Discrete geometry, also called combinatorial geometry, is the branch of geometry that studies the combinatorial properties and constructive methods of discrete geometric objects such as points, lines, polygons and packings. This description is adapted from Wikipedia contributors under CC BY-SA 4.0; changes were made. https://creativecommons.org/licenses/by-sa/4.0/
Facts
Central QuestionHow densely non-overlapping shapes, most famously equal spheres, can be packed into a containing space, and whether a proposed densest arrangement can be proved optimal rather than merely observed to be efficient. 1 Key DebateWhether the arrangement of equal spheres that Johannes Kepler conjectured in 1611 to be the densest possible, the same face-centered cubic packing seen in stacked cannonballs and fruit at a market, is truly optimal. Polyhedra and tessellations had been studied by people such as Kepler and Augustin-Louis Cauchy for centuries before discrete geometry took shape as its own subject in the late nineteenth century, and Kepler's own packing conjecture waited nearly four centuries for a computer-assisted proof. 1 Classification
Pure or Applied Connections
Associated With
Includes
Source Fano Plane (Wikipedia)
Source Hilbert Curve (Wikipedia)
Primary research field per the source's own opening sentence: discrete, convex and combinatorial geometry, including finite sphere packings and the sausage conjecture.
Source Joerg Wills (Wikipedia, German)
Additional Source Kepler Conjecture (Wikipedia)Introduction
Source Sierpiński Triangle (Wikipedia)
Proved the Kepler conjecture on sphere-packing density (1998, formally verified 2014) and the honeycomb and dodecahedral conjectures, all discrete geometry results.
Source Thomas Hales (Wikipedia)
Sources
1. Discrete Geometry (Wikipedia)
WikipediaLead section
Discrete geometry and combinatorial geometry are branches of geometry that study combinatorial properties and constructive methods of discrete geometric objects.
Packings, coverings and tilings
A sphere packing is an arrangement of non-overlapping spheres within a containing space.
History
Polyhedra and tessellations had been studied for many years by people such as Kepler and Cauchy, modern discrete geometry has its origins in the late 19th century.
View the Source Thomas Hales (Wikipedia)
Wikimedia FoundationIncludes: Thomas Hales, InfoboxQuote, Includes: Thomas Hales, Infobox
Born (1958-06-04) June 4, 1958 (age 68) San Antonio, Texas ... Known for Proof of the Kepler conjecture Proof of the honeycomb conjecture Proof of the dodecahedral conjecture
Joerg Wills (Wikipedia, German)
Wikimedia FoundationIncludes: Jorg Wills, opening paragraphQuote, Includes: Jorg Wills, opening paragraph
Joerg Michael Wills (born 5 March 1937 in Berlin) is a German mathematician working in discrete, convex and combinatorial geometry.
Kepler Conjecture (Wikipedia)
Wikimedia FoundationIncludes: Kepler Conjecture, IntroductionQuote, Includes: Kepler Conjecture, Introduction
is a mathematical theorem about sphere packing in three-dimensional Euclidean space.
Sierpiński Triangle (Wikipedia)
Hilbert Curve (Wikipedia)
Fano Plane (Wikipedia)
Reader Challenges (0)
No disputes yet. Spotted an error or a better source? Open the first one.
Sign in to dispute this or suggest a correction.