Stereographic Projection of a 3-Sphere

A four-dimensional hypersphere of radius and center has equation . The unit 3-sphere is the four-dimensional hypersphere of radius and center . This Demonstration lets you rotate the unit 3-sphere around its six directional planes (-, -, -, -, -, -), showing the stereographic projection of its parallels, meridians, and hypermeridians in three-dimensional space. Although the circles seen in 3D seem to intersect themselves when the hypersphere is rotated, in 4D, the 3-sphere does not self-intersect.
  • Contributed by: John Na
  • (Mathematica Summer Camp 2014)


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