SettingsDiscrete geometry
Ammann-Beenker tiling
In geometry, an Ammann–Beenker tiling is a nonperiodic tiling generated by an aperiodic set of prototiles named after Robert Ammann, who first discovered the tilings in the 1970s, and after F. P...
In geometry, an Ammann–Beenker tiling is a nonperiodic tiling generated by an aperiodic set of prototiles named after Robert Ammann, who first discovered the tilings in the 1970s, and after F. P...
Ammann–Beenker tiling
In geometry, an Ammann–Beenker tiling is a nonperiodic tiling generated by an aperiodic set of prototiles named after Robert Ammann, who first discovered the tilings in the 1970s, and after F. P...
In geometry, an Ammann–Beenker tiling is a nonperiodic tiling generated by an aperiodic set of prototiles named after Robert Ammann, who first discovered the tilings in the 1970s, and after F. P...
Arrangement of hyperplanes
In geometry and combinatorics, an arrangement of hyperplanes is a finite set A of hyperplanes in a linear, affine, or projective space S.
In geometry and combinatorics, an arrangement of hyperplanes is a finite set A of hyperplanes in a linear, affine, or projective space S.
Arrangement of lines
In geometry an arrangement of lines is the partition of the plane formed by a collection of lines.
In geometry an arrangement of lines is the partition of the plane formed by a collection of lines.
Beck's theorem (geometry)
Beck's theorem says that finite collections of points in the plane fall into one of two extremes; one where a large fraction of points lie on a single line, and one where a large number of lines...
Beck's theorem says that finite collections of points in the plane fall into one of two extremes; one where a large fraction of points lie on a single line, and one where a large number of lines...
Bedlam cube
The Bedlam cube is a solid dissection puzzle invented by British puzzle expert Bruce Bedlam.
The Bedlam cube is a solid dissection puzzle invented by British puzzle expert Bruce Bedlam.
Bolyai-Gerwien theorem
In geometry, the Bolyai–Gerwien theorem, named after Farkas Bolyai and Paul Gerwien, states that any two simple polygons of equal area are equidecomposable; i.e. one can cut the first into f...
In geometry, the Bolyai–Gerwien theorem, named after Farkas Bolyai and Paul Gerwien, states that any two simple polygons of equal area are equidecomposable; i.e. one can cut the first into f...
Bolyai–Gerwien theorem
In geometry, the Bolyai–Gerwien theorem, named after Farkas Bolyai and Paul Gerwien, states that any two simple polygons of equal area are equidecomposable; i.e. one can cut the first into f...
In geometry, the Bolyai–Gerwien theorem, named after Farkas Bolyai and Paul Gerwien, states that any two simple polygons of equal area are equidecomposable; i.e. one can cut the first into f...
Borsuk's conjecture
The Borsuk problem in geometry, for historical reasons incorrectly called a Borsuk conjecture, is a question in discrete geometry.
The Borsuk problem in geometry, for historical reasons incorrectly called a Borsuk conjecture, is a question in discrete geometry.
Carathéodory's theorem (convex hull)
In convex geometry Carathéodory's theorem states that if a point x of Rd lies in the convex hull of a set P, there is a subset P′ of P consisting of d+1...
In convex geometry Carathéodory's theorem states that if a point x of Rd lies in the convex hull of a set P, there is a subset P′ of P consisting of d+1...
Carpenter's rule problem
The carpenter's rule problem is a discrete geometry problem, which can be stated in the following manner: Can a simple planar polygon be moved continuously to a position where all its vertices...
The carpenter's rule problem is a discrete geometry problem, which can be stated in the following manner: Can a simple planar polygon be moved continuously to a position where all its vertices...
Cauchy's theorem (geometry)
Cauchy's theorem is a theorem in geometry, named after Augustin Cauchy.
Cauchy's theorem is a theorem in geometry, named after Augustin Cauchy.
Centroidal Voronoi tessellation
In geometry, a centroidal Voronoi tessellation is a special type of Voronoi tessellation or Voronoi diagrams.
