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Parameter used to characterize molecular geometry
crystallography, the geometry index or structural parameter (τ) is a number ranging from 0 to 1 that indicates what the geometry of the coordination center
Geometry_index
Branch of mathematics
curvature and index theory. Ideas now grouped under noncommutative geometry developed from several areas, including operator algebra theory, index theory, algebraic
Noncommutative_geometry
Mathematical result in differential geometry
In differential geometry, the Atiyah–Singer index theorem, proved by Michael Atiyah and Isadore Singer (1963), states that for an elliptic differential
Atiyah–Singer_index_theorem
Branch of mathematics
Differential geometry is a mathematical discipline that studies the geometry of smooth shapes and smooth spaces, otherwise known as smooth manifolds.
Differential_geometry
Academic journal
on discrete geometry and computational geometry. The journal is indexed in: Mathematical Reviews Zentralblatt MATH Science Citation Index Current Contents
Discrete & Computational Geometry
Discrete_&_Computational_Geometry
Database of data representing objects in geometric space
ST_Distance(geometry, geometry) : number ST_Equals(geometry, geometry) : boolean ST_Disjoint(geometry, geometry) : boolean ST_Intersects(geometry, geometry) :
Spatial_database
Academic journal
Computational Geometry, also known as Computational Geometry: Theory and Applications, is a peer-reviewed mathematics journal for research in theoretical
Computational Geometry (journal)
Computational_Geometry_(journal)
Area of differential geometry and topology
spin geometry is the area of differential geometry and topology where objects like spin manifolds and Dirac operators, and the various associated index theorems
Spin_geometry
Geospatial vector data format
format; the feature geometry itself. Content-type: application/vnd.shp .shx Shape index format; a positional index of the feature geometry to allow seeking
Shapefile
Shape
term is not very specific, but in some areas of mathematics (projective geometry, technical drawing, etc.), it is given a more precise definition, which
Oval
Tensor index notation for tensor-based calculations
.} Abstract index notation Connection Curvilinear coordinates Tensors in curvilinear coordinates Differential form Differential geometry Exterior algebra
Ricci_calculus
This is a list of differential geometry topics. See also glossary of differential and metric geometry and list of Lie group topics. List of curves topics
List of differential geometry topics
List_of_differential_geometry_topics
Academic journal
The International Journal of Computational Geometry and Applications (IJCGA) is a bimonthly journal published since 1991, by World Scientific. It covers
International Journal of Computational Geometry and Applications
International_Journal_of_Computational_Geometry_and_Applications
Mathematics journal
abstracted and indexed in EBSCO databases, Emerging Sources Citation Index, Scopus, and zbMATH Open. "Brief review of two new journals of geometry", Pi Mu Epsilon
Journal_of_Geometry
Shorthand notation for tensor operations
especially the usage of linear algebra in mathematical physics and differential geometry, Einstein notation (also known as the Einstein summation convention or
Einstein_notation
Mathematical function of two variables; outputs 1 if they are equal, 0 otherwise
versions of the Kronecker delta have found applications in differential geometry and modern tensor calculus, particularly in formulations of gauge theory
Kronecker_delta
Algebra associated to any vector space
product was introduced originally as an algebraic construction used in geometry to study areas, volumes, and their higher-dimensional analogues: the magnitude
Exterior_algebra
Index of articles associated with the same name
In geometry, Max Dehn introduced two examples of planes, a semi-Euclidean geometry and a non-Legendrian geometry, that have infinitely many lines parallel
Dehn_plane
Type of program in computer graphics
Shaders act on data such as vertices and primitives, generate or morph geometries and fragments, and calculate the colors in a rendered image. Shaders can
Shader
Data structure for query optimization in databases
no overlapping time ranges or no intersecting geometry objects would be stored in the table. An index supporting fast searching for records satisfying
