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 conventional pyramid-shaped cannonball association. during this ebook, a brand new facts of the conjecture is gifted that makes it obtainable for the 1st time to a vast 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 cellphone in a sphere packing, and Fejes Tóth's conjecture describing all packings of congruent balls during which each ball touches twelve others. This publication can also be presently getting used as a blueprint for a large-scale formal facts undertaking, which goals to envision each logical inference of the facts of the Kepler conjecture by means of computing device. this is often an crucial source in case you are looking to be mentioned thus far with learn at the Kepler conjecture.

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