In geometry, a centroidal Voronoi tessellation is a special type of Voronoi tessellation or Voronoi diagrams.
Close-packing of equal spheres
In geometry, close-packing of spheres is a dense arrangement of equal spheres in an infinite, regular arrangement (or lattice).
In geometry, close-packing of spheres is a dense arrangement of equal spheres in an infinite, regular arrangement (or lattice).
Close-packing of spheres
In geometry, close-packing of spheres is a dense arrangement of equal spheres in an infinite, regular arrangement (or lattice).
In geometry, close-packing of spheres is a dense arrangement of equal spheres in an infinite, regular arrangement (or lattice).
Constrained Delaunay triangulation
In computational geometry, a constrained Delaunay triangulation is a generalization of the Delaunay triangulation that forces certain required segments into the triangulation.
In computational geometry, a constrained Delaunay triangulation is a generalization of the Delaunay triangulation that forces certain required segments into the triangulation.
Conway puzzle
Conway's puzzle is a packing problem using rectangular blocks, named after its inventor, mathematician John Conway.
Conway's puzzle is a packing problem using rectangular blocks, named after its inventor, mathematician John Conway.
Covering problem of Rado
The covering problem of Rado is an unsolved problem in geometry concerning covering planar sets by squares.
The covering problem of Rado is an unsolved problem in geometry concerning covering planar sets by squares.
Davenport-Schinzel sequence
In combinatorics, a Davenport–Schinzel sequence is a sequence of symbols in which the number of times any two symbols may appear in alternation is limited.
In combinatorics, a Davenport–Schinzel sequence is a sequence of symbols in which the number of times any two symbols may appear in alternation is limited.
Davenport–Schinzel sequence
In combinatorics, a Davenport–Schinzel sequence is a sequence of symbols in which the number of times any two symbols may appear in alternation is limited.
In combinatorics, a Davenport–Schinzel sequence is a sequence of symbols in which the number of times any two symbols may appear in alternation is limited.
De Bruijn's theorem
De Bruijn's theorem is a theorem concerning computational geometry and packing problems attributed to Nicolaas Govert de Bruijn.
De Bruijn's theorem is a theorem concerning computational geometry and packing problems attributed to Nicolaas Govert de Bruijn.
De Bruijn-Erdős theorem (incidence geometry)
In incidence geometry, the De Bruijn–Erdős theorem, originally published by Nicolaas Govert de Bruijn and Paul Erdős, states a lower bound on the number of lines determined by n points in a ...
In incidence geometry, the De Bruijn–Erdős theorem, originally published by Nicolaas Govert de Bruijn and Paul Erdős, states a lower bound on the number of lines determined by n points in a ...
De Bruijn–Erdős theorem (incidence geometry)
In incidence geometry, the De Bruijn–Erdős theorem, originally published by Nicolaas Govert de Bruijn and Paul Erdős, states a lower bound on the number of lines determined by n points in a ...
In incidence geometry, the De Bruijn–Erdős theorem, originally published by Nicolaas Govert de Bruijn and Paul Erdős, states a lower bound on the number of lines determined by n points in a ...
Delaunay triangulation
In mathematics and computational geometry, a Delaunay triangulation for a set P of points in the plane is a triangulation DT(P) such that no point in P is inside the circumcir...
In mathematics and computational geometry, a Delaunay triangulation for a set P of points in the plane is a triangulation DT(P) such that no point in P is inside the circumcir...
Discrete geometry
Discrete geometry and combinatorial geometry are branches of geometry that study combinatorial properties and constructive methods of discrete geometric objects.
Discrete geometry and combinatorial geometry are branches of geometry that study combinatorial properties and constructive methods of discrete geometric objects.
Dissection problem
In geometry, a dissection problem is the problem of partitioning a geometric figure (such as a polytope or ball) into smaller pieces that may be rearranged into a new figure of equal content.
In geometry, a dissection problem is the problem of partitioning a geometric figure (such as a polytope or ball) into smaller pieces that may be rearranged into a new figure of equal content.
Erdős distinct distances problem
In discrete geometry, the Erdős distinct distances problem states that between distinct points on a plane there are at least distinct distances.