Database_index
Tensor in differential geometry
In differential geometry, the Ricci curvature tensor, named after Gregorio Ricci-Curbastro, measures how a curved space locally differs from flat space
Ricci_curvature
JSTOR 109316 Eisenbud, David (2005). The Geometry of Syzygies. A second course in commutative algebra and algebraic geometry. Graduate Texts in Mathematics. Vol
Clifford's theorem on special divisors
Clifford's_theorem_on_special_divisors
Straight path on a curved surface or a Riemannian manifold
In geometry, a geodesic (/ˌdʒiː.əˈdɛsɪk, -oʊ-, -ˈdiːsɪk, -zɪk/) is a curve representing in some sense the locally shortest path (arc) between two points
Geodesic
Exterior algebraic map taking tensors from p forms to n-p forms
naturality of the star operator means it can play a role in differential geometry when applied to the cotangent bundle of a pseudo-Riemannian manifold, and
Hodge_star_operator
Method for specifying point positions
In geometry, a coordinate system is a system that uses one or more numbers, or coordinates, to uniquely determine and standardize the position of the points
Coordinate_system
Algebraic object with geometric applications
concept enabled an alternative formulation of the intrinsic differential geometry of a manifold in the form of the Riemann curvature tensor. Although seemingly
Tensor
Mathematical function, in linear algebra
Victor (2001) [1994], "Index theory", Encyclopedia of Mathematics, EMS Press: "The main question in index theory is to provide index formulas for classes
Linear_map
Fundamental object of geometry
In geometry, a point is an abstract idealization of an exact position, without size, in physical space, or its generalization to other kinds of mathematical
Point_(geometry)
Matrix operation which flips a matrix over its diagonal
theory Scope Mathematics Coordinate system Differential geometry Dyadic algebra Euclidean geometry Exterior calculus Multilinear algebra Tensor algebra Tensor
Transpose
Compound with a metal center bound to ligands
coordinations for five-coordinated complexes, the τ geometry index was invented by Addison et al. This index depends on angles by the coordination center and
Coordination_complex
Set of vectors used to define coordinates
number of basis functions) are the same. Rees, Elmer G. (2005). Notes on Geometry. Berlin: Springer. p. 7. ISBN 978-3-540-12053-7. Kuczma, Marek (1970).
Basis_(linear_algebra)
High school math competition
Geometry Algebra 2012: Geometry Algebra Algebra Geometry/Algebra Algebra Geometry 2011: Number Theory Algebra Geometry/Algebra Combinatorics Geometry
United States of America Mathematical Olympiad
United_States_of_America_Mathematical_Olympiad
Academic journal
Differential Geometry, the editorial board meets every couple of months and debates each paper in detail." The journal is abstracted and indexed in MathSciNet
Journal of Differential Geometry
Journal_of_Differential_Geometry
Isomorphism between the tangent and cotangent bundles of a manifold
In mathematics—more specifically, in differential geometry—the musical isomorphism (or canonical isomorphism) is an isomorphism between the tangent bundle
Musical_isomorphism
Differential form of degree one or section of a cotangent bundle
Look up one-form in Wiktionary, the free dictionary. In differential geometry, a one-form (or covector field) on a differentiable manifold is a differential
One-form
Mathematical operation on vector spaces
theory Scope Mathematics Coordinate system Differential geometry Dyadic algebra Euclidean geometry Exterior calculus Multilinear algebra Tensor algebra Tensor
Tensor_product
Array of numbers describing a metric connection
metric, allowing distances to be measured on that surface. In differential geometry, an affine connection can be defined without reference to a metric, and
Christoffel_symbols
Vector behavior under coordinate changes
represented by its components, although modern differential geometry uses more sophisticated index-free methods to represent tensors. In tensor analysis, a
Covariance and contravariance of vectors
Covariance_and_contravariance_of_vectors
Geometry definition file format
optional, one can define geometry without them, but one must put two slashes after the vertex index before putting the normal index. f v1//vn1 v2//vn2 v3//vn3
Wavefront_.obj_file
Three dimensional analogue of uniformization conjecture
