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

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

Galileo Galilei, who mentioned Kepler's discoveries in his work. He is also known for postulating the Kepler conjecture. Kepler lived in an era when there...

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

complexity theory, information theory, and graph theory. In 1998, the Kepler conjecture on sphere packing seemed to also be partially proven by computer....

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...

conjecture (Montserrat Teixidor i Bigas and Barbara Russo, 1999) Bogomolov conjecture (Emmanuel Ullmo, 1998, Shou-Wu Zhang, 1998) Kepler conjecture (Samuel...

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...

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

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

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

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

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

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...

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

fewer dimensions, and the proof of the three-dimensional version (the Kepler conjecture) involved long computer calculations. In contrast, Viazovska's proof...

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...

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...

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...

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

down. The most prominent examples are the four color theorem and the Kepler conjecture. Both of these theorems are only known to be true by reducing them...

Wu-Yi Hsiang [de] (born 1937), Chinese-American mathematician; see Kepler conjecture Xiang Army raised in Hunan by Zeng Guofan during the Qing dynasty...

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...

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

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

approximation to algebraic numbers. The 2-dimensional analog of Kepler's conjecture: the regular hexagonal packing is the densest circle packing in the...

refraction law valid for small angles. 1611 – Johannes Kepler first states the Kepler conjecture about sphere packing in three-dimensional Euclidean space...

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

densest possible sphere packings in three-dimensional space (the Kepler conjecture, proved by Thomas Hales), both have each sphere touching twelve other...

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