In discrete geometry, the Erdős distinct distances problem states that between distinct points on a plane there are at least distinct distances.
Erdős-Anning theorem
The Erdős–Anning theorem states that an infinite number of points in the plane can have mutual integer distances only if all the points lie on a straight line.
The Erdős–Anning theorem states that an infinite number of points in the plane can have mutual integer distances only if all the points lie on a straight line.
Erdős-Diophantine graph
An Erdős–Diophantine graph is an object in the mathematical subject of Diophantine equations consisting of a set of integer points at integer distances in the plane that cannot be extended by an...
An Erdős–Diophantine graph is an object in the mathematical subject of Diophantine equations consisting of a set of integer points at integer distances in the plane that cannot be extended by an...
Erdős-Nagy theorem
The Erdős–Nagy theorem is a result in discrete geometry about making a non-convex simple polygon into a convex by a finite sequence of flips.
The Erdős–Nagy theorem is a result in discrete geometry about making a non-convex simple polygon into a convex by a finite sequence of flips.
Erdős-Szekeres theorem
In mathematics, the Erdős–Szekeres theorem is a finitary result that makes precise one of the corollaries of Ramsey's theorem.
In mathematics, the Erdős–Szekeres theorem is a finitary result that makes precise one of the corollaries of Ramsey's theorem.
Erdős–Anning theorem
The Erdős–Anning theorem states that an infinite number of points in the plane can have mutual integer distances only if all the points lie on a straight line.
The Erdős–Anning theorem states that an infinite number of points in the plane can have mutual integer distances only if all the points lie on a straight line.
Erdős–Diophantine graph
An Erdős–Diophantine graph is an object in the mathematical subject of Diophantine equations consisting of a set of integer points at integer distances in the plane that cannot be extended by an...
An Erdős–Diophantine graph is an object in the mathematical subject of Diophantine equations consisting of a set of integer points at integer distances in the plane that cannot be extended by an...
Erdős–Nagy theorem
The Erdős–Nagy theorem is a result in discrete geometry about making a non-convex simple polygon into a convex by a finite sequence of flips.
The Erdős–Nagy theorem is a result in discrete geometry about making a non-convex simple polygon into a convex by a finite sequence of flips.
Erdős–Szekeres theorem
In mathematics, the Erdős–Szekeres theorem is a finitary result that makes precise one of the corollaries of Ramsey's theorem.
In mathematics, the Erdős–Szekeres theorem is a finitary result that makes precise one of the corollaries of Ramsey's theorem.
Flexible polyhedron
In geometry, a flexible polyhedron is a polyhedral surface that allows continuous non-rigid deformations such that all faces remain rigid.
In geometry, a flexible polyhedron is a polyhedral surface that allows continuous non-rigid deformations such that all faces remain rigid.
Four-vertex theorem
The four-vertex theorem states that the curvature function of a simple, closed, smooth plane curve has at least four local extrema.
The four-vertex theorem states that the curvature function of a simple, closed, smooth plane curve has at least four local extrema.
Geombinatorics
Geombinatorics is a mathematical research journal founded by Alexander Soifer and published by the University of Colorado, USA, since 1991 under an international board of editors.
Geombinatorics is a mathematical research journal founded by Alexander Soifer and published by the University of Colorado, USA, since 1991 under an international board of editors.
Geometric combinatorics
Geometric combinatorics is a branch of mathematics in general and combinatorics in particular.
Geometric combinatorics is a branch of mathematics in general and combinatorics in particular.
Guillotine problem
The guillotine problem is a problem in combinatorial geometry and in printing.
The guillotine problem is a problem in combinatorial geometry and in printing.
Hadwiger conjecture (combinatorial geometry)
In combinatorial geometry, the Hadwiger conjecture states that any convex body in n-dimensional Euclidean space can be covered by 2n or fewer smaller bodies homothetic with the ori...
In combinatorial geometry, the Hadwiger conjecture states that any convex body in n-dimensional Euclidean space can be covered by 2n or fewer smaller bodies homothetic with the ori...
