AI & ChatGPT searches , social queries for CONVEX GEOMETRY
Search references for CONVEX GEOMETRY. Phrases containing CONVEX GEOMETRY
See searches and references containing CONVEX GEOMETRY!
Search references for CONVEX GEOMETRY. Phrases containing CONVEX GEOMETRY
See searches and references containing CONVEX GEOMETRY!CONVEX GEOMETRY
Branch of geometry
In mathematics, convex geometry is the branch of geometry studying convex sets, mainly in Euclidean space. Convex sets occur naturally in many areas:
Convex_geometry
In geometry, set whose intersection with every line is a single line segment
In geometry, a set of points is convex if it contains every line segment between two points in the set. For example, a solid cube is a convex set, but
Convex_set
Smallest convex set containing a given set
In geometry, the convex hull, convex envelope or convex closure of a shape is the smallest convex set that contains it. The convex hull may be defined
Convex_hull
Polygon that is the boundary of a convex set
In geometry, a convex polygon is a polygon that is the boundary of a convex set. This means that the line segment between two points of the polygon is
Convex_polygon
Branch of mathematics
groups are sometimes regarded as strongly geometric as well. Convex geometry investigates convex shapes in the Euclidean space and its more abstract analogues
Geometry
Russian mathematician (born 1966)
in the field of convex geometry. His first published article studied the combinatorial structures arising from intersections of convex polyhedra.[P85]
Grigori_Perelman
Application of geometry in number theory
and lattice theory. The geometry of numbers contributed to the development of convex geometry. A central operation on convex bodies is the Minkowski sum
Geometry_of_numbers
Overview of and topical guide to geometry
solid geometry Contact geometry Convex geometry Descriptive geometry Differential geometry Digital geometry Discrete geometry Distance geometry Elliptic
Outline_of_geometry
Planar surface that forms part of the boundary of a solid object
Discrete Geometry, Graduate Texts in Mathematics, vol. 212, Springer, ISBN 9780387953748, MR 1899299 Rockafellar, R. T. (1997) [1970]. Convex Analysis
Face_(geometry)
Type of plane curve
In geometry, a convex curve is a plane curve that has a supporting line through each of its points. There are many other equivalent definitions of these
Convex_curve
Mathematical set closed under positive linear combinations
(disambiguation) Cone (geometry) Cone (topology) Farkas' lemma Bipolar theorem Ordered vector space Boyd, Stephen; Vandenberghe, Lieven (2004-03-08). Convex Optimization
Convex_cone
Convex hull of a finite set of points in a Euclidean space
Ziegler on the subject, as well as in many other texts in discrete geometry, convex polytopes are often simply called "polytopes". Grünbaum points out
Convex_polytope
Point in the convex hull of a set P in Rd, is the convex combination of d+1 points in P
Carathéodory's theorem is a theorem in convex geometry. It states that if a point x {\displaystyle x} lies in the convex hull C o n v ( P ) {\displaystyle
Carathéodory's theorem (convex hull)
Carathéodory's_theorem_(convex_hull)
Flat-sided three-dimensional shape
biological creatures, nature, and modern computational geometry. There are several standard definitions of convex polyhedra, but except for certain degenerate cases
Polyhedron
Branch of geometry that studies combinatorial properties and constructive methods
Discrete geometry has a large overlap with convex geometry and computational geometry, and is closely related to subjects such as finite geometry, combinatorial
Discrete_geometry
Class of algorithms in computational geometry
construct convex hulls of various objects have a broad range of applications in mathematics and computer science. In computational geometry, numerous
Convex_hull_algorithms
Mathematics of convex functions and sets
convex geometry, economics, and related fields. A set is convex if it contains every line segment joining two of its points. A function is convex if
Convex_analysis
Linear combination of points where all coefficients are non-negative and sum to 1
In convex geometry and vector algebra, a convex combination is a linear combination of points (which can be vectors, scalars, or more generally points
Convex_combination
Algebraic variety containing an algebraic torus
information is also encoded in a convex polytope, which creates a powerful connection of the subject with convex geometry. Familiar examples of toric varieties
