Démonstration de la conjecture de Kepler

Christian Marchal (1)

1 ONERA - The French Aerospace Lab [Palaiseau]

The Kepler's conjecture goes back to 1611 and was expressed in a letter answering to the British mathematician and astronomer Thomas Harriot : "The most compact packings of equal spheres are certainly the "compact face centered cubic lattice" and the equivalent ones. They give a proportion of occupation of space of pi/sqrt(18), that is more than 74%". The demonstration of this conjecture has attracted many mathematicians including Gauss (who demonstrated that the conjecture is true for regular lattices) and Hilbert which listed it as the eighteenth problem of his list of 23 major mathematical problems. In 1998 Thomas C. Hales presented a 250 pages proof associated with giant numerical computations. That proof was given to a team of twelve specialists that, after four years of examination, concluded that "they are 99% certain of the validity of the proof". It is possible to simplify greatly this question and to give two simple independent demonstrations. The first demonstration is the subject of this paper.

Mots clés: rangement; compact; Kepler; sphère; conjecture

Domaines: Géométrie métrique [math.MG]; Sciences de l'ingénieur [physics]

Christian Marchal. Démonstration de la conjecture de Kepler. 2007, 42 p. ⟨hal-00160350⟩