Home▸Mathematics▸Mathematics Probability Simulation

🧪 Mathematics Probability Simulation

Interactive 3D simulator of Bertrand's Paradox: draw random chords of a circle three different ways and watch the probability that a chord is longer than the inscribed equilateral triangle's side converge to 1/3, 1/2, or 1/4 depending on how 'random' is defined.

Mathematics2DModerate60 FPS📱 Mobile-adapted

This simulator draws random chords of a circle using three different, equally "reasonable" random-sampling procedures and tracks how often each chord ends up longer than the side of the circle's inscribed equilateral triangle. Switch between the Endpoints, Radial-Point, and Midpoint methods to watch the running probability estimate converge to a different theoretical value each time — 1/3, 1/2, and 1/4 — a classic 1889 demonstration by Joseph Bertrand that "pick a random X" is meaningless until the sampling procedure generating that randomness is pinned down.

⚙ Under the hood

This simulation explores probability concepts through interactive experiments. Users can manipulate variables to see how they affect probabilities and learn about distributions like the normal distribution.

ProbabilityStatisticsInteractive

2D · HTML5 Canvas 2D · 60 FPS target · runs fully client-side, no install