Toric_variety
Structure in convex geometry
In mathematics, specifically convex geometry, the normal fan of a convex polytope P is a polyhedral fan that is dual to P. Normal fans have applications
Normal_fan
Generalization of the tangent space to a manifold to the case of certain spaces
ISBN 978-0-8176-4848-0. A. D. Aleksandrov (2006). Intrinsic geometry of convex surfaces. Chapman & Hall/CRC Press. Chapman & Hall/CRC Press. doi:10
Tangent_cone
of "convexity" on metric spaces. Karl Menger defined a metric space as convex if any "segment" joining two points in that space has other points in it
Convex_metric_space
Non-empty convex set in Euclidean space
contained in, an n-dimensional convex object Brunn–Minkowski theorem, which has many implications relevant to the geometry of convex bodies. Hug, Daniel; Weil
Convex_body
Greek mathematician (1873–1950)
Carathéodory's theorem in convex geometry states that if a point x {\displaystyle x} of R d {\displaystyle \mathbb {R} ^{d}} lies in the convex hull of a set P
Constantin_Carathéodory
German mathematician and physicist (1864–1909)
Lithuanian-German, or Russian. He created and developed the geometry of numbers and elements of convex geometry, and used geometrical methods to solve problems in
Hermann_Minkowski
mathematics, a convex space (or barycentric algebra) is a space in which it is possible to take convex combinations of any finite set of points. A convex space
Convex_space
Convex polyhedron with regular faces
In geometry, a Johnson solid, sometimes also known as a Johnson–Zalgaller solid, is a convex polyhedron whose faces are regular polygons and that is not
Johnson_solid
Four-dimensional analogues of the regular polyhedra in three dimensions
Still "Convex and abstract polytopes", Programme and abstracts, MIT, 2005 Johnson, Norman W. (2018). "§ 11.5 Spherical Coxeter groups". Geometries and Transformations
Regular_4-polytope
German mathematician (1905–1988)
mathematician known for his contributions to geometry and to optimization theory. Fenchel established the basic results of convex analysis and nonlinear optimization
Werner_Fenchel
A convex cap is a well defined structure in mathematics commonly used in convex geometry for approximating convex shapes. It is used in the construction
Convex_cap
Measure method in computational geometry
images Convex polygon Convex hull Smallest enclosing box "Rotating Calipers" at Toussaint's home page Shamos, Michael (1978). "Computational Geometry" (PDF)
Rotating_calipers
onto convex sets (POCS), sometimes known as the alternating projection method, is a method to find a point in the intersection of two closed convex sets
Projections_onto_convex_sets
Branch of computer science
Computational geometry is a branch of computer science devoted to the study of algorithms that can be stated in terms of geometry. Some purely geometrical
Computational_geometry
Distance from origin of tangent hyperplanes
in convex geometry. The support function h A : R n → R {\displaystyle h_{A}\colon \mathbb {R} ^{n}\to \mathbb {R} } of a non-empty closed convex set
Support_function
Branch of mathematics
objects, such as convex bodies and normed spaces, as the dimension tends to infinity. It is at the intersection of convex geometry and functional analysis
Asymptotic_geometry
Mathematical theorem
mathematical theorem in the fields of mathematical statistics and convex geometry. The Gaussian correlation inequality states: Let μ {\displaystyle \mu
Gaussian correlation inequality
Gaussian_correlation_inequality
Mathematical subject
faces of convex polyhedra), convex geometry (the study of convex sets, in particular combinatorics of their intersections), and discrete geometry, which
Geometric_combinatorics
Convex plane region bounded by two circular arcs
2-dimensional geometry, a lens is a convex region bounded by two circular arcs joined to each other at their endpoints. In order for this shape to be convex, both
Lens_(geometry)
Kakutani's theorem is a result in geometry named after Shizuo Kakutani. It states that every convex body in 3-dimensional space has a circumscribed cube
Kakutani's_theorem_(geometry)
Theorem in geometry about convex sets
In geometry, Radon's theorem on convex sets, published by Johann Radon in 1921, states that: Any set of d + 2 points in Rd can be partitioned into two
Radon's_theorem
problems in mathematical programming can be formulated as problems on convex sets or convex bodies. Six kinds of problems are particularly important: optimization
