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Point (geometry)

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In modern mathematics, a point refers usually to an element of some set called a space. [1]

55 relations: Affine space, Alfred North Whitehead, Algebra of sets, Area, Axiom, Boundary (topology), C*-algebra, Classical electromagnetism, Complete Heyting algebra, Continuous function, Convention (norm), Cover (topology), Critical point (mathematics), Cusp (singularity), Degeneracy (mathematics), Dimension, Element (mathematics), Euclid, Euclidean geometry, Euclidean space, Foundations of geometry, Function (mathematics), Generalized function, Horizontal and vertical, Horizontal plane, Infimum and supremum, Infinity, Integral, Kronecker delta, Length, Limit point, Line (geometry), Line segment, Linear independence, Mathematics, Metric space, Noncommutative geometry, Ordered pair, Paul Dirac, Plane (geometry), Point particle, Pointless topology, Pointwise, Position (vector), Primitive notion, Process and Reality, Set (mathematics), Signal processing, Singular point of a curve, Space (mathematics), ..., Trinity College, Cambridge, Tuple, Volume, Whitehead's point-free geometry, Zero-dimensional space. Expand index (5 more) »

Affine space

In mathematics, an affine space is a geometric structure that generalizes the properties of Euclidean spaces in such a way that these are independent of the concepts of distance and measure of angles, keeping only the properties related to parallelism and ratio of lengths for parallel line segments.

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Alfred North Whitehead

Alfred North Whitehead (15 February 1861 – 30 December 1947) was an English mathematician and philosopher.

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Algebra of sets

The algebra of sets defines the properties and laws of sets, the set-theoretic operations of union, intersection, and complementation and the relations of set equality and set inclusion.

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Area

Area is the quantity that expresses the extent of a two-dimensional figure or shape, or planar lamina, in the plane.

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Axiom

An axiom or postulate is a statement that is taken to be true, to serve as a premise or starting point for further reasoning and arguments.

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Boundary (topology)

In topology and mathematics in general, the boundary of a subset S of a topological space X is the set of points which can be approached both from S and from the outside of S. More precisely, it is the set of points in the closure of S not belonging to the interior of S. An element of the boundary of S is called a boundary point of S. The term boundary operation refers to finding or taking the boundary of a set.

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C*-algebra

C∗-algebras (pronounced "C-star") are an area of research in functional analysis, a branch of mathematics.

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Classical electromagnetism

Classical electromagnetism or classical electrodynamics is a branch of theoretical physics that studies the interactions between electric charges and currents using an extension of the classical Newtonian model.

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Complete Heyting algebra

In mathematics, especially in order theory, a complete Heyting algebra is a Heyting algebra that is complete as a lattice.

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Continuous function

In mathematics, a continuous function is a function for which sufficiently small changes in the input result in arbitrarily small changes in the output.

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Convention (norm)

A convention is a set of agreed, stipulated, or generally accepted standards, norms, social norms, or criteria, often taking the form of a custom.

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Cover (topology)

In mathematics, a cover of a set X is a collection of sets whose union contains X as a subset.

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Critical point (mathematics)

In mathematics, a critical point or stationary point of a differentiable function of a real or complex variable is any value in its domain where its derivative is 0.

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Cusp (singularity)

In mathematics a cusp, sometimes called spinode in old texts, is a point on a curve where a moving point on the curve must start to move backward.

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Degeneracy (mathematics)

In mathematics, a degenerate case is a limiting case in which an element of a class of objects is qualitatively different from the rest of the class and hence belongs to another, usually simpler, class.

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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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Element (mathematics)

In mathematics, an element, or member, of a set is any one of the distinct objects that make up that set.

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Euclid

Euclid (Εὐκλείδης Eukleidēs; fl. 300 BC), sometimes given the name Euclid of Alexandria to distinguish him from Euclides of Megara, was a Greek mathematician, often referred to as the "founder of geometry" or the "father of geometry".

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Euclidean geometry

Euclidean geometry is a mathematical system attributed to Alexandrian Greek mathematician Euclid, which he described in his textbook on geometry: the Elements.

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Euclidean space

In geometry, Euclidean space encompasses the two-dimensional Euclidean plane, the three-dimensional space of Euclidean geometry, and certain other spaces.

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Foundations of geometry

Foundations of geometry is the study of geometries as axiomatic systems.

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Function (mathematics)

In mathematics, a function was originally the idealization of how a varying quantity depends on another quantity.

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Generalized function

In mathematics, generalized functions, or distributions, are objects extending the notion of functions.

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Horizontal and vertical

The usage of the inter-related terms horizontal and vertical as well as their symmetries and asymmetries vary with context (e.g. two vs. three dimensions or calculations using a flat earth approximation vs. spherical earth).

