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Mathematical idealization of the surface of a body
In mathematics, a surface is a mathematical model of the common concept of a surface. It is a generalization of a plane, but, unlike a plane, it may be
Surface_(mathematics)
Surface that locally minimizes its area
In mathematics, a minimal surface is a surface that locally minimizes its area. This is equivalent to having zero mean curvature (see definitions below)
Minimal_surface
Topics referred to by the same term
trigonometric tables Generating a curve Generating a surface (mathematics) Generation of primes Generator (mathematics) Other: Generated collection, in music theory
Generate
Outermost layer of a physical object
other objects first interact. The concept of surface has been abstracted and formalized in mathematics, specifically in geometry. Depending on the properties
Surface
Field of knowledge
Mathematics is a field of knowledge concerned with abstract concepts such as numbers, geometric shapes, sets, functions, and probabilities. It uses logical
Mathematics
Topics referred to by the same term
Surface (film), a 2014 American film Surface (mathematics), a generalization of a plane which needs not be flat Surface (differential geometry), a differentiable
Surface_(disambiguation)
One-dimensional complex manifold
In mathematics, particularly in complex analysis, a Riemann surface is a connected one-dimensional complex manifold. These surfaces were first studied
Riemann_surface
Non-orientable surface with one edge
In mathematics, a Möbius strip, Möbius band, or Möbius loop is a surface that can be formed by attaching the ends of a strip of paper together with a
Möbius_strip
Iranian mathematician (1977–2017)
June 2020. Secrets of the Surface: The Mathematical Vision of Maryam Mirzakhani on IMdB "Secrets of the Surface The Mathematical Vision of Maryam Mirzakhani"
Maryam_Mirzakhani
Number of "holes" of a surface
In mathematics, genus (pl.: genera) has a few different, but closely related, meanings. Intuitively, the genus is the number of "holes" of a surface. A
Genus_(mathematics)
Two-dimensional manifold
within mathematics, such as differential geometry and complex analysis. The various mathematical notions of surface can be used to model surfaces in the
Surface_(topology)
Type of surface in algebraic geometry
Torino, 39: 778–792 Kulikov, Vik.S. (2001) [1994], "Fano surface", Encyclopedia of Mathematics, EMS Press Murre, J. P. (1972), "Algebraic equivalence modulo
Fano_surface
Self-intersecting compact surface, an immersion of the real projective plane
into three-space. The Wikibook Famous Theorems of Mathematics has a page on the topic of: Boy's surface If w is replaced by the negative reciprocal of its
Boy's_surface
Surface containing a line through every point
no non-planar triply ruled surfaces", Mathematical Omnibus: Thirty Lectures on Classic Mathematics, American Mathematical Society, p. 228, ISBN 9780821843161
Ruled_surface
list of surfaces in mathematics. They are divided into minimal surfaces, ruled surfaces, non-orientable surfaces, quadrics, pseudospherical surfaces, algebraic
List_of_surfaces
Branch of mathematics
Geometry is a branch of mathematics concerned with properties of space such as the distance, shape, size, and relative position of figures. Geometry is
Geometry
Algebraic surface with special triviality properties
In mathematics, Enriques surfaces are algebraic surfaces such that the irregularity q = 0 and the canonical line bundle K is non-trivial but has trivial
Enriques_surface
In mathematics, a Riemann surface
In mathematics, the Bolza surface, alternatively, complex algebraic Bolza curve (introduced by Oskar Bolza (1887)), is a compact Riemann surface of genus
Bolza_surface
Ruled surface over the projective line
In mathematics, a Hirzebruch surface is a ruled surface over the projective line. They were studied by Friedrich Hirzebruch (1951). The Hirzebruch surface
Hirzebruch_surface
Mathematical measure of how much a curve or surface deviates from flatness
In mathematics, curvature is any of several strongly related concepts in geometry that intuitively measure the amount by which a curve deviates from being
Curvature
Periodic minimal surface
In mathematics, a Scherk surface (named after Heinrich Scherk) is an example of a minimal surface. Scherk described two complete embedded minimal surfaces
Scherk_surface
Non-singular cubic surface in mathematics
In mathematics, the Clebsch diagonal cubic surface, or Klein's icosahedral cubic surface, is a non-singular cubic surface, studied by Clebsch (1871) and
Clebsch_surface
Integration over a non-flat region in 3D space
In mathematics, particularly multivariable calculus, a surface integral is a generalization of multiple integrals to integration over surfaces. It can
Surface_integral
Smooth closed surface with g holes
In mathematics, a genus g surface (also known as a g-torus or g-holed torus) is a surface formed by the connected sum of g distinct tori: the interior
Genus_g_surface
Size of a two-dimensional surface
as three such squares. In mathematics, the unit square is defined to have area one, and the area of any other shape or surface is a dimensionless real number
