Broken Stick Triangle Simulation: Can Random Breaks Form a Triangle?

This simulation demonstrates the classic broken stick problem: a stick is randomly broken into three pieces, and the program dynamically counts how often these pieces can form a triangle, visualizing the geometric probability. Core mathematical concepts include the triangle inequality (sum of any two sides greater than the third), geometric probability, random simulation and statistical convergence, and the use of the median line in the condition. Construction highlights: using GeoGebra commands such as Min, Max, Length, RemoveUndefined, Polygon, and Segment to generate and display the three segment lengths; buttons (button2, button3, button4) control simulation count, speed, and reset; sliders (n, speed) adjust parameters; real-time updates of statistics and graphics. Suitable for high school and above for learning probability, statistics, inequalities, or mathematical experimentation, and also useful for introductory probability courses at university level.