Sampling Random Distributions with Sphere Reflection Geometry

This example demonstrates “March Randomness #3” by combining stochastic sampling with 3D geometric effects: random outputs are sampled and displayed in a table, while sphere-related geometry illustrates reflection and similarity transformation behavior so that randomness and spatial transformation become visually linked. The key math concepts include the geometric distribution versus the normal distribution (highlighting discrete-to-continuous comparison and approximation intuition), together with solid geometry notions on a sphere and the mapping induced by reflection and similarity transformations. Construction-wise, the provided GeoGebra commands show the workflow: Sample generates random samples, and TableText renders the sampled results as readable entries; the objects Pouch, takeTwo, button1, and text1 support user-triggered execution, bundling/producing sample pairs, and showing dynamic textual/statistical information. Suitable for late secondary students and undergraduates in probability & statistics and geometry/transformations, as a classroom demo or project-based learning activity.