non-compact. If it is compact, then the 2 geometries can be distinguished by whether or not π1(M) has a finite index subgroup that splits as a semidirect product
Geometrization_conjecture
Algebraic operation on coordinate vectors
(usually coordinate vectors), and returns a single number. In Euclidean geometry, the scalar product of two vectors is the dot product of their Cartesian
Dot_product
Antisymmetric permutation object acting on tensors
mathematics, particularly in linear algebra, tensor analysis, and differential geometry, the Levi-Civita symbol or Levi-Civita epsilon represents a collection
Levi-Civita_symbol
Study of angle-preserving transformations of a geometric space
conformal geometry is the study of the set of angle-preserving (conformal) transformations on a space. In a real two dimensional space, conformal geometry is
Conformal_geometry
British-Lebanese mathematician (1929–2019)
British-Lebanese mathematician specialising in geometry. His contributions include the Atiyah–Singer index theorem and co-founding topological K-theory
Michael_Atiyah
Part of a series on Mathematics History Index Areas Number theory Geometry Algebra Calculus and Analysis Discrete mathematics Logic Probability and Statistics
List_of_mathematics_books
Academic journal
annual Symposium on Computational Geometry to a special issue. The Journal of Computational Geometry is abstracted and indexed in MathSciNet, Zentralblatt Math
Journal of Computational Geometry
Journal_of_Computational_Geometry
Operation in mathematics
Semi-Riemannian Geometry with Applications to Relativity. Academic Press. p. 86. ISBN 0-12-526740-1. Hartshorne, Robin (1977). Algebraic Geometry. New York:
Tensor_contraction
Academic journal
journal is indexed by Mathematical Reviews and Zentralblatt MATH. Its 2016 MCQ was 0.45, and its 2021 impact factor was 0.763. "Advances in Geometry". De Gruyter
Advances_in_Geometry
Continuous surjection satisfying a local triviality condition
other more general vector bundles, play an important role in differential geometry and differential topology, as do principal bundles. Mappings between total
Fiber_bundle
In mathematics, the Hodge index theorem for an algebraic surface V determines the signature of the intersection pairing on the algebraic curves C on V
Hodge_index_theorem
The Adamic–Adar index is a measure introduced in 2003 by Lada Adamic and Eytan Adar to predict links in a social network, according to the amount of shared
Adamic–Adar_index
Expression that may be integrated over a region
was pioneered by Élie Cartan. It has many applications, especially in geometry, topology and physics. For instance, the expression f ( x ) d x {\displaystyle
Differential_form
Number of times a curve wraps around a point in the plane
in vector calculus, complex analysis, geometric topology, differential geometry, and physics (such as in string theory). Suppose we are given a closed
Winding_number
Academic journal
and covers all aspects of groups, group actions, geometry and dynamical systems. The journal is indexed by Mathematical Reviews and Zentralblatt MATH. Its
Groups, Geometry, and Dynamics
Groups,_Geometry,_and_Dynamics
Study of complex manifolds and several complex variables
geometry is the study of geometric structures and constructions arising out of, or described by, the complex numbers. In particular, complex geometry
Complex_geometry
Branch of geometry
In mathematics, contact geometry is the study of a geometric structure on smooth manifolds given by a hyperplane distribution in the tangent bundle satisfying
Contact_geometry
Maslov index is an integer-valued invariant in symplectic geometry, microlocal analysis, and semiclassical analysis. It is associated most classically
Maslov_index
Specification of a derivative along a tangent vector of a manifold
context to include a wider range of possible geometries. In the 1940s, practitioners of differential geometry began introducing other notions of covariant
Covariant_derivative
Topological space that locally resembles Euclidean space
projective plane. The concept of a manifold is central to many parts of geometry and modern mathematical physics because it allows complicated structures
Manifold
Property of a mathematical space
back to René Descartes, substantial development of a higher-dimensional geometry only began in the 19th century, via the work of Arthur Cayley, William
Dimension