Area
Minimal surface
Enneper's surface, Commentarii Mathematici Helvetici 1996, Volume 71, Issue 1, pp 556-569 E. Güler, Family of Enneper minimal surfaces. Mathematics. 2018;
Enneper_surface
Mathematical classification of surfaces
In mathematics, the Enriques–Kodaira classification groups compact complex surfaces into ten classes, each parametrized by a moduli space. For most of
Enriques–Kodaira classification
Enriques–Kodaira_classification
Concept in differential geometry
{\displaystyle \mathbb {R} ^{3}} ): from a mathematical standpoint they are the most interesting (since self-intersecting surfaces are trivially abundant). All connected
Triply periodic minimal surface
Triply_periodic_minimal_surface
Mathematics award
The Breakthrough Prize in Mathematics is an annual award of the Breakthrough Prize series announced in 2013. It is supported by foundations co-founded
Breakthrough Prize in Mathematics
Breakthrough_Prize_in_Mathematics
Measure of surface finish or texture
perception of the surface texture. From a mathematical perspective it is related to the spatial variability structure of surfaces, and inherently it
Surface_roughness
In mathematics, a hyperelliptic surface, or bi-elliptic surface, is a minimal surface whose Albanese morphism is an elliptic fibration without singular
Hyperelliptic_surface
In mathematics, a fake projective plane (or Mumford surface) is one of the 50 complex algebraic surfaces that have the same Betti numbers as the projective
Fake_projective_plane
Geometric figure which has infinite surface area but finite volume
"mathematical" paint, it does not follow in the first place that an infinite surface area requires an infinite volume of paint, as infinite surface area
Gabriel's_horn
In mathematics, Bour's minimal surface is a two-dimensional minimal surface, embedded with self-crossings into three-dimensional Euclidean space. It is
Bour's_minimal_surface
In mathematics, a Lorentz surface is a two-dimensional oriented smooth manifold with a conformal equivalence class of Lorentzian metrics. It is the analogue
Lorentz_surface
Concept in algebraic geometry
In mathematics, an abelian surface is a 2-dimensional abelian variety. One-dimensional complex tori are just elliptic curves and are all algebraic, but
Abelian_surface
Topological space that locally resembles Euclidean space
In mathematics, a manifold is a topological space that locally resembles Euclidean space near each point. More precisely, an n {\displaystyle n} -dimensional
Manifold
Branch of mathematics
words τόπος, 'place, location', and λόγος, 'study') is the branch of mathematics concerned with the properties of a geometric object that are preserved
Topology
Topics referred to by the same term
In mathematics, regular surface may refer to: Regular surface (differential geometry) Non-singular algebraic variety of dimension two This disambiguation
Regular_surface
Algebraic variety of dimension two
In mathematics, an algebraic surface is an algebraic variety of dimension two. Thus, an algebraic surface is a solution of a set of polynomial equations
Algebraic_surface
Surface in algebraic geometry
In algebraic geometry, a branch of mathematics, a rational surface is a surface birationally equivalent to the projective plane, or in other words a rational
Rational_surface
In mathematics, a branched surface is a generalization of both surfaces and train tracks. A surface is a space that locally looks like R 2 {\displaystyle
Branched_surface
S2CID 120699065 Mumford, David (1979), "An algebraic surface with K ample, (K2)=9, pg=q=0", American Journal of Mathematics, 101 (1), The Johns Hopkins University Press:
Bogomolov–Miyaoka–Yau inequality
Bogomolov–Miyaoka–Yau_inequality
Rational surface in 5-dimensional projective space
In mathematics, the Veronese surface is an algebraic surface in five-dimensional projective space, and is realized by the Veronese embedding, the embedding
Veronese_surface
Mathematical concept
In mathematics, Costa's surface is an embedded minimal surface discovered in 1982 by the Brazilian mathematician Celso José da Costa. It is also a surface
Costa's_minimal_surface
Algebraic surface defined by a cubic polynomial
In mathematics, a cubic surface is a surface in 3-dimensional space defined by one polynomial equation of degree 3. Cubic surfaces are fundamental examples
Cubic_surface
Concept in algebraic geometry
In mathematics, a del Pezzo surface or Fano surface is a two-dimensional Fano variety, in other words a non-singular projective algebraic surface with
Del_Pezzo_surface
2D representation of a 3D surface
In mathematics, geology, and cartography, a surface map is a 2D perspective representation of a 3-dimensional surface. Surface maps usually represent
Surface_map
Type of surface singularity used in algebraic geometry
Wagreich, Philip (April 1970), "Elliptic singularities of surfaces", American Journal of Mathematics, vol. 92, no. 2, The Johns Hopkins University Press, pp
Elliptic_singularity
Possibility of a consistent definition of "clockwise" in a mathematical space
In mathematics, orientability is a property of some topological spaces such as real vector spaces, Euclidean spaces, surfaces, and more generally manifolds
