Temari Ball Geometry: Interactive Spherical Arcs on a Sphere

This example demonstrates a Temari-ball style construction that produces structured, repeating patterns on a sphere by drawing and transforming circular arcs. Viewers can interact with parameters to see how the arc segments change while the overall symmetry and arrangement remain consistent. The core mathematics includes sphere/solid geometry, circle and circumcircle-arc construction, and symmetry via geometric transformations—especially Mirror and Rotate—together with iterative generation of multiple segments using Sequence (helpful for thinking in terms of fractions/segment proportions and countable structures). Construction uses GeoGebra commands: Sphere to build the sphere, PointIn to place points on the surface, Circle to define circles, CircumcircleArc to create the circular arc segments, Sequence to generate repeated elements, and Mirror/Rotate to replicate the arcs around the sphere into a coherent decorative pattern. Key objects include the sphere center and radius elements (O, R) and a hierarchy of arc/point outputs (e.g., l2, l2', l2'', l2'_1, etc.), along with rendered image objects (image1, image2) for the final visual effect. Suitable for middle school through early university geometry, classroom demonstrations of transformations, and student interactive explorations of spherical constructions.