The Kepler conjecture, named after the 17th-century mathematician and astronomer Johannes Kepler, is a mathematical theorem about sphere packing in three-dimensional...

discrete geometry, he settled the Kepler conjecture on the density of sphere packings and the honeycomb conjecture. In 2014, he announced the completion...

later became known as the Kepler conjecture, a statement about the most efficient arrangement for packing spheres. Kepler wrote the influential mathematical...

mathematician should verify each part of the proof. In 1998, the Kepler conjecture on sphere packing seemed to also be partially proven by computer....

conjecture is therefore related to the Kepler conjecture about sphere packing. Since the solution to the Kepler conjecture establishes that identical balls...

lengthy arguments, proved the central conjecture, and remarked that this theorem is equivalent to Kepler conjecture for regular arrangements. In two papers...

conjecture Kelvin's conjecture Kouchnirenko's conjecture Mertens conjecture Pólya conjecture, 1919 (1958) Ragsdale conjecture Schoenflies conjecture (disproved...

Ullmo, 1998, Shou-Wu Zhang, 1998) Kepler conjecture (Samuel Ferguson, Thomas Callister Hales, 1998) Dodecahedral conjecture (Thomas Callister Hales, Sean...

packing in a square Circle packing in a circle Inversive distance Kepler conjecture Malfatti circles Packing problem Chang, Hai-Chau; Wang, Lih-Chung...

including structures that are aperiodic in the stacking direction. The Kepler conjecture states that this is the highest density that can be achieved by any...

Kepler (1571 – 1630). Kepler conjecture Kepler triangle Kepler–Bouwkamp constant Kepler–Poinsot polyhedron Kepler's laws of planetary motion Kepler's...

Callister Hales (almost certainly) proves the Kepler conjecture. 1999 – the full Taniyama–Shimura conjecture is proven. 2000 – the Clay Mathematics Institute...

Johannes Kepler conjectured that this is the maximum possible density amongst both regular and irregular arrangements—this became known as the Kepler conjecture...

the Kepler conjecture). He also investigated the sphere packing problem. He was the first to show, in 1953, that proof of the Kepler conjecture can be...

the value of the optimal packing fraction is a corollary of the Kepler conjecture: it can be achieved by putting a rhombicuboctahedron in each cell...

the most dense arrangement of atoms has an APF of about 0.74 (see Kepler conjecture), obtained by the close-packed structures. For multiple-component...

The proof takes about 500 pages spread over about 20 papers. 2005 Kepler conjecture. Hales's proof of this involves several hundred pages of published...

equivalent to the Kepler conjecture. In 1998, American mathematician Thomas Callister Hales gave a computer-aided proof of the Kepler conjecture. It shows that...

this is almost certainly true for any arrangement of spheres (the Kepler conjecture). Twelve is also the kissing number in three dimensions. There are...

Specific topics in this area include: Circle packings Sphere packings Kepler conjecture Quasicrystals Aperiodic tilings Periodic graph Finite subdivision...

densest possible packing of equal spheres in ordinary space (see Kepler conjecture). It consists of copies of a single cell, the rhombic dodecahedron...

algorithms. Thomas C. Hales and Samuel P. Ferguson, for proving the Kepler conjecture on the densest possible sphere packings. 2012: Sanjeev Arora, Satish...

2000 book, because the sphere-packing problem (also known as the Kepler conjecture) was unsolved, but a solution to it has now been claimed. Hilbert...

the value of the optimal packing fraction is a corollary of the Kepler conjecture: it can be achieved by putting a rhombicuboctahedron in each cell...

many spheres has a longer history of investigation, from which the Kepler conjecture is most well-known. Atoms in crystal structures can be simplistically...

packing constant of K. The Kepler conjecture is concerned with the packing constant of 3-balls. Ulam's packing conjecture states that 3-balls have the...

polynomial Leech lattice Minkowski's theorem Packing Sphere packing Kepler conjecture Kissing number problem Honeycomb Andreini tessellation Uniform tessellation...

Sean McLaughlin proved the conjecture in 1998, following the same strategy that led Hales to his proof of the Kepler conjecture. The proofs rely on extensive...

related sphere packing problem has been studied since the 17th century (Kepler conjecture)). Industrial applications of cutting-stock problems for high production...

computer-assisted proof by exhaustion Thomas Hales's proof of the Kepler conjecture. Various proofs of the four colour theorem. Clement Lam's proof of...