Algorithmic problems on convex sets
Algorithmic_problems_on_convex_sets
Hyperplane in geometry
In geometry, a supporting hyperplane of a set S {\displaystyle S} in Euclidean space R n {\displaystyle \mathbb {R} ^{n}} is a hyperplane that has both
Supporting_hyperplane
Sequences of convex sets in a bounded set have convergent subsequences
topology and convex geometry about sequences of convex sets. Specifically, given a sequence { K n } {\displaystyle \{K_{n}\}} of convex sets contained
Blaschke_selection_theorem
Topics referred to by the same term
affine geometry Conical hull, in convex geometry Convex hull, in convex geometry Carathéodory's theorem (convex hull) Holomorphically convex hull, in
Hull
Skeletonized version of algebraic geometry
Convex Geometry as the Ricardian Theory of International Trade" draft paper. Zhang, Liwen; Naitzat, Gregory; Lim, Lek-Heng (2018). "Tropical Geometry
Tropical_geometry
Sums vector sets A and B by adding each vector in A to each vector in B
Polygons", Discrete & Computational Geometry, 35 (2): 223–240, doi:10.1007/s00454-005-1206-y. Schneider, Rolf (1993), Convex bodies: the Brunn-Minkowski theory
Minkowski_addition
Theorem in convex and algebraic geometry
Gordan's lemma is a lemma in convex geometry and algebraic geometry. It can be stated in several ways. Let A {\displaystyle A} be a matrix of integers
Gordan's_lemma
Theorem about the intersections of d-dimensional convex sets
Helly's theorem is a basic result in discrete geometry on the intersection of convex sets. It was discovered by Eduard Helly in 1913, but not published
Helly's_theorem
Rigidity theorem for convex polyhedra
Cauchy's theorem is a theorem in geometry, named after Augustin Cauchy. It states that convex polytopes in three dimensions with congruent corresponding
Cauchy's_theorem_(geometry)
mathematics, more specifically, in convex geometry, the mixed volume is a way to associate a non-negative number to a tuple of convex bodies in R n {\displaystyle
Mixed_volume
theorem (discrete geometry) Busemann's theorem (Euclidean geometry) Carathéodory's theorem (convex geometry) Cauchy's theorem (geometry) Classification
List_of_theorems
manifold. Convex analysis the study of properties of convex functions and convex sets. Convex geometry part of geometry devoted to the study of convex sets
Glossary of areas of mathematics
Glossary_of_areas_of_mathematics
In discrete geometry, a polytope is projectively unique (or projectively stable) if it has a unique convex realization up to projective transformations
Projectively_unique_polytope
Polytope combining two smaller polytopes
In convex geometry and the geometry of convex polytopes, the Blaschke sum of two polytopes is a polytope that has a facet parallel to each facet of the
Blaschke_sum
Polyhedra are determined by surface distance
describing three-dimensional convex polyhedra in terms of the distances between points on their surfaces. It implies that convex polyhedra with distinct shapes
Alexandrov's theorem on polyhedra
Alexandrov's_theorem_on_polyhedra
Convex and balanced set
of a real or complex vector space is said to be absolutely convex or disked if it is convex and balanced (some people use the term "circled" instead of
Absolutely_convex_set
On the existence of hyperplanes separating disjoint convex sets
In geometry, the hyperplane separation theorem is a theorem about disjoint convex sets in n-dimensional Euclidean space. There are several rather similar
Hyperplane_separation_theorem
Raphael (2020), "Topological drawings meet classical theorems from convex geometry", Proceedings of the 28th International Symposium on Graph Drawing
Kirchberger's_theorem
usually mentioned in any good reference on convex geometry, for instance, Selected topics in convex geometry by Maria Moszyńska (Birkhäuser, Boston 2006)
Mean_width
On partitions into intersecting convex hulls
In discrete geometry, Tverberg's theorem, first stated by Helge Tverberg in 1966, is the result that sufficiently many points in Euclidean space can be
Tverberg's_theorem
the k {\displaystyle k} -skeleton of the polytope. The edge graph of a convex polytope is a finite simple graph. It is connected, since a path between
Graph_of_a_polytope
Russian mathematician (born 1936)
June 1936) is a Russian mathematician. He works in differential and convex geometry. Burago studied at Leningrad University, where he obtained his Ph.D
Yuri_Burago