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Horizontal plane

In geometry, physics, astronomy, geography, and related sciences, a plane is said to be horizontal at a given point if it is perpendicular to the gradient of the gravity field at that point – in other words, if apparent gravity makes a plumb bob hang perpendicular to the plane at that point.

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Infimum and supremum

In mathematics, the infimum (abbreviated inf; plural infima) of a subset S of a partially ordered set T is the greatest element in T that is less than or equal to all elements of S, if such an element exists.

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Infinity

Infinity (symbol) is a concept describing something without any bound or larger than any natural number.

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Integral

In mathematics, an integral assigns numbers to functions in a way that can describe displacement, area, volume, and other concepts that arise by combining infinitesimal data.

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Kronecker delta

In mathematics, the Kronecker delta (named after Leopold Kronecker) is a function of two variables, usually just non-negative integers.

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Length

In geometric measurements, length is the most extended dimension of an object.

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Limit point

In mathematics, a limit point (or cluster point or accumulation point) of a set S in a topological space X is a point x that can be "approximated" by points of S in the sense that every neighbourhood of x with respect to the topology on X also contains a point of S other than x itself.

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Line (geometry)

The notion of line or straight line was introduced by ancient mathematicians to represent straight objects (i.e., having no curvature) with negligible width and depth.

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Line segment

In geometry, a line segment is a part of a line that is bounded by two distinct end points, and contains every point on the line between its endpoints.

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Linear independence

In the theory of vector spaces, a set of vectors is said to be if one of the vectors in the set can be defined as a linear combination of the others; if no vector in the set can be written in this way, then the vectors are said to be.

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Mathematics

Mathematics (from Greek μάθημα máthēma, "knowledge, study, learning") is the study of such topics as quantity, structure, space, and change.

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Metric space

In mathematics, a metric space is a set for which distances between all members of the set are defined.

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Noncommutative geometry

Noncommutative geometry (NCG) is a branch of mathematics concerned with a geometric approach to noncommutative algebras, and with the construction of spaces that are locally presented by noncommutative algebras of functions (possibly in some generalized sense).

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Ordered pair

In mathematics, an ordered pair (a, b) is a pair of objects.

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Paul Dirac

Paul Adrien Maurice Dirac (8 August 1902 – 20 October 1984) was an English theoretical physicist who is regarded as one of the most significant physicists of the 20th century.

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Plane (geometry)

In mathematics, a plane is a flat, two-dimensional surface that extends infinitely far.

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Point particle

A point particle (ideal particle or point-like particle, often spelled pointlike particle) is an idealization of particles heavily used in physics.

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Pointless topology

In mathematics, pointless topology (also called point-free or pointfree topology, or locale theory) is an approach to topology that avoids mentioning points.

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Pointwise

In mathematics, the qualifier pointwise is used to indicate that a certain property is defined by considering each value f(x) of some function f. An important class of pointwise concepts are the pointwise operations — operations defined on functions by applying the operations to function values separately for each point in the domain of definition.

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Position (vector)

In geometry, a position or position vector, also known as location vector or radius vector, is a Euclidean vector that represents the position of a point P in space in relation to an arbitrary reference origin O. Usually denoted x, r, or s, it corresponds to the straight-line from O to P. The term "position vector" is used mostly in the fields of differential geometry, mechanics and occasionally vector calculus.

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Primitive notion

In mathematics, logic, and formal systems, a primitive notion is an undefined concept.

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Process and Reality

Process and Reality is a book by Alfred North Whitehead, in which Whitehead propounds a philosophy of organism, also called process philosophy.

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Set (mathematics)

In mathematics, a set is a collection of distinct objects, considered as an object in its own right.

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Signal processing

Signal processing concerns the analysis, synthesis, and modification of signals, which are broadly defined as functions conveying "information about the behavior or attributes of some phenomenon", such as sound, images, and biological measurements.

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Singular point of a curve

In geometry, a singular point on a curve is one where the curve is not given by a smooth embedding of a parameter.

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Space (mathematics)

In mathematics, a space is a set (sometimes called a universe) with some added structure.

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Trinity College, Cambridge

Trinity College is a constituent college of the University of Cambridge in England.

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Tuple

In mathematics, a tuple is a finite ordered list (sequence) of elements.

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Volume

Volume is the quantity of three-dimensional space enclosed by a closed surface, for example, the space that a substance (solid, liquid, gas, or plasma) or shape occupies or contains.

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Whitehead's point-free geometry

In mathematics, point-free geometry is a geometry whose primitive ontological notion is region rather than point.

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Zero-dimensional space

In mathematics, a zero-dimensional topological space (or nildimensional) is a topological space that has dimension zero with respect to one of several inequivalent notions of assigning a dimension to a given topological space.

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0-simplex, Point (mathematics), Point (spatial), Point (topology).

References

[1] https://en.wikipedia.org/wiki/Point_(geometry)

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