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...n|year=1976}}.<ref>{{Citation | last1=Jørgensen | first1=Troels | title=On discrete groups of Möbius transformations | jstor=2373814 | mr=0427627 | year=1976 | The inequality states that if ''A'' and ''B'' generate a non-elementary discrete subgroup of the SL₂('''C'''), then ...

...is the [[discrete geometry]] analogue of the concept of [[convex set]] in geometry. ....<ref name=":1">{{Cite journal|last=Yang|first=Zaifu|date=2009-12-01|title=Discrete fixed point analysis and its applications|journal=Journal of Fixed Point Th ...

...by [[Joseph O'Rourke (professor)|Joseph O'Rourke]], and published in 1987 in the International Series of Monographs on Computer Science of the [[Oxford ...the book has as a theme "the interplay between discrete and computational geometry".{{r|avis}} ...

...version of the theorem states that, if a finite set of red and blue points in the [[Euclidean plane]] has the property that, for every four points, there {{quote|If sheep and goats are grazing in a field and for every four animals there exists a line separating the sheep ...

...the number of constraints of the problem and [[fixed-parameter tractable]] in its {{nowrap|dimension.{{r|ads}}}} The same theorem applies more generally ...s]] David E. Bell and [[Herbert Scarf]], who both rediscovered it {{nowrap|in 1977{{r|bell|scarf}}}} and pointed out its applications to integer {{nowrap ...

...cess-date=2020-02-20}}</ref> His main research interest is [[computational geometry]]. ...enclosing boxes.|volume=14|year=1985|issue=3|s2cid=8311538}}. As reviewed in {{zbl|0582.68067}}</ref> ...

...nsions require characteristic 0.<ref>{{Springer|id=B/b015770|title=Bertini theorems}}</ref><ref>Hartshorne, Ch. III.10.</ref> ...ive variety over an algebraically closed field, embedded in a [[algebraic geometry of projective spaces|projective space]] <math>\mathbf P^n</math>. ...

...em''' is a result in the intersection of [[combinatorics]] and [[algebraic geometry]] used to represent [[algebraic manifold|algebraic]] (or [[semialgebraic se : Let <math>V</math> be a semialgebraic variety in <math>{\mathbb R}^n</math> defined over the integers. Then <math>V</math> i ...

In [[geometry]], the '''tennis ball theorem''' states that any [[smooth curve]] on the su ...Segre]], and the tennis ball theorem itself is a special case of a theorem in a 1977 paper by Joel L. Weiner.{{r|segre|global}} The name of the theorem c ...

...between any two vertices for which the corresponding binary strings differ in exactly one bit. Every middle layer graph is Hamiltonian.{{sfnp|Mütze|2016} ...b>2</sub>) and DCD(3) is the [[Desargues configuration]] (10₃). In {{sfnp|Gévay|2018}} configurations DCD(n) were further generalized to the u ...

{{Short description|Mathematical theory in the field of algebraic geometry}} ...\times_S S' \to S'</math> is semistable (i.e., the singularities are mild in some sense). Precise formulations depend on the specific versions of the th ...

...|minimum number of edge crossings]] in a plane drawing of a given [[Graph (discrete mathematics)|graph]], as a function of the number of [[Edge (graph theory)| It has applications in [[VLSI]] design and [[combinatorial geometry]], ...

{{Short description|Theorem in computational and discrete geometry}} [[File:Zone theorem.svg|thumb|upright=1.35|The zone of a line (red) in an arrangement of lines, consisting of all faces that touch the given line] ...

{{Short description|Class of algebraic theorems}} '''Local rigidity''' theorems in the theory of discrete subgroups of [[Lie group]]s are results which show that small deformations ...

In [[general topology]], a '''remote point''' is a [[Point (geometry)|point]] <math>p</math> that belongs to the [[Stone–Čech compactification]] Let <math>\R</math> be the [[real line]] with the standard topology. In 1962, [[Nathan Fine]] and [[Leonard Gillman]] proved that, assuming the [[c ...

{{Short description|On triangles in line arrangements}} ...(mathematician)|Samuel Roberts]], a British mathematician who published it in 1889.{{r|grunbaum|roberts}} ...

...tive space]] with the property that the line through any two of the points in the subset also passes through at least one other point of the subset. ...ne containing the pair and that every line contains at least three points. In this more general form they are also called '''Sylvester–Gallai designs'''. ...

...ic techniques for using polynomials and ideas from areas such as algebraic geometry to solve combinatorics problems. While a few techniques that follow the fr ...journal|last1=Dvir|first1=Zeev|year=2008|title=On the size of Kakeya sets in finite fields|journal=Journal of the American Mathematical Society|volume=2 ...

...Borsuk–Ulam Theorem: Lectures on Topological Methods in Combinatorics and Geometry ...thematician)|Jiří Matoušek]], and published in 2003 by [[Springer-Verlag]] in their Universitext series ({{ISBN|978-3-540-00362-5}}).{{r|dzedzej|popliche ...

[[File:De Bruijn theorem coloring.svg|thumb|A coloring of the unit cubes in a <math>6\cdot 6\cdot 6</math> box that may be used to prove the impossibil ...de Bruijn's theorem'''. According to this theorem, a "harmonic brick" (one in which each side length is a multiple of the next smaller side length) can o ...