Download Dense Sphere Packings (London Mathematical Society Lecture by Thomas Hales PDF

By Thomas Hales

The 400-year-old Kepler conjecture asserts that no packing of congruent balls in 3 dimensions could have a density exceeding the usual pyramid-shaped cannonball association. during this publication, a brand new evidence of the conjecture is gifted that makes it obtainable for the 1st time to a wide mathematical viewers. The booklet additionally provides strategies to different formerly unresolved conjectures in discrete geometry, together with the powerful dodecahedral conjecture at the smallest floor region of a Voronoi mobile in a sphere packing, and Fejes Tóth's conjecture describing all packings of congruent balls within which each ball touches twelve others. This booklet can be at present getting used as a blueprint for a large-scale formal facts venture, which goals to examine each logical inference of the facts of the Kepler conjecture by way of computing device. this is often an imperative source should you are looking to be pointed out up to now with examine at the Kepler conjecture.

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