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Analytic geometry

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In classical mathematics, analytic geometry, also known as coordinate geometry or Cartesian geometry, is the study of geometry using a coordinate system. [1]

97 relations: Affine coordinate system, Affine transformation, Algebraic equation, Algebraic geometry, Ancient Greece, Angle, Apollonius of Perga, Aviation, Calculus, Cantor–Dedekind axiom, Cartesian coordinate system, Circle, Computational geometry, Cone, Conic section, Coordinate system, CRC Press, Cross product, Cubic function, Curve, Cylinder, Cylindrical coordinate system, Dependent and independent variables, Derivative, Differential geometry, Discourse on the Method, Discrete geometry, Discriminant, Distance, Dot product, Ellipse, Ellipsoid, Engineering, Equation, Euclidean geometry, Euclidean space, Euclidean vector, Force, Formula, French language, Geometry, Geometry Center, Graph of a function, Hyperbola, Hyperboloid, Infinitesimal, Internet Archive, Intersection (set theory), James Stewart (mathematician), John Casey (mathematician), ..., La Géométrie, Latin, Line (geometry), Linear equation, Locus (mathematics), Menaechmus, Normal (geometry), Omar Khayyam, Ordered pair, Orthogonality, Outline of space science, Parabola, Paraboloid, Parametric equation, Perpendicular, Persian people, Physics, Pierre de Fermat, Plane (geometry), Point (geometry), Polar coordinate system, Projective space, Pythagorean theorem, Quadratic equation, Quadratic function, Radius, Real number, René Descartes, Rocket, Slope, Solution set, Spaceflight, Sphere, Spherical coordinate system, Square, Subset, Surface (mathematics), Synthetic geometry, Tangent, Tangent space, Three-dimensional space, Tuple, Two-dimensional space, University of Minnesota, Vector space, Y-intercept, Zero of a function. Expand index (47 more) »

Affine coordinate system

In mathematics, an affine coordinate system is a coordinate system on an affine space where each coordinate is an affine map to the number line.

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Affine transformation

In geometry, an affine transformation, affine mapBerger, Marcel (1987), p. 38.

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Algebraic equation

In mathematics, an algebraic equation or polynomial equation is an equation of the form where P and Q are polynomials with coefficients in some field, often the field of the rational numbers.

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Algebraic geometry

Algebraic geometry is a branch of mathematics, classically studying zeros of multivariate polynomials.

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Ancient Greece

Ancient Greece was a civilization belonging to a period of Greek history from the Greek Dark Ages of the 13th–9th centuries BC to the end of antiquity (AD 600).

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In plane 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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Apollonius of Perga

Apollonius of Perga (Ἀπολλώνιος ὁ Περγαῖος; Apollonius Pergaeus; late 3rdearly 2nd centuries BC) was a Greek geometer and astronomer known for his theories on the topic of conic sections.

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Aviation, or air transport, refers to the activities surrounding mechanical flight and the aircraft industry.

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Calculus (from Latin calculus, literally 'small pebble', used for counting and calculations, as on an abacus), 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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Cantor–Dedekind axiom

In mathematical logic, the Cantor–Dedekind axiom is the thesis that the real numbers are order-isomorphic to the linear continuum of geometry.

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Cartesian coordinate system

A Cartesian coordinate system is a coordinate system that specifies each point uniquely in a plane by a pair of numerical coordinates, which are the signed distances to the point from two fixed perpendicular directed lines, measured in the same unit of length.

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A circle is a simple closed shape.

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Computational geometry

Computational geometry is a branch of computer science devoted to the study of algorithms which can be stated in terms of geometry.

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A cone is a three-dimensional geometric shape that tapers smoothly from a flat base (frequently, though not necessarily, circular) to a point called the apex or vertex.

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Conic section

In mathematics, a conic section (or simply conic) is a curve obtained as the intersection of the surface of a cone with a plane.

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Coordinate system

In geometry, a coordinate system is a system which 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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CRC Press

The CRC Press, LLC is a publishing group based in the United States that specializes in producing technical books.

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Cross product

In mathematics and vector algebra, the cross product or vector product (occasionally directed area product to emphasize the geometric significance) is a binary operation on two vectors in three-dimensional space \left(\mathbb^3\right) and is denoted by the symbol \times.

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Cubic function

In algebra, a cubic function is a function of the form in which is nonzero.

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In mathematics, a curve (also called a curved line in older texts) is, generally speaking, an object similar to a line but that need not be straight.

