B4-1: Sphere – Exploring Natural Numbers, Equations, and Parametric Curves in So

This example demonstrates the construction of a sphere and its associated geometric elements, using natural number parameters and equations to generate the spherical surface, and illustrating intersections between the sphere, planes, and curves. Core mathematical concepts include the sphere equation, parametric curves, natural numbers, cube and volume relationships, as well as tangents and angles. Construction highlights: the Sphere command creates the sphere, IntersectPath finds intersection paths, and Point, Circle, Tangent, Angle commands build auxiliary points, circles, tangents, and angles. Objects include A, a, b, c, B, C, X, e, Y, f, g, h, i, j, α, β, and text labels. Suitable for high school or university courses in solid geometry and analytic geometry, helping students understand sphere equations, parametric representations, and spatial geometric construction techniques.