Orientability
Species of mathematical spline
Bézier surfaces are a type of mathematical spline used in computer graphics, computer-aided design, and finite element modeling. As with Bézier curves
Bézier_surface
Infinite mathematical manifold
In mathematics, Jacob's ladder is a surface with infinite genus and two ends. It was named after Jacob's ladder by Étienne Ghys, because the surface can
Jacob's_ladder_surface
Mathematical theorem
In mathematics, the Riemann–Roch theorem for surfaces describes the dimension of linear systems on an algebraic surface. The classical form of it was first
Riemann–Roch theorem for surfaces
Riemann–Roch_theorem_for_surfaces
Surface in 3D space defined by an implicit function of three variables
In mathematics, an implicit surface is a surface in Euclidean space defined by an equation F ( x , y , z ) = 0. {\displaystyle F(x,y,z)=0.} An implicit
Implicit_surface
Non-orientable mathematical surface
In mathematics, the Klein bottle (/ˈklaɪn/) is an example of a surface with no distinct inside or outside. In other words, it is a one-sided surface which
Klein_bottle
Mathematics award
International Congress of Mathematicians (ICM) of the International Mathematical Union (IMU), a convention which takes place every four years. The name
Fields_Medal
Counterintuitive mathematical object
In mathematics, when a mathematical phenomenon runs counter to some intuition, then the phenomenon is sometimes called pathological. On the other hand
Pathological_(mathematics)
In mathematics, an arithmetic surface over a Dedekind domain R {\displaystyle R} with fraction field K {\displaystyle K} is a geometric object having one
Arithmetic_surface
Branch of mathematics
Differential geometry is a mathematical discipline that studies the geometry of smooth shapes and smooth spaces, otherwise known as smooth manifolds. It
Differential_geometry
Type of smooth complex surface of kodaira dimension 0
p. 546), describing the reason for the name "K3 surface" In mathematics, a complex analytic K3 surface is a compact connected complex manifold of dimension
K3_surface
Mathematical concept
In mathematics, an elliptic surface is a surface that has an elliptic fibration, in other words a proper morphism with connected fibers to an algebraic
Elliptic_surface
Ancient Egyptian mathematical manuscript
those in the Rhind Mathematical Papyrus. The papyrus is well known for some of its geometry problems. Problems 10 and 14 compute a surface area and the volume
Moscow_Mathematical_Papyrus
Surface drawn by a moving line passing through a fixed point
ruled surfaces", Modern Differential Geometry of Curves and Surfaces with Mathematica (2nd ed.), CRC Press, pp. 439–441, ISBN 9780849371646 Mathematical Society
Conical_surface
Submanifold of Lorentzian manifold
In the mathematical field of Lorentzian geometry, a Cauchy surface, also called more properly Cauchy hypersurface, is a certain kind of submanifold of
Cauchy_surface
In mathematics, a Beauville surface is one of the surfaces of general type introduced by Arnaud Beauville (1996, exercise X.13 (4)). They are examples
Beauville_surface
In mathematics, Fresnel's wave surface, found by Augustin-Jean Fresnel in 1822, is a quartic surface describing the propagation of light in an optically
Wave_surface
In mathematics a translation surface is a surface obtained from identifying the sides of a polygon in the Euclidean plane by translations. An equivalent
Translation_surface
Mathematical concept applicable to physics
(whether it actually moves or not) through a surface or substance. Flux is a concept in applied mathematics and vector calculus which has many applications
Flux
In mathematics, a Kodaira surface is a compact complex surface of Kodaira dimension 0 and odd first Betti number. The concept is named after Kunihiko
Kodaira_surface
The history of mathematics deals with the origin of discoveries in mathematics and the mathematical methods and notation of the past. Before the modern
History_of_mathematics
Simply connected Riemann surface is equivalent to an open disk, complex plane, or sphere
mathematics, the uniformization theorem states that every simply connected Riemann surface is conformally equivalent to one of three Riemann surfaces:
Uniformization_theorem
Differentiable function whose derivative is everywhere injective
In mathematics, an immersion is a differentiable function between differentiable manifolds whose differential pushforward is everywhere injective. Explicitly
Immersion_(mathematics)
Mathematical algorithm
elliptic surfaces. It determines whether a given set of sections of an elliptic surface provides a basis, up to torsion, for the surface's Mordell–Weil
Cox–Zucker_machine
Mathematical surface of constant unit negative Gaussian curvature
The Kuen surface is a mathematical surface of constant negative unit Gaussian curvature, making it an example of a pseudospherical surface. It can be
Kuen_surface
Russian mathematician (born 1966)
пространствах [Saddle surfaces in Euclidean spaces] (in Russian). Ленинградский государственный университет. Biography portal Mathematics portal Russia portal