Quadrilateral symmetric across a diagonal
In Euclidean geometry, a kite is a quadrilateral with reflection symmetry across a diagonal. Because of this symmetry, a kite has two equal angles and
Kite_(geometry)
Shape with three sides
polygon with three corners and three sides, one of the basic shapes in geometry. The corners, also called vertices, are zero-dimensional points while the
Triangle
Class of convex shapes
In convex geometry, a zonoid is a type of centrally symmetric convex body. The zonoids have several definitions, equivalent up to translations of the
Zonoid
Doignon's theorem in geometry is an analogue of Helly's theorem for the integer lattice. It states that, if a family of convex sets in d {\displaystyle
Doignon's_theorem
German American mathematician
geometry. Providence, Rhode Island: American Mathematical Society. ISBN 978-0-8218-5198-2. Sturmfels, Bernd (1998). "Polynomial equations and convex polytopes"
Bernd_Sturmfels
Optimization algorithm
the intersection of convex sets, and is a variant of the alternating projection method (also called the projections onto convex sets method). In its
Dykstra's projection algorithm
Dykstra's_projection_algorithm
Branch of discrete mathematics
discrete geometry. It includes a number of subareas such as polyhedral combinatorics (the study of faces of convex polyhedra), convex geometry (the study
Combinatorics
Concepts in convex analysis
Dual cone and polar cone are closely related concepts in convex analysis, a branch of mathematics. The dual cone C* of a subset C in a linear space X over
Dual_cone_and_polar_cone
Method of determining minimum distance between two convex sets
distance algorithm is a method of determining the minimum distance between two convex sets, first published by Elmer G. Gilbert, Daniel W. Johnson, and S. Sathiya
Gilbert–Johnson–Keerthi distance algorithm
Gilbert–Johnson–Keerthi_distance_algorithm
Theorem in geometry
much insight into the geometry of high dimensional convex bodies. In this section we sketch a few of those insights. Consider a convex body K ⊆ R n {\textstyle
Brunn–Minkowski_theorem
Mexican mathematician
whose research interests include discrete geometry, combinatorics, and convex geometry, including the geometry of bodies of constant width and related topics
Déborah_Oliveros
In convex geometry, the projection body Π K {\displaystyle \Pi K} of a convex body K {\displaystyle K} in n-dimensional Euclidean space is the convex body
Projection_body
Topics referred to by the same term
Look up convex or convexity in Wiktionary, the free dictionary. Convex or convexity may refer to: Convex lens, in optics Convex set, containing the whole
Convex
In mathematics, most commonly in convex geometry, an extreme set or face of a set C ⊆ V {\displaystyle C\subseteq V} in a vector space V {\displaystyle
Extreme_set
German mathematician
University of Freiburg. His main research interests are convex geometry and stochastic geometry. Schneider completed his PhD 1967 with Ruth Moufang at
Rolf_Schneider
Minimal superset that intersects each axis-parallel line in an interval
In geometry, a set K ⊂ Rd is defined to be orthogonally convex if, for every line L that is parallel to one of standard basis vectors, the intersection
Orthogonal_convex_hull
Theorem in topology
any continuous function f {\displaystyle f} mapping a nonempty compact convex set to itself, there is a point x 0 {\displaystyle x_{0}} such that f (
Brouwer_fixed-point_theorem
Point where two or more curves, lines, or edges meet
In geometry, a vertex (pl.: vertices or vertexes), also called a corner, is a point where two or more curves, lines, or line segments meet or intersect
Vertex_(geometry)
glossary. A caveat: many terms in Riemannian and metric geometry, such as convex function, convex set and others, do not have exactly the same meaning as
Glossary of Riemannian and metric geometry
Glossary_of_Riemannian_and_metric_geometry
Point not between two other points
In mathematics, an extreme point of a convex set S {\displaystyle S} in a real or complex vector space or affine space is a point in S {\displaystyle S}
Extreme_point
In geometry, a convex polyhedron whose faces are regular polygons is known as a Johnson solid, or sometimes as a Johnson–Zalgaller solid. Some authors
List_of_Johnson_solids
Chinese-American mathematician (born 1949)
differential geometry and geometric analysis. The impact of Yau's work are also seen in the mathematical and physical fields of convex geometry, algebraic
Shing-Tung_Yau
