demonstration, we estimate the value of π by randomly throwing "darts" at a square and counting how many land inside a circle.

The Method

We inscribe a circle inside a square. The ratio of their areas is π/4. By randomly throwing points at the square and counting how many fall inside the circle, we can estimate π:

π ≈ 4 × (points inside circle / total points)

How to Use

• Click "Start" to begin throwing darts randomly
• Watch as the estimate converges toward π (approximately 3.14159...)
• Green dots represent darts that landed inside the circle
• Red dots represent darts that landed outside the circle but inside the square
• The more samples, the more accurate the estimate becomes

Key Insights

• This demonstrates the Law of Large Numbers in statistics
• Random processes can solve deterministic problems
• More samples = better accuracy (but diminishing returns)