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Wikenigma - an Encyclopedia of Unknowns Wikenigma - an Encyclopedia of the Unknown Wikenigma - an Encyclopaedia of Unknowns Wikenigma - an Encyclopaedia of the Unknown

Ulam's packing conjecture

When packing convex 3-dimensional objects into a defined space, is a sphere the most efficient shape? Packed spheres leave around 25.95% of space unfilled - and intuitively would seem to be the most efficient shape.

To date, however, no mathematical proof has been discovered to show that the sphere is the most efficient.

See: > math > arXiv:1305.0289, 2013

Note: In 2-dimensional and 4-dimensional space, proofs have been provided for special shapes.

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