Intersection-Based Construction of the Viviani Curve

This GeoGebra example demonstrates how the Viviani curve arises as an intersection (a space locus) between standard 3D surfaces such as a sphere and a cylinder/rotation body. By adjusting an underlying parameter, students can observe how the intersection curve behaves and connect the geometry of the solid with the resulting planar/Cartesian description. Key math concepts include solid-geometry surface intersection, locus/trajectory thinking in 3D, vector representation for defining directions and constructing reference points, and the curve’s relationship to trigonometric expressions (e.g., cosine-type parameters) alongside the broader calculus context (useful for later discussion of tangents/derivatives). Construction highlights: Cylinder and Sphere are used to build the two surfaces (e.g., objects r, c1, along with g, h, i), Intersect computes their intersection curve, CurveCartesian provides the Cartesian parametric/graph form of the resulting curve, and Point/Vector create essential points and direction vectors (objects A, B, u, a, b). Text labels (text1, text2) help communicate the parameters and geometric roles. Suitable for high-school advanced geometry through early university calculus/precalculus learners, especially for interactive lessons on 3D-to-curve connections.