Monte Carlo Pi Estimation with Random Shots: Frequency Stabilization

This GeoGebra example demonstrates how the Monte Carlo (random sampling) method can estimate pi (π) by counting “hits” of randomly generated points inside a target region. It shows how empirical frequencies stabilize as the number of trials increases, illustrating the link between probability and long-run frequency. Key concepts include the Monte Carlo method, probability vs. frequency convergence, statistical estimation of π from a hit ratio, and visual interpretation of variability/error (e.g., standard-deviation-like fluctuations) as sample size grows. Construction highlights from the provided summary: it uses CountIf to count successful outcomes, If to apply hit/miss conditions, Length to measure relevant geometric quantities, and Textfield to continuously display computed estimates. Objects and controls include dianas (target/criterion objects), disparos (the set of shots/points), and buttons such as disparar, dispararC, and dispararT to generate new random shots and update grouped statistics; companion objects like dianasT/disparosT and dianasR support comparative or filtered tracking. The example is suitable for high school through early university levels for probability & statistics, numerical experimentation, and classroom demonstrations of the law of large numbers and error reduction under repeated sampling.