Happy Ending problem
The Happy Ending problem (so named by Paul Erdős because it led to the marriage of George Szekeres and Esther Klein) is the following statement: :Theorem.
The Happy Ending problem (so named by Paul Erdős because it led to the marriage of George Szekeres and Esther Klein) is the following statement: :Theorem.
Heilbronn triangle problem
In mathematics, the Heilbronn triangle problem is a typical question in the area of irregularities of distribution, within elementary geometry.
In mathematics, the Heilbronn triangle problem is a typical question in the area of irregularities of distribution, within elementary geometry.
Helly's theorem
Helly's theorem is a basic result in discrete geometry describing the ways that convex sets may intersect each other.
Helly's theorem is a basic result in discrete geometry describing the ways that convex sets may intersect each other.
Heronian triangle
In geometry, a Heronian triangle is a triangle whose sidelengths and area are all rational numbers.
In geometry, a Heronian triangle is a triangle whose sidelengths and area are all rational numbers.
Honeycomb conjecture
The honeycomb conjecture states that a regular hexagonal grid or honeycomb is the best way to divide a surface into regions of equal area with the least total perimeter.
The honeycomb conjecture states that a regular hexagonal grid or honeycomb is the best way to divide a surface into regions of equal area with the least total perimeter.
Integer triangle
An integer triangle or integral triangle is a triangle all of whose sides have lengths that are integers.
An integer triangle or integral triangle is a triangle all of whose sides have lengths that are integers.
K-set (geometry)
In particular, when k = n/2 (where n is the size of S), the line or hyperplane that separates a k-set from the rest of S is a halving line or halving plane.
In particular, when k = n/2 (where n is the size of S), the line or hyperplane that separates a k-set from the rest of S is a halving line or halving plane.
Kakeya set
In mathematics, a Kakeya set, or Besicovitch set, is any set of points in Euclidean space which contains a unit line segment in every direction.
In mathematics, a Kakeya set, or Besicovitch set, is any set of points in Euclidean space which contains a unit line segment in every direction.
Kepler conjecture
The Kepler conjecture, named after Johannes Kepler, is a mathematical conjecture about sphere packing in three-dimensional Euclidean space.
The Kepler conjecture, named after Johannes Kepler, is a mathematical conjecture about sphere packing in three-dimensional Euclidean space.
Kissing number problem
In geometry, a kissing number is defined as the number of non-overlapping unit spheres that touch another given unit sphere.
In geometry, a kissing number is defined as the number of non-overlapping unit spheres that touch another given unit sphere.
Kobon triangle problem
The Kobon triangle problem is an unsolved problem in combinatorial geometry first stated by Kobon Fujimura.
The Kobon triangle problem is an unsolved problem in combinatorial geometry first stated by Kobon Fujimura.
Krein-Milman theorem
In the mathematical theory of functional analysis, the Krein–Milman theorem is a proposition about convex sets in topological vector spaces.
In the mathematical theory of functional analysis, the Krein–Milman theorem is a proposition about convex sets in topological vector spaces.
Krein–Milman theorem
In the mathematical theory of functional analysis, the Krein–Milman theorem is a proposition about convex sets in topological vector spaces.
In the mathematical theory of functional analysis, the Krein–Milman theorem is a proposition about convex sets in topological vector spaces.
McMullen problem
The McMullen problem is an open problem in discrete geometry.
The McMullen problem is an open problem in discrete geometry.
Moser's worm problem
Moser's worm problem was formulated by the Austrian-Canadian mathematician Leo Moser in 1966.
Moser's worm problem was formulated by the Austrian-Canadian mathematician Leo Moser in 1966.
Mountain climbing problem
In mathematics, the mountain climbing problem is a problem of finding conditions two functions forming profiles of a two-dimensional mountain must satisfy, so that two climbers can start on the ...
In mathematics, the mountain climbing problem is a problem of finding conditions two functions forming profiles of a two-dimensional mountain must satisfy, so that two climbers can start on the ...
Moving sofa problem
The moving sofa problem was formulated by the Austrian-Canadian mathematician Leo Moser in 1966.
