Estimate π with Monte Carlo
Run a real stochastic simulation in the browser, then read the evidence bundle it produces.
The model
A unit square contains a quarter-circle of radius 1. If we drop random points uniformly inside the square, the fraction that land inside the quarter-circle approaches π/4 as the sample size grows. Multiplying that fraction by 4 gives an estimate of π.
The claim boundary
This estimate is a bounded numerical model: it converges slowly (1/√N) and relies on a pseudorandom generator. The evidence bundle will record the sample size, the estimated value, and the substrate so the claim is shown at its real boundary, not as a proof.
Run the simulation
Choose a sample size and run the estimator. The same computation runs in your browser that a studio would emit as a verb result.
Inspect the evidence
The bundle shows the empirical level, evidence kind, claim status and validity domain. A larger sample shrinks the statistical uncertainty, but the claim stays a bounded model because the source is a simulation.
Part of these topics.
The research topics this lesson sits inside — the science, the studios, and the literature.