D’Alembert Coin Problem: Rotation-Based Geometric Probability Demo

This GeoGebra example visualizes a coin’s repeated flipping/rotation process and demonstrates how the probabilities of different outcomes (e.g., head-head, head-tail, tail-tail) can be computed and displayed for multiple steps. The key mathematical ideas include 2D geometry with vector/rotation transformations, event counting, and discrete probability (using random trials and/or structured probability components). Construction highlights: Random is used to generate stochastic outcomes, while CountIf tallies how many trials satisfy each outcome condition. Textfield together with LaTeX and text objects presents parameters and probability formulas clearly. Geometric scaffolding is built with Point, Segment, OrthogonalLine, and Intersect to create the schematic configuration used in the illustration. Variables and interface controls (buttons and input boxes) manage the number of steps and parameter updates, producing labeled probability outputs for the different outcome categories. Suitable for high school to early university audiences for teaching probabilistic reasoning, simulation-based verification, and connecting geometric transformations to discrete event probabilities.