Sphere and Step Functions: Dynamic Sequence and Circle Interaction

This GeoGebra example demonstrates a dynamic mathematical visualization combining a sphere, step functions, sequences, and circles, illustrating the interplay between discrete sequences and continuous geometric objects. Core mathematical concepts include sequence recursion and summation, step function graphs, circle equations, and spherical representation in 3D space. The construction uses commands such as Point, Vector, Textfield, and Sequence to create dynamic point sets and input boxes, with sliders and text controls to adjust parameters. A list (list1) and multiple auxiliary points (A1–A10, B1–B10) generate step-like graphs, while circle and sphere equations reveal geometric relationships. This resource is suitable for high school or early college students to explore sequence limits, function approximation, and the integration of algebra and geometry, and can serve as material for math labs or inquiry-based learning.