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Sphere packing in a sphere is a three-dimensional packing problem with the objective of packing a given number of equal spheres inside a unit sphere. It is the three-dimensional equivalent of the circle packing in a circle problem in two dimensions.
The strictly jammed (mechanically stable even as a finite system) regular sphere packing with the lowest known density is a diluted ("tunneled") fcc crystal with a density of only π √ 2 /9 ≈ 0.49365. [6] The loosest known regular jammed packing has a density of approximately 0.0555. [7]
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The four Euclidean coordinates for S 3 are redundant since they are subject to the condition that x 0 2 + x 1 2 + x 2 2 + x 3 2 = 1. As a 3-dimensional manifold one should be able to parameterize S 3 by three coordinates, just as one can parameterize the 2-sphere using two coordinates (such as latitude and longitude).
2-sphere wireframe as an orthogonal projection Just as a stereographic projection can project a sphere's surface to a plane, it can also project a 3-sphere into 3-space. This image shows three coordinate directions projected to 3-space: parallels (red), meridians (blue), and hypermeridians (green).
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