Fixed-point theorem for set-valued functions
It provides sufficient conditions for a set-valued function defined on a convex, compact subset of a Euclidean space to have a fixed point, i.e. a point
Kakutani_fixed-point_theorem
Sums of sets of vectors are nearly convex
The Shapley–Folkman lemma is a result in convex geometry that describes the Minkowski addition of sets in a vector space. The lemma may be intuitively
Shapley–Folkman_lemma
Convex quadrilateral with at least one pair of parallel sides
usually considered to be a convex quadrilateral in Euclidean geometry, but there are also crossed cases. If shape ABCD is a convex trapezoid, then the ABDC
Trapezoid
Type of non-Euclidean geometry
mathematics, hyperbolic geometry (also called Lobachevskian geometry or Bolyai–Lobachevskian geometry) is a non-Euclidean geometry. The parallel postulate
Hyperbolic_geometry
computational geometry, a set of points in the Euclidean plane or a higher-dimensional Euclidean space is said to be in convex position or convex independent
Convex_position
In functional analysis, the class of B-convex spaces is a class of Banach space. The concept of B-convexity was defined and used to characterize Banach
B-convex_space
Minkowsi sum of line segments
A zonotope is a convex polytope that can be described as the Minkowski sum of a finite set of line segments in R d {\displaystyle \mathbb {R} ^{d}} or
Zonotope
On when a space equals the closed convex hull of its extreme points
compact convex sets in locally convex topological vector spaces (TVSs). Krein–Milman theorem—A compact convex subset of a Hausdorff locally convex topological
Krein–Milman_theorem
Part of a line that is bounded by two distinct end points; line with two endpoints
is the convex hull of two points. Thus, the line segment can be expressed as a convex combination of the segment's two end points. In geometry, one might
Line_segment
Line segment joining two adjacent vertices in a polygon or polytope
edges of a 3-dimensional convex polyhedron are its ridges, and the edges of a 4-dimensional polytope are its peaks. Base (geometry) Extended side Ziegler
Edge_(geometry)
Theorem on extension of bounded linear functionals
theorem or the hyperplane separation theorem, and has numerous uses in convex geometry. The theorem is named for the mathematicians Hans Hahn and Stefan Banach
Hahn–Banach_theorem
Graph whose biconnected components are all cliques
the connected subsets of vertices in a connected block graph form a convex geometry, a property that is not true of any graphs that are not block graphs
Block_graph
combinations and hulls may be considered as convex combinations and convex hulls in the projective space. While the convex hull of a compact set is also a compact
Conical_combination
Technique in statistics
theory, affine differential geometry, convex analysis and many other fields. One of the most perspective information geometry approaches find applications
Information_geometry
Branch of mathematical statistics
instance, multilinear algebra, commutative algebra, algebraic geometry, convex geometry, combinatorics, theoretical problems in statistics, and their
Algebraic_statistics
Straight figure with zero width and depth
In geometry, a straight line, usually abbreviated line, is an infinitely long object with no width, depth, or curvature. It is a special case of a curve
Line_(geometry)
CONVEX GEOMETRY
CONVEX GEOMETRY
Surname or Lastname
Italian
Italian : from the title of rank conte ‘count’ (from Latin comes, genitive comitis ‘companion’). Probably in this sense (and the Late Latin sense of ‘traveling companion’), it was a medieval personal name; as a title it was no doubt applied ironically as a nickname for someone with airs and graces or simply for someone who worked in the service of a count.English : variant of Count, cognate with 1.French : nickname for someone in the service of a count or for someone who behaved pretentiously, from Old French conte, cunte ‘count’ (of the same derivation as 1).French (Conté) : variant of Comté (see Comte).
Boy/Male
Irish American
Hound lover. Full of desire; much desire.
Boy/Male
Irish American
Strong willed or wise. Also a : Hero.
Boy/Male
American, British, English
Dove
Surname or Lastname
English
English : from Old French covine ‘fraud’, ‘deceit’, hence a derogatory nickname for a trickster.English : habitational name from a place in Staffordshire named Coven ‘(place) at the huts or shelters (Old English cofa, dative plural cofum)’.