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A cylinder (from Greek κύλινδρος – kulindros, "roller, tumbler"), has traditionally been a three-dimensional solid, one of the most basic of curvilinear geometric shapes.

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Cylindrical coordinate system

A cylindrical coordinate system is a three-dimensional coordinate system that specifies point positions by the distance from a chosen reference axis, the direction from the axis relative to a chosen reference direction, and the distance from a chosen reference plane perpendicular to the axis.

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Dependent and independent variables

In mathematical modeling, statistical modeling and experimental sciences, the values of dependent variables depend on the values of independent variables.

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The derivative of a function of a real variable measures the sensitivity to change of the function value (output value) with respect to a change in its argument (input value).

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Differential geometry

Differential geometry is a mathematical discipline that uses the techniques of differential calculus, integral calculus, linear algebra and multilinear algebra to study problems in geometry.

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Discourse on the Method

The Discourse on the Method (Discours de la méthode) is a philosophical and autobiographical treatise published by René Descartes in 1637.

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Discrete geometry

Discrete geometry and combinatorial geometry are branches of geometry that study combinatorial properties and constructive methods of discrete geometric objects.

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In algebra, the discriminant of a polynomial is a polynomial function of its coefficients, which allows deducing some properties of the roots without computing them.

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Distance is a numerical measurement of how far apart objects are.

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Dot product

In mathematics, the dot product or scalar productThe term scalar product is often also used more generally to mean a symmetric bilinear form, for example for a pseudo-Euclidean space.

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In mathematics, an ellipse is a curve in a plane surrounding two focal points such that the sum of the distances to the two focal points is constant for every point on the curve.

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An ellipsoid is a surface that may be obtained from a sphere by deforming it by means of directional scalings, or more generally, of an affine transformation.

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Engineering is the creative application of science, mathematical methods, and empirical evidence to the innovation, design, construction, operation and maintenance of structures, machines, materials, devices, systems, processes, and organizations.

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In mathematics, an equation is a statement of an equality containing one or more variables.

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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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Euclidean vector

In mathematics, physics, and engineering, a Euclidean vector (sometimes called a geometric or spatial vector, or—as here—simply a vector) is a geometric object that has magnitude (or length) and direction.

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In physics, a force is any interaction that, when unopposed, will change the motion of an object.

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In science, a formula is a concise way of expressing information symbolically, as in a mathematical formula or a chemical formula.

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French language

French (le français or la langue française) is a Romance language of the Indo-European family.

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Geometry (from the γεωμετρία; geo- "earth", -metron "measurement") is a branch of mathematics concerned with questions of shape, size, relative position of figures, and the properties of space.

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Geometry Center

The Geometry Center was a mathematics research and education center at the University of Minnesota.

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Graph of a function

In mathematics, the graph of a function f is, formally, the set of all ordered pairs, and, in practice, the graphical representation of this set.

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In mathematics, a hyperbola (plural hyperbolas or hyperbolae) is a type of smooth curve lying in a plane, defined by its geometric properties or by equations for which it is the solution set.

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In geometry, a hyperboloid of revolution, sometimes called circular hyperboloid, is a surface that may be generated by rotating a hyperbola around one of its principal axes.

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In mathematics, infinitesimals are things so small that there is no way to measure them.

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Internet Archive

The Internet Archive is a San Francisco–based nonprofit digital library with the stated mission of "universal access to all knowledge." It provides free public access to collections of digitized materials, including websites, software applications/games, music, movies/videos, moving images, and nearly three million public-domain books.

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Intersection (set theory)

In mathematics, the intersection A ∩ B of two sets A and B is the set that contains all elements of A that also belong to B (or equivalently, all elements of B that also belong to A), but no other elements.

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James Stewart (mathematician)

James Drewry Stewart, (March 29, 1941December 3, 2014) was a Canadian mathematician, violinist, and professor emeritus of mathematics at McMaster University.

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John Casey (mathematician)

John Casey (12 May 1820, Kilbehenny, Co. Limerick, Ireland – 3 January 1891, Dublin) was a respected Irish geometer.

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La Géométrie

La Géométrie was published in 1637 as an appendix to Discours de la méthode (Discourse on the Method), written by René Descartes.

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Latin (Latin: lingua latīna) is a classical language belonging to the Italic branch of the Indo-European languages.

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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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Linear equation

In mathematics, a linear equation is an equation that may be put in the form where x_1, \ldots, x_n are the variables or unknowns, and c, a_1, \ldots, a_n are coefficients, which are often real numbers, but may be parameters, or even any expression that does not contain the unknowns.