Index of articles associated with the same name
occur in fields such as calculus, differential equations and Riemannian geometry. In the theory of differential equations, comparison theorems assert particular
Comparison_theorem
In the mathematical field of algebraic geometry, purity is a theme covering a number of results and conjectures, which collectively address the question
Purity_(algebraic_geometry)
Polyhedron with 42 faces
In geometry, the great rhombidodecahedron is a nonconvex uniform polyhedron, indexed as U73. It has 42 faces (30 squares, 12 decagrams), 120 edges and
Great_rhombidodecahedron
Notation used for Weyl spinors
Wiss. Göttingen Math.-Phys. ohne Angabe: 100–109. Veblen O. (1933). "Geometry of two-component Spinors". Proc. Natl. Acad. Sci. USA. 19 (4): 462–474
Van_der_Waerden_notation
British mathematician
specialising in geometry. His discovery of far-reaching topological relations between algebraic geometry and differential geometry—an area now called
W._V._D._Hodge
Study of curves from a differential point of view
Differential geometry of curves is the branch of geometry that deals with smooth curves in the plane and the Euclidean space by methods of differential
Differentiable_curve
Mathematics of smooth surfaces
In mathematics, the differential geometry of surfaces deals with the differential geometry of smooth surfaces with various additional structures, most
Differential geometry of surfaces
Differential_geometry_of_surfaces
Feature of geometric structures
In geometry, a facet is a feature of a polyhedron, polytope, or related geometric structure, generally of dimension one less than the structure itself
Facet_(geometry)
Library classification system
Mathematics 516 Geometry 516.3 Analytic geometries 516.37 Metric differential geometries
Dewey_Decimal_Classification
Academic journal
Geometry & Topology is a peer-refereed, international mathematics research journal devoted to geometry and topology, and their applications. It is currently
Geometry_&_Topology
In differential geometry, the equivariant index theorem, of which there are several variants, computes the (graded) trace of an element of a compact Lie
Equivariant_index_theorem
Assignment of a tensor continuously varying across a region of space
unit of measurement. Tensor fields are used in differential geometry, algebraic geometry, general relativity, in the analysis of stress and strain in
Tensor_field
System of moving vectors in differential geometry
In differential geometry, parallel transport (or parallel translation) is a way of transporting geometrical data along smooth curves in a manifold. If
Parallel_transport
Collection of random variables
defined as a family of random variables in a probability space, where the index of the family often has the interpretation of time. Stochastic processes
Stochastic_process
Field of knowledge
properties), algebra (the study of operations and the structures they form), geometry (the study of shapes and spaces that contain them), analysis (the quantitative
Mathematics
Conjecture in differential geometry
In differential geometry, the Carathéodory conjecture is a mathematical conjecture attributed to Constantin Carathéodory by Hans Ludwig Hamburger, stating
Carathéodory_conjecture
Curve from a cone intersecting a plane
type of conic is determined by the value of the eccentricity. In analytic geometry, a conic may be defined as a plane algebraic curve of degree 2; that is
Conic_section
Length of a line segment
ancient Greek mathematicians Euclid and Pythagoras. In the Greek deductive geometry exemplified by Euclid's Elements, distances were not represented as numbers
Euclidean_distance
Gives general conditions under which sheaf cohomology groups with indices > 0 are zero
theorem is a basic result of complex manifold theory and complex algebraic geometry, describing general conditions under which sheaf cohomology groups with
Kodaira_vanishing_theorem
Set of polygons to define the surface of a 3D model
generating a face index list, which is usually done only when the geometry changes. Winged-edge meshes are ideally suited for dynamic geometry, such as subdivision
Polygon_mesh
Academic journal
Journal of Geometry and Physics is a scientific journal in mathematical physics. Its scope is to stimulate the interaction between geometry and physics
Journal of Geometry and Physics
Journal_of_Geometry_and_Physics
Index of articles associated with the same name
