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Indexed under : Mathematics

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

The Kelvin problem (3-D packing)

In 2 dimensions, the most efficient packing mechanism is an array of hexagons - a honeycomb. In 1887, William Thomson (Lord Kelvin) asked the question 'What is the most efficient 3-D packing system?“

See (the original paper) : On the Division of Space with Minimla Partitional Area Open Access

He suggested that it was the 'bi-truncated cubic honeycomb' which, until 1993, was widely recognised as the most efficient possible.

It was succeeded, however, by the Weaire–Phelan Structure (see Wikipedia) - found by computerised simulations of foam generation - which is currently the most efficient form yet found.

The question of whether the Weaire–Phelan Structure is the most efficient 3-D packing structure - having the smallest surface area per cell - is however still open. Subsequent mathematical simulations suggest that it is optimal - but this remains unproven.

Also see : Ulam's packing conjectureplugin-autotooltip__plain plugin-autotooltip_bigUlam's packing conjecture

When packing convex identical 3-dimensional objects into a defined space, is a sphere the most 'efficient' shape when considering the amount of free space in the gaps?

According to the conjecture, the sphere is the convex solid which forces t…

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