Discover one of the most beautiful objects in mathematics through 15 interactive demonstrations. See how every point on a sphere corresponds to a circle in 3-space, and why every pair of these circles is linked.
See also: Topology for fibrations and homotopy groups, Lie Groups for the underlying SU(2) to S² quotient structure, and Differential Geometry for the smooth fiber bundle structure on S³.
Understand S¹ fibers over S² and how every point on the 2-sphere corresponds to a circle in 3-space
Map the 3-sphere into 3D space and see how fibers become circles and lines
Visualize dozens of fibers simultaneously, colored by their base point on S²
Discover why every pair of fibers is linked exactly once — a topological invariant
Click points on S² and watch their fibers appear in real time — build your own fibration