The moving sofa problem was formulated by the Austrian-Canadian mathematician Leo Moser in 1966.
Napkin folding problem
The napkin folding problem in geometry explores whether folding a square or a rectangular napkin can increase its perimeter.
The napkin folding problem in geometry explores whether folding a square or a rectangular napkin can increase its perimeter.
Nearest neighbor search
Nearest neighbor search (NNS), also known as proximity search, similarity search or closest point search, is an optimization problem for finding closest points in metric ...
Nearest neighbor search (NNS), also known as proximity search, similarity search or closest point search, is an optimization problem for finding closest points in metric ...
Necklace splitting problem
In mathematics, and in particular combinatorics, the necklace splitting problem arises in a variety of contexts including exact division; its picturesque name is due to mathematicians Noga Alon ...
In mathematics, and in particular combinatorics, the necklace splitting problem arises in a variety of contexts including exact division; its picturesque name is due to mathematicians Noga Alon ...
Orchard-planting problem
In discrete geometry, the orchard-planting problem asks for the maximum number of 3-point lines attainable by a configuration of points in the plane.
In discrete geometry, the orchard-planting problem asks for the maximum number of 3-point lines attainable by a configuration of points in the plane.
Oriented matroid
An oriented matroid is a mathematical structure that abstracts the properties of directed graphs and of arrangements of vectors in a vector space over an ordered field (particularly for partial...
An oriented matroid is a mathematical structure that abstracts the properties of directed graphs and of arrangements of vectors in a vector space over an ordered field (particularly for partial...
Packing problem
Packing problems are a class of optimization problems in mathematics which involve attempting to pack objects together (often inside a container), as densely as possible.
Packing problems are a class of optimization problems in mathematics which involve attempting to pack objects together (often inside a container), as densely as possible.
Penrose tiling
A Penrose tiling is a non-periodic tiling generated by an aperiodic set of prototiles named after Sir Roger Penrose, who investigated these sets in the 1970s.
A Penrose tiling is a non-periodic tiling generated by an aperiodic set of prototiles named after Sir Roger Penrose, who investigated these sets in the 1970s.
Pinwheel tiling
Pinwheel tilings are aperiodic tilings defined by Charles Radin and based on a construction due to John Conway.
Pinwheel tilings are aperiodic tilings defined by Charles Radin and based on a construction due to John Conway.
Pitteway triangulation
In computational geometry, a Pitteway triangulation is a point set triangulation in which the nearest neighbor of any point p within the triangulation is one of the vertices of the triangle ...
In computational geometry, a Pitteway triangulation is a point set triangulation in which the nearest neighbor of any point p within the triangulation is one of the vertices of the triangle ...
Point set triangulation
A triangulation of a set of points P in the plane is a triangulation of the convex hull of P, with all points from P being among the vertices of the triangulation.
A triangulation of a set of points P in the plane is a triangulation of the convex hull of P, with all points from P being among the vertices of the triangulation.
Quaquaversal tiling
The quaquaversal tiling is a nonperiodic tiling of the euclidean 3-space introduced by John Conway and Charles Radin.
The quaquaversal tiling is a nonperiodic tiling of the euclidean 3-space introduced by John Conway and Charles Radin.
Radon's theorem
In geometry, Radon's theorem on convex sets, named after Johann Radon, states that any set of d + 2 points in Rd can be partitioned into two (disjoint) sets whose c...
In geometry, Radon's theorem on convex sets, named after Johann Radon, states that any set of d + 2 points in Rd can be partitioned into two (disjoint) sets whose c...
Regular map (graph theory)
In mathematics, a regular map is a symmetric tessellation of a closed surface.
In mathematics, a regular map is a symmetric tessellation of a closed surface.
Self-avoiding walk
In mathematics, a self-avoiding walk (SAW) is a sequence of moves on a lattice that does not visit the same point more than once.
In mathematics, a self-avoiding walk (SAW) is a sequence of moves on a lattice that does not visit the same point more than once.
