Branch of geometry that studies combinatorial properties and constructive methods
"Combinatorial geometry" redirects here. The term combinatorial geometry is also used in the theory of matroids to refer to a simple matroid, especially in older texts.
A collection of circles and the corresponding unit disk graph
Discrete geometry and combinatorial geometry are branches of geometry that study combinatorial properties and constructive methods of discrete geometric objects. Most questions in discrete geometry involve finite or discrete sets of basic geometric objects, such as points, lines, planes, circles, spheres, polygons, and so forth. The subject focuses on the combinatorial properties of these objects, such as how they intersect one another, or how they may be arranged to cover a larger object.
Discrete geometry has a large overlap with convex geometry and computational geometry, and is closely related to subjects such as finite geometry, combinatorial optimization, digital geometry, discrete differential geometry, geometric graph theory, toric geometry, and combinatorial topology.
Discretegeometry and combinatorial geometry are branches of geometry that study combinatorial properties and constructive methods of discrete geometric...
numbers, calculus or Euclidean geometry. Discrete objects can often be enumerated by integers; more formally, discrete mathematics has been characterized...
Discrete differential geometry is the study of discrete counterparts of notions in differential geometry. Instead of smooth curves and surfaces, there...
examples for design theory. It should not be confused with discretegeometry (combinatorial geometry). Order theory is the study of partially ordered sets...
computational geometry are: Combinatorial computational geometry, also called algorithmic geometry, which deals with geometric objects as discrete entities...
computational geometry, convex analysis, discretegeometry, functional analysis, geometry of numbers, integral geometry, linear programming, probability theory...
Digital geometry deals with discrete sets (usually discrete point sets) considered to be digitized models or images of objects of the 2D or 3D Euclidean...
incidence geometry and discretegeometry. For instance, the Sylvester–Gallai theorem of incidence geometry states that if n points of Euclidean geometry are...
methods, mainly homological algebra. Discretegeometry, the study of finite configurations in geometry. Convex geometry, the study of convex sets, which takes...
algebra, analysis, combinatorics, algebraic, differential, discrete and Euclidean geometries, graph theory, group theory, model theory, number theory,...
Alexander Grothendieck (1928–2014) – algebraic geometry Branko Grünbaum (1929–2018) – discretegeometry Michael Atiyah (1929–2019) Lev Semenovich Pontryagin...
Gruber, Convex and discretegeometry, Springer-Verlag, New York, 2007. P. M. Gruber, J. M. Wills (editors), Handbook of convex geometry. Vol. A. B, North-Holland...
foundation of most modern fields of geometry, including algebraic, differential, discrete and computational geometry. Usually the Cartesian coordinate system...
p. 106, ISBN 978-3-527-63457-6 Matoušek, Jiří (2002), Lectures on DiscreteGeometry, Graduate Texts in Mathematics, Springer, p. 349, ISBN 978-0-387-95373-1...
in natural languages Computational algebraic geometry Computational group theory Computational geometry Computational number theory Computational topology...
In discretegeometry and mechanics, structural rigidity is a combinatorial theory for predicting the flexibility of ensembles formed by rigid bodies connected...
sites are allowed in the definition (this setting has applications in geometry of numbers and crystallography), but again, in many cases only finitely...
Baker. There are many projective geometries, which may be divided into discrete and continuous: a discretegeometry comprises a set of points, which may...
Synthetic geometry (sometimes referred to as axiomatic geometry or even pure geometry) is geometry without the use of coordinates. It relies on the axiomatic...
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