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Locus (mathematics)

In geometry, a locus (plural: loci) (Latin word for "place", "location") is a set of all points (commonly, a line, a line segment, a curve or a surface), whose location satisfies or is determined by one or more specified conditions.

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Menaechmus (Μέναιχμος, 380–320 BC) was an ancient Greek mathematician and geometer born in Alopeconnesus in the Thracian Chersonese, who was known for his friendship with the renowned philosopher Plato and for his apparent discovery of conic sections and his solution to the then-long-standing problem of doubling the cube using the parabola and hyperbola.

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Normal (geometry)

In geometry, a normal is an object such as a line or vector that is perpendicular to a given object.

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Omar Khayyam

Omar Khayyam (عمر خیّام; 18 May 1048 – 4 December 1131) was a Persian mathematician, astronomer, and poet.

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Ordered pair

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

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In mathematics, orthogonality is the generalization of the notion of perpendicularity to the linear algebra of bilinear forms.

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Outline of space science

The following outline is provided as an overview of and topical guide to space science: Space science encompasses all of the scientific disciplines that involve space exploration and study natural phenomena and physical bodies occurring in outer space, such as space medicine and astrobiology.

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In mathematics, a parabola is a plane curve which is mirror-symmetrical and is approximately U-shaped.

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In geometry, a paraboloid is a quadric surface that has (exactly) one axis of symmetry and no center of symmetry.

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Parametric equation

In mathematics, a parametric equation defines a group of quantities as functions of one or more independent variables called parameters.

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In elementary geometry, the property of being perpendicular (perpendicularity) is the relationship between two lines which meet at a right angle (90 degrees).

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Persian people

The Persians--> are an Iranian ethnic group that make up over half the population of Iran.

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Physics (from knowledge of nature, from φύσις phýsis "nature") is the natural science that studies matterAt the start of The Feynman Lectures on Physics, Richard Feynman offers the atomic hypothesis as the single most prolific scientific concept: "If, in some cataclysm, all scientific knowledge were to be destroyed one sentence what statement would contain the most information in the fewest words? I believe it is that all things are made up of atoms – little particles that move around in perpetual motion, attracting each other when they are a little distance apart, but repelling upon being squeezed into one another..." and its motion and behavior through space and time and that studies the related entities of energy and force."Physical science is that department of knowledge which relates to the order of nature, or, in other words, to the regular succession of events." Physics is one of the most fundamental scientific disciplines, and its main goal is to understand how the universe behaves."Physics is one of the most fundamental of the sciences. Scientists of all disciplines use the ideas of physics, including chemists who study the structure of molecules, paleontologists who try to reconstruct how dinosaurs walked, and climatologists who study how human activities affect the atmosphere and oceans. Physics is also the foundation of all engineering and technology. No engineer could design a flat-screen TV, an interplanetary spacecraft, or even a better mousetrap without first understanding the basic laws of physics. (...) You will come to see physics as a towering achievement of the human intellect in its quest to understand our world and ourselves."Physics is an experimental science. Physicists observe the phenomena of nature and try to find patterns that relate these phenomena.""Physics is the study of your world and the world and universe around you." Physics is one of the oldest academic disciplines and, through its inclusion of astronomy, perhaps the oldest. Over the last two millennia, physics, chemistry, biology, and certain branches of mathematics were a part of natural philosophy, but during the scientific revolution in the 17th century, these natural sciences emerged as unique research endeavors in their own right. Physics intersects with many interdisciplinary areas of research, such as biophysics and quantum chemistry, and the boundaries of physics are not rigidly defined. New ideas in physics often explain the fundamental mechanisms studied by other sciences and suggest new avenues of research in academic disciplines such as mathematics and philosophy. Advances in physics often enable advances in new technologies. For example, advances in the understanding of electromagnetism and nuclear physics led directly to the development of new products that have dramatically transformed modern-day society, such as television, computers, domestic appliances, and nuclear weapons; advances in thermodynamics led to the development of industrialization; and advances in mechanics inspired the development of calculus.

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Pierre de Fermat

Pierre de Fermat (Between 31 October and 6 December 1607 – 12 January 1665) was a French lawyer at the Parlement of Toulouse, France, and a mathematician who is given credit for early developments that led to infinitesimal calculus, including his technique of adequality.

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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 (geometry)

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

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Polar coordinate system

In mathematics, the polar coordinate system is a two-dimensional coordinate system in which each point on a plane is determined by a distance from a reference point and an angle from a reference direction.