Slothouber-Graatsma puzzle
The Slothouber–Graatsma puzzle is a packing problem that calls for packing six 1 × 2 × 2 blocks and three 1 × 1 × 1 blocks into a 3 × 3 × 3 box.
The Slothouber–Graatsma puzzle is a packing problem that calls for packing six 1 × 2 × 2 blocks and three 1 × 1 × 1 blocks into a 3 × 3 × 3 box.
Slothouber–Graatsma puzzle
The Slothouber–Graatsma puzzle is a packing problem that calls for packing six 1 × 2 × 2 blocks and three 1 × 1 × 1 blocks into a 3 × 3 × 3 box.
The Slothouber–Graatsma puzzle is a packing problem that calls for packing six 1 × 2 × 2 blocks and three 1 × 1 × 1 blocks into a 3 × 3 × 3 box.
Sphere packing
In mathematics sphere packing problems concern arrangements of non-overlapping spheres within a containing space.
In mathematics sphere packing problems concern arrangements of non-overlapping spheres within a containing space.
Squaring the square
Squaring the square is the problem of tiling an integral square using only other integral squares.
Squaring the square is the problem of tiling an integral square using only other integral squares.
Straight skeleton
In geometry, a straight skeleton is a method of representing a polygon by a topological skeleton.
In geometry, a straight skeleton is a method of representing a polygon by a topological skeleton.
Szemerédi-Trotter theorem
The Szemerédi–Trotter theorem is a mathematical result in the field of combinatorial geometry.
The Szemerédi–Trotter theorem is a mathematical result in the field of combinatorial geometry.
Szemerédi–Trotter theorem
The Szemerédi–Trotter theorem is a mathematical result in the field of combinatorial geometry.
The Szemerédi–Trotter theorem is a mathematical result in the field of combinatorial geometry.
Tarski's circle-squaring problem
Tarski's circle-squaring problem is the challenge, posed by Alfred Tarski in 1925, to take a disc in the plane, cut it into finitely many pieces, and reassemble the pieces so as to get a square ...
Tarski's circle-squaring problem is the challenge, posed by Alfred Tarski in 1925, to take a disc in the plane, cut it into finitely many pieces, and reassemble the pieces so as to get a square ...
Tverberg's theorem
In discrete geometry, Tverberg's theorem, first stated by, is the result that sufficiently many points in d-dimensional Euclidean space can be partitioned into subsets with intersecting conv...
In discrete geometry, Tverberg's theorem, first stated by, is the result that sufficiently many points in d-dimensional Euclidean space can be partitioned into subsets with intersecting conv...
Vertex enumeration problem
In mathematics, the vertex enumeration problem for a polyhedron, a polyhedral cell complex, a hyperplane arrangement, or some other object of discrete geometry, is the problem of determination o...
In mathematics, the vertex enumeration problem for a polyhedron, a polyhedral cell complex, a hyperplane arrangement, or some other object of discrete geometry, is the problem of determination o...
Voronoi diagram
In mathematics, a Voronoi diagram is a special kind of decomposition of a given space, e.g., a metric space, determined by distances to a specified family of objects in the space.
In mathematics, a Voronoi diagram is a special kind of decomposition of a given space, e.g., a metric space, determined by distances to a specified family of objects in the space.
Wallace-Bolyai-Gerwien theorem
In geometry, the Wallace–Bolyai–Gerwien theorem, named after William Wallace, Farkas Bolyai and Paul Gerwien, states that any two simple polygons of equal area are equidecomposable; i.e. one...
In geometry, the Wallace–Bolyai–Gerwien theorem, named after William Wallace, Farkas Bolyai and Paul Gerwien, states that any two simple polygons of equal area are equidecomposable; i.e. one...
Weighted Voronoi diagram
In mathematics, a weighted Voronoi diagram in n dimensions is a Voronoi diagram for which the Voronoi cells are defined in terms of a distance defined by some common metrics modified by weig...
In mathematics, a weighted Voronoi diagram in n dimensions is a Voronoi diagram for which the Voronoi cells are defined in terms of a distance defined by some common metrics modified by weig...