Center of Rotation: 3D Point and Image Rotation on a Sphere

This GeoGebra example demonstrates the rotation of points A and B, along with an image object pic1, around a designated center C in three-dimensional space, producing the rotated image pic1'. The core mathematical concept is the 3D rotation transformation, emphasizing the role of the rotation center, rotation angle, and how rotation affects points, images, and spherical surfaces. The construction uses the Rotate command on points A, B, and the image pic1, while incorporating elements such as a sphere, conic sections, trigonometric functions, and a pie chart to create a rich visual context. Likely, a slider controls the rotation angle for dynamic exploration. This example is suitable for high school or early college students learning 3D geometric transformations, and serves as an intuitive teaching tool for visualizing rotation in space and its coordinate effects.