Geometry & Surface (topology) - Unionpedia, the concept map

Aerodynamics

Aerodynamics (ἀήρ aero (air) + δυναμική (dynamics)) is the study of the motion of air, particularly when affected by a solid object, such as an airplane wing.

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Algebraic curve

In mathematics, an affine algebraic plane curve is the zero set of a polynomial in two variables.

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Algebraic geometry

Algebraic geometry is a branch of mathematics which uses abstract algebraic techniques, mainly from commutative algebra, to solve geometrical problems.

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Angle

In Euclidean geometry, an angle is the figure formed by two rays, called the sides of the angle, sharing a common endpoint, called the vertex of the angle.

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Ball (mathematics)

In mathematics, a ball is the solid figure bounded by a sphere; it is also called a solid sphere.

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Calculus

Calculus is the mathematical study of continuous change, in the same way that geometry is the study of shape, and algebra is the study of generalizations of arithmetic operations.

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Compact space

In mathematics, specifically general topology, compactness is a property that seeks to generalize the notion of a closed and bounded subset of Euclidean space.

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Complex analysis

Complex analysis, traditionally known as the theory of functions of a complex variable, is the branch of mathematical analysis that investigates functions of complex numbers.

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Complex manifold

In differential geometry and complex geometry, a complex manifold is a manifold with an atlas of charts to the open unit disc in the complex coordinate space \mathbb^n, such that the transition maps are holomorphic.

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Coordinate system

In geometry, a coordinate system is a system that uses one or more numbers, or coordinates, to uniquely determine the position of the points or other geometric elements on a manifold such as Euclidean space.

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Cylinder

A cylinder has traditionally been a three-dimensional solid, one of the most basic of curvilinear geometric shapes.

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Degrees of freedom

In many scientific fields, the degrees of freedom of a system is the number of parameters of the system that may vary independently.

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Diffeomorphism

In mathematics, a diffeomorphism is an isomorphism of differentiable manifolds.

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Differential geometry

Differential geometry is a mathematical discipline that studies the geometry of smooth shapes and smooth spaces, otherwise known as smooth manifolds.

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Dimension

In physics and mathematics, the dimension of a mathematical space (or object) is informally defined as the minimum number of coordinates needed to specify any point within it.

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Distance

Distance is a numerical or occasionally qualitative measurement of how far apart objects, points, people, or ideas are.

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Embedding

In mathematics, an embedding (or imbedding) is one instance of some mathematical structure contained within another instance, such as a group that is a subgroup.

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Engineering

Engineering is the practice of using natural science, mathematics, and the engineering design process to solve technical problems, increase efficiency and productivity, and improve systems.

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Euclidean plane

In mathematics, a Euclidean plane is a Euclidean space of dimension two, denoted \textbf^2 or \mathbb^2.

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Euclidean space

Euclidean space is the fundamental space of geometry, intended to represent physical space.

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Felix Klein

Felix Christian Klein (25 April 1849 – 22 June 1925) was a German mathematician and mathematics educator, known for his work in group theory, complex analysis, non-Euclidean geometry, and the associations between geometry and group theory.

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Gaussian curvature

In differential geometry, the Gaussian curvature or Gauss curvature of a smooth surface in three-dimensional space at a point is the product of the principal curvatures, and, at the given point: K.

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Geodesic

In geometry, a geodesic is a curve representing in some sense the shortest path (arc) between two points in a surface, or more generally in a Riemannian manifold.

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Henri Poincaré

Jules Henri Poincaré (29 April 185417 July 1912) was a French mathematician, theoretical physicist, engineer, and philosopher of science.

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Homeomorphism

In mathematics and more specifically in topology, a homeomorphism (from Greek roots meaning "similar shape", named by Henri Poincaré), also called topological isomorphism, or bicontinuous function, is a bijective and continuous function between topological spaces that has a continuous inverse function.

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Manifold

In mathematics, a manifold is a topological space that locally resembles Euclidean space near each point.

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Mathematics

Mathematics is a field of study that discovers and organizes abstract objects, methods, theories and theorems that are developed and proved for the needs of empirical sciences and mathematics itself.

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Neighbourhood (mathematics)

In topology and related areas of mathematics, a neighbourhood (or neighborhood) is one of the basic concepts in a topological space.

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Physics

Physics is the natural science of matter, involving the study of matter, its fundamental constituents, its motion and behavior through space and time, and the related entities of energy and force.

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Riemann surface

In mathematics, particularly in complex analysis, a Riemann surface is a connected one-dimensional complex manifold.

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Riemannian manifold

In differential geometry, a Riemannian manifold is a geometric space on which many geometric notions such as distance, angles, length, volume, and curvature are defined.

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Solid geometry

Solid geometry or stereometry is the geometry of three-dimensional Euclidean space (3D space).

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Sphere

A sphere (from Greek) is a geometrical object that is a three-dimensional analogue to a two-dimensional circle.

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Surface (mathematics)

In mathematics, a surface is a mathematical model of the common concept of a surface.

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Surface of revolution

A surface of revolution is a surface in Euclidean space created by rotating a curve (the generatrix) one full revolution around an axis of rotation (normally not intersecting the generatrix, except at its endpoints).

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Three-dimensional space

In geometry, a three-dimensional space (3D space, 3-space or, rarely, tri-dimensional space) is a mathematical space in which three values (coordinates) are required to determine the position of a point.

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Topological space

In mathematics, a topological space is, roughly speaking, a geometrical space in which closeness is defined but cannot necessarily be measured by a numeric distance.

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Topology

Topology (from the Greek words, and) is the branch of mathematics concerned with the properties of a geometric object that are preserved under continuous deformations, such as stretching, twisting, crumpling, and bending; that is, without closing holes, opening holes, tearing, gluing, or passing through itself.

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Zero of a function

In mathematics, a zero (also sometimes called a root) of a real-, complex-, or generally vector-valued function f, is a member x of the domain of f such that f(x) vanishes at x; that is, the function f attains the value of 0 at x, or equivalently, x is a solution to the equation f(x).

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