Stereographic Projection of a 3-Sphere
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.
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2
(z-c)
2
(w-d)
2
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1
(0,0,0,0)
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