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Projective space

In mathematics, a projective space can be thought of as the set of lines through the origin of a vector space V. The cases when and are the real projective line and the real projective plane, respectively, where R denotes the field of real numbers, R2 denotes ordered pairs of real numbers, and R3 denotes ordered triplets of real numbers.

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Pythagorean theorem

In mathematics, the Pythagorean theorem, also known as Pythagoras' theorem, is a fundamental relation in Euclidean geometry among the three sides of a right triangle.

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Quadratic equation

In algebra, a quadratic equation (from the Latin quadratus for "square") is any equation having the form where represents an unknown, and,, and represent known numbers such that is not equal to.

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Quadratic function

In algebra, a quadratic function, a quadratic polynomial, a polynomial of degree 2, or simply a quadratic, is a polynomial function in one or more variables in which the highest-degree term is of the second degree.

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In classical geometry, a radius of a circle or sphere is any of the line segments from its center to its perimeter, and in more modern usage, it is also their length.

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Real number

In mathematics, a real number is a value of a continuous quantity that can represent a distance along a line.

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René Descartes

René Descartes (Latinized: Renatus Cartesius; adjectival form: "Cartesian"; 31 March 1596 – 11 February 1650) was a French philosopher, mathematician, and scientist.

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A rocket (from Italian rocchetto "bobbin") is a missile, spacecraft, aircraft or other vehicle that obtains thrust from a rocket engine.

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In mathematics, the slope or gradient of a line is a number that describes both the direction and the steepness of the line.

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Solution set

In mathematics, a solution set is the set of values that satisfy a given set of equations or inequalities.

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Spaceflight (also written space flight) is ballistic flight into or through outer space.

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A sphere (from Greek σφαῖρα — sphaira, "globe, ball") is a perfectly round geometrical object in three-dimensional space that is the surface of a completely round ball (viz., analogous to the circular objects in two dimensions, where a "circle" circumscribes its "disk").

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Spherical coordinate system

In mathematics, a spherical coordinate system is a coordinate system for three-dimensional space where the position of a point is specified by three numbers: the radial distance of that point from a fixed origin, its polar angle measured from a fixed zenith direction, and the azimuth angle of its orthogonal projection on a reference plane that passes through the origin and is orthogonal to the zenith, measured from a fixed reference direction on that plane.

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In geometry, a square is a regular quadrilateral, which means that it has four equal sides and four equal angles (90-degree angles, or (100-gradian angles or right angles). It can also be defined as a rectangle in which two adjacent sides have equal length. A square with vertices ABCD would be denoted.

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In mathematics, a set A is a subset of a set B, or equivalently B is a superset of A, if A is "contained" inside B, that is, all elements of A are also elements of B. A and B may coincide.

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Surface (mathematics)

In mathematics, a surface is a generalization of a plane which needs not be flat, that is, the curvature is not necessarily zero.

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Synthetic geometry

Synthetic geometry (sometimes referred to as axiomatic or even pure geometry) is the study of geometry without the use of coordinates or formulas.

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In geometry, the tangent line (or simply tangent) to a plane curve at a given point is the straight line that "just touches" the curve at that point.

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Tangent space

In mathematics, the tangent space of a manifold facilitates the generalization of vectors from affine spaces to general manifolds, since in the latter case one cannot simply subtract two points to obtain a vector that gives the displacement of the one point from the other.

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Three-dimensional space

Three-dimensional space (also: 3-space or, rarely, tri-dimensional space) is a geometric setting in which three values (called parameters) are required to determine the position of an element (i.e., point).

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

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Two-dimensional space

Two-dimensional space or bi-dimensional space is a geometric setting in which two values (called parameters) are required to determine the position of an element (i.e., point).

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University of Minnesota

The University of Minnesota, Twin Cities (often referred to as the University of Minnesota, Minnesota, the U of M, UMN, or simply the U) is a public research university in Minneapolis and Saint Paul, Minnesota.

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Vector space

A vector space (also called a linear space) is a collection of objects called vectors, which may be added together and multiplied ("scaled") by numbers, called scalars.

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In analytic geometry, using the common convention that the horizontal axis represents a variable x and the vertical axis represents a variable y, a y-intercept or vertical intercept is a point where the graph of a function or relation intersects the y-axis of the coordinate system.

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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, x is a solution of the equation f(x).

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[1] https://en.wikipedia.org/wiki/Analytic_geometry

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