Related Problems
- Thue's theorem
- The regular hexagonal packing is the densest sphere packing in the plane. (1890)
- The 2-dimensional analog of the Kepler conjecture; the proof is elementary. Henk and Ziegler attribute this result to Lagrange, in 1773 (see references, pag. 770).
- The hexagonal honeycomb conjecture
- The most efficient partition of the plane into equal areas is the regular hexagonal tiling. Hales' proof (1999).
- Related to Thue's theorem.
- The dodecahedron conjecture
- The volume of the Voronoi polyhedron of a sphere in a packing of equal spheres is at least the volume of a regular dodecahedron with inradius 1. McLaughlin's proof, for which he received the 1999 Morgan Prize.
- A related problem, whose proof uses similar techniques to Hales' proof of the Kepler conjecture. Conjecture by L. Fejes Tóth in the 1950s.
- The Kelvin problem
- What is the most efficient foam in 3 dimensions? This was conjectured to be solved by the Kelvin structure, and this was widely believed for over 100 years, until disproved by the discovery of the Weaire–Phelan structure. The surprising discovery of the Weaire–Phelan structure and disproof of the Kelvin conjecture is one reason for the caution in accepting Hales' proof of the Kepler conjecture.
- Sphere packing in higher dimensions
- The optimal sphere packing question in dimensions bigger than 3 is still open.
Read more about this topic: Kepler Conjecture
Famous quotes containing the words related and/or problems:
“Just as a new scientific discovery manifests something that was already latent in the order of nature, and at the same time is logically related to the total structure of the existing science, so the new poem manifests something that was already latent in the order of words.”
—Northrop Frye (b. 1912)
“To be a philosopher is not merely to have subtle thoughts, nor even to found a school, but so to love wisdom as to live according to its dictates a life of simplicity, independence, magnanimity, and trust. It is to solve some of the problems of life, not only theoretically, but practically.”
—Henry David Thoreau (1817–1862)