Boy/Male
British, Christian, English
Wagoner; To Convey
Surname or Lastname
English
English : metathesized form of the occupational name Coyner.English : possibly an occupational name for a dealer in rabbits or rabbit skins, from an agent derivative of Middle English cony ‘rabbit’ (see Coney).
Surname or Lastname
English
English : habitational name from a place named Cove, examples of which are found in Devon, Hampshire, and Suffolk, from Old English cofa ‘cove’, ‘bay’, ‘inlet’, also ‘shelter’, ‘hut’, or a topographic name with the same meaning.
Surname or Lastname
English
English : unexplained.
Boy/Male
Irish
Hero.
Boy/Male
American, Christian, German, Indian
High Desire
Surname or Lastname
Irish
Irish : variant spelling of Connor, now common in Scotland.English : occupational name for an inspector of weights and measures, Middle English connere, cunnere ‘inspector’, an agent derivative of cun(nen) ‘to examine’.
Surname or Lastname
English
English : from Middle English cony ‘rabbit’ (a back-formation from conies, from Old French conis, plural of conil), a nickname for someone thought to resemble a rabbit in some way or a metonymic occupational name for a dealer in rabbits or rabbit skins.
Boy/Male
Indian, Kannada, Tamil
God Murugan
Boy/Male
Irish
Hound of the plains.
Male
English
Variant spelling of English Connor, CONNER means "hound-lover."
Male
English
Anglicized form of Irish Gaelic Conláed, CONLEY means "purifying fire."
Surname or Lastname
Spanish and Portuguese
Spanish and Portuguese : nickname from the title of rank conde ‘count’, a derivative of Latin comes, comitis ‘companion’.English : unexplained.
Surname or Lastname
English (Leicestershire)
English (Leicestershire) : variant of Culver.
Boy/Male
American, British, English
Shepherd
CONVEX GEOMETRY
CONVEX GEOMETRY
Boy/Male
Tamil
Another name of Lord Vishnu
Boy/Male
Tamil
Cloud
Boy/Male
Hindu, Indian, Marathi
God of Medicine and Immortality
Boy/Male
Arabic
Generosity
Boy/Male
Indian
Sun
Girl/Female
German American English Latin Italian Spanish
From the Old German Betlindis, which is derived from the word for snake.
Girl/Female
Indian
One who has only friends and no enemies
Boy/Male
Bengali, British, Celebrity, English, Gujarati, Hindu, Indian, Kannada, Malayalam, Marathi, Sanskrit, Sindhi, Tamil, Telugu, Traditional
Victory; Lord Shiva; Dhritarashtra's Charioteer; Triumphant; Caring; Victorious
Boy/Male
Hindu, Indian
Truth
Biblical
a ruling; commanding; coming down
CONVEX GEOMETRY
CONVEX GEOMETRY
CONVEX GEOMETRY
CONVEX GEOMETRY
CONVEX GEOMETRY
a.
Specifically, having such a combination of concave and convex sides as makes the focal axis the shortest line between them. See Illust. under Lens.
v. t.
To accompany; to convoy.
v. t.
To call before a judge or judicature; to summon; to convene.
a.
Convex on both sides; as, a biconvex lens.
a.
Convex on one side, and concave on the other. The curves of the convex and concave sides may be alike or may be different. See Meniscus.
v. t.
To context.
n. & v.
See Conge, Conge.
dv.
In a convex form; convexly.
a.
Convex on one side, and flat on the other; plano-convex.
v. t.
To exchange for some specified equivalent; as, to convert goods into money.
adv.
In a convex form; as, a body convexly shaped.
a.
Convex on both sides; double convex. See under Convex, a.
n.
The conger eel; -- called also congeree.
v. t.
To cause to pass from one place or person to another; to serve as a medium in carrying (anything) from one place or person to another; to transmit; as, air conveys sound; words convey ideas.
n.
A convex body or surface.
a.
Concave on one side and convex on the other, as an eggshell or a crescent.
imp. & p. p.
of Cove
a.
Made convex; protuberant in a spherical form.
v. t.
To impart or communicate; as, to convey an impression; to convey information.
a.
Plane or flat on one side, and convex on the other; as, a plano-convex lens. See Convex, and Lens.