Grigori_Perelman
Many mathematical problems have been stated but not yet solved. These problems come from many areas of mathematics, such as theoretical physics, computer
List of unsolved problems in mathematics
List_of_unsolved_problems_in_mathematics
Method for specifying point positions
x-coordinate". The coordinates are taken to be real numbers in elementary mathematics, but may be complex numbers or elements of a more abstract system such
Coordinate_system
Soviet mathematician
Arakelov (1974). "Intersection theory of divisors on an arithmetic surface". Mathematics of the USSR-Izvestiya. 8 (6): 1167–1180. doi:10.1070/IM1974v008n06ABEH002141
Suren_Arakelov
One of the surfaces of general type introduced by Lucien Godeaux in 1931
In mathematics, a Godeaux surface is one of the surfaces of general type introduced by Lucien Godeaux in 1931. Other surfaces constructed in a similar
Godeaux_surface
distance above the reference geoid, a mathematical model of the Earth's sea level as an equipotential gravitational surface. Of all countries, Lesotho has the
List of elevation extremes by country
List_of_elevation_extremes_by_country
Costa, Antonio F. (1994), "Study of the symmetries of the Macbeath surface", Mathematical contributions, Madrid: Editorial Complutense, pp. 375–385, MR 1303808
MacBeath_surface
German research institute
Oberwolfach Research Institute for Mathematics (German: Mathematisches Forschungsinstitut Oberwolfach) is a center for mathematical research in Oberwolfach, Germany
Oberwolfach Research Institute for Mathematics
Oberwolfach_Research_Institute_for_Mathematics
Part of the Kodaira classification
In mathematics, surfaces of class VII are non-algebraic complex surfaces studied by (Kodaira 1964, 1968) that have Kodaira dimension −∞ and first Betti
Surface_of_class_VII
In mathematics, an incompressible surface is a surface properly embedded in a 3-manifold, which, in intuitive terms, is a "nontrivial" surface that cannot
Incompressible_surface
Measure of a two-dimensional surface
The surface area (symbol A) of a solid object is a measure of the total area that the surface of the object occupies. The mathematical definition of surface
Surface_area
Method of representing curves and surfaces in computer graphics
(NURBS) is a mathematical model using basis splines (B-splines) that is commonly used in computer graphics for representing curves and surfaces. It offers
Non-uniform_rational_B-spline
Tendency of a liquid surface to shrink to reduce surface area
subvolume V {\displaystyle V} containing a surface of discontinuity, the volume is divided by the mathematical surface into two parts A and B, with volumes
Surface_tension
In mathematics, the Noether inequality, named after Max Noether, is a property of compact minimal complex surfaces that restricts the topological type
Noether_inequality
Orientable surface whose boundary is a knot or link
In mathematics, a Seifert surface (named after German mathematician Herbert Seifert) is an orientable surface whose boundary is a given knot or link. Such
Seifert_surface
Flat-sided three-dimensional shape
polyhedral surface intersecting every line parallel to some particular line in a connected set or the empty set Polytope model, a mathematical framework
Polyhedron
Study of discrete mathematical structures
Discrete mathematics is the study of mathematical structures that can be considered "discrete" (in a way analogous to discrete variables, having a one-to-one
Discrete_mathematics
Set of points equidistant from a center
ancient Greek mathematicians. The sphere is a fundamental surface in many fields of mathematics. Spheres and nearly-spherical shapes also appear in nature
Sphere
Surface of general type, in mathematics
In mathematics, a Burniat surface is one of the surfaces of general type introduced by Pol Burniat (1966). The geometric genus and irregularity are both
Burniat_surface
Region between two concentric circles
In mathematics, an annulus (pl.: annuli or annuluses) is the region between two concentric circles. Informally, it is shaped like a ring or a hardware
Annulus_(mathematics)
Operation in calculus
In mathematics, an integral is the continuous analog of a sum, and is used to calculate areas, volumes, and their generalizations. The process of computing
Integral
Lists of mathematics topics cover a variety of topics related to mathematics. Some of these lists link to hundreds of articles; some link to only a few
Lists_of_mathematics_topics
To find the minimal surface with a given boundary
In mathematics, Plateau's problem is to show the existence of a minimal surface with a given boundary. The problem is considered part of the calculus of
Plateau's_problem
2D surface which extends indefinitely
In mathematics, a plane is a two-dimensional space or flat surface that extends indefinitely. A plane is the two-dimensional analogue of a point (zero
Plane_(mathematics)
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
PDE surfaces use partial differential equations to generate a surface which usually satisfy a mathematical boundary value problem. PDE surfaces were
PDE_surface
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