## Kepler conjecture

31 examples (0.03 sec)
• Info The Kepler conjecture, named after the 17th-century German mathematician and astronomer Johannes Kepler, is a mathematical conjecture about sphere packing in three-dimensional Euclidean space. more...
• But eliminating all possible irregular arrangements is very difficult, and this is what made the Kepler conjecture so hard to prove.
• After Gauss, no further progress was made towards proving the Kepler conjecture in the nineteenth century.
• The Kepler conjecture says that this is the best that can be done -- no other arrangement of spheres has a higher average density.
• Although it expressly includes shapes other than spheres, it is generally taken as equivalent to the Kepler conjecture.
• In dimensions four and above, the situation is complicated by the fact that the analogs of the Kepler conjecture remains open.
• The Kepler conjecture states that this is the highest density that can be achieved by any arrangement of spheres, either regular or irregular.
• This conjecture is therefore related to the Kepler conjecture about sphere packing.
• This meant that any packing arrangement that disproved the Kepler conjecture would have to be an irregular one.
• What is the densest packing of spheres of equal size in space (Kepler conjecture)?
• American mathematician Thomas Callister Hales has given a computer-aided proof of the Kepler conjecture.
• In 1998 Thomas Hales, following an approach suggested by, announced that he had a proof of the Kepler conjecture.
• In January 2003, Hales announced the start of a collaborative project to produce a complete formal proof of the Kepler conjecture.
• If a lower bound (for the function value) could be found for every one of these configurations that was greater than the value of the function for the cubic close packing arrangement, then the Kepler conjecture would be proved.
• He was the first to show, in 1953, that proof of the Kepler conjecture can be reduced to a finite case analysis and, later, that the problem might be solved using a computer.
• Kepler did not have a proof of the conjecture, and the next step was taken by, who proved that the Kepler conjecture is true if the spheres have to be arranged in a regular lattice.
• An elementary exposition of the proof of the Kepler conjecture.
• He is also known for his 1998 computer-aided proof of the Kepler conjecture, a centuries-old problem in discrete geometry which states that the most space-efficient way to pack spheres is in a pyramid shape.
• Hales's current project, called Flyspeck, seeks to formalize his proof of the Kepler conjecture in the computer theorem prover HOL Light.
• Referees have said that they are "99% certain" of the correctness of Hales' proof, so the Kepler conjecture is now very close to being accepted as a theorem.
• The densest three-dimensional lattice sphere packing has each sphere touching 12 others, and this is almost certainly true for any arrangement of spheres (the Kepler conjecture).