Isaacs, I. Martin (2009). Geometry for college students. American Mathematical Society. p. 50. ISBN 978-0-8218-4794-7. This set index article includes a list
Circumscribed_circle
2D graphics library written in C++
Anti-Grain Geometry (AGG) is a 2D rendering graphics library written in C++. It features anti-aliasing and sub-pixel resolution. It is not a graphics library
Anti-Grain_Geometry
Canonical connection on a pseudo-Riemannian manifold
In Riemannian or pseudo-Riemannian geometry (in particular the Lorentzian geometry of general relativity), the Levi-Civita connection is the unique affine
Levi-Civita_connection
(theorem of zeroes) (commutative algebra, algebraic geometry) Hironaka theorem (algebraic geometry) Hodge index theorem (algebraic surfaces) Katz–Lang finiteness
List_of_theorems
American annual mathematics conference
The Geometry Festival is an annual mathematics conference held in the United States. The festival has been held since 1985 at the University of Pennsylvania
Geometry_Festival
Mathematical notation for tensors and spinors
Abstract index notation (also referred to as slot-naming index notation) is a mathematical notation for tensors and spinors that uses indices to indicate
Abstract_index_notation
In noncommutative geometry and related branches of mathematics and mathematical physics, a spectral triple is a set of data which encodes a geometric phenomenon
Spectral_triple
Mathematical theory
In mathematics, Arakelov theory (or Arakelov geometry) is an approach to Diophantine geometry, named for Suren Arakelov. It is used to study Diophantine
Arakelov_theory
Polymer with refractive index > 1.50
sensors. The refractive index of a polymer is based on several factors which include polarizability, chain flexibility, molecular geometry and the polymer backbone
High-refractive-index_polymer
Uniform star polyhedron with 124 faces
In geometry, the great dirhombicosidodecahedron (or great snub disicosidisdodecahedron) is a degenerate nonconvex uniform polyhedron, indexed last as U75
Great dirhombicosidodecahedron
Great_dirhombicosidodecahedron
Coordinate system using perpendicular axes
In geometry, a Cartesian coordinate system (UK: /kɑːrˈtiːzjən/, US: /kɑːrˈtiːʒən/) in a plane is a coordinate system that specifies each point uniquely
Cartesian_coordinate_system
Ancient Greek mathematician (fl. 300 BC)
Considered the "father of geometry", he is chiefly known for the Elements treatise, which established the foundations of geometry that largely dominated
Euclid
Construct allowing differentiation of tangent vector fields of manifolds
In differential geometry, an affine connection is a geometric object on a smooth manifold which connects nearby tangent spaces, so it permits tangent vector
Affine_connection
Symbol used in coordination chemistry
indicate the approximate coordination geometry around the central atom. One or more italicised letters indicate the geometry, e.g. TP-3 which is followed by
Polyhedral_symbol
Theory of gravitation as curved spacetime
seen as a prediction of general relativity for the almost flat spacetime geometry around stationary mass distributions. Some predictions of general relativity
General_relativity
Result in algebraic geometry
In mathematics, specifically in algebraic geometry, the Grothendieck–Riemann–Roch theorem is a far-reaching result on coherent cohomology. It is a generalisation
Grothendieck–Riemann–Roch theorem
Grothendieck–Riemann–Roch_theorem
File format for representing 3D interactive vector graphics
the same scene as X3D § Example. #VRML V2.0 utf8 Shape { geometry IndexedFaceSet { coordIndex [ 0, 1, 2 ] coord Coordinate { point [ 0, 0, 0, 1, 0, 0,
VRML
surface Hodge index theorem Elliptic surface Surface of general type Zariski surface Algebraic variety Hypersurface Quadric (algebraic geometry) Dimension
List of algebraic geometry topics
List_of_algebraic_geometry_topics
Curve simplification algorithm
703–718. Bibcode:2009IJGIS..23..703F. doi:10.1080/13658810701703001. Boost.Geometry support Douglas–Peucker simplification algorithm Implementation of Ramer–Douglas–Peucker
Ramer–Douglas–Peucker algorithm
Ramer–Douglas–Peucker_algorithm
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GEOMETRY INDEX
GEOMETRY INDEX
GEOMETRY INDEX
GEOMETRY INDEX
GEOMETRY INDEX
GEOMETRY INDEX
GEOMETRY INDEX
GEOMETRY INDEX
GEOMETRY INDEX
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