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Stereographic projection

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In geometry, the stereographic projection is a particular mapping (function) that projects a sphere onto a plane. [1]

120 relations: Alexandroff extension, Algebraic geometry, American Mathematical Society, Ancient Egypt, Angle, Antipodal point, Astrolabe, Astronomical clock, Azimuth, Beam compass, Bernhard Riemann, Bijection, Calculus, Cartesian coordinate system, Cartography, Central angle, Circle of a sphere, Circle of latitude, Complex analysis, Complex number, Computer, Conformal geometry, Conformal map, Contour line, Crystal, Crystallography, Cut-the-Knot, Cylindrical coordinate system, Degeneracy (mathematics), Eastern Hemisphere, Edmond Halley, Electron diffraction, Embedding, Equator, Euclidean space, Ewald's sphere, Fault (geology), Fisheye lens, Foliation (geology), François d'Aguilon, Fubini–Study metric, Function (mathematics), Gaussian curvature, Geology, Geometry, George Wulff, Glossary of arithmetic and diophantine geometry, Graph paper, Hemispheres of Earth, Hipparchus, ..., Homeomorphism, Homogeneous coordinates, Hyperbolic geometry, Hyperplane, Integral, Isaac Newton, Isometry, Jean Roze, Kikuchi line, Lambert azimuthal equal-area projection, Lineation (geology), List of map projections, List of trigonometric identities, Logarithmic spiral, Manifold, Map projection, Mathematics, Möbius transformation, Meridian (geography), Meromorphic function, Miller index, N-sphere, Nadir, Navigation, Orientation (vector space), Panorama Tools, Parametrization, Photography, Plane (geometry), PlanetMath, Planisphaerium, Planisphere, Poincaré disk model, Point at infinity, Polar coordinate system, Polytope, Projective geometry, Projective space, Ptolemy, Pythagorean triple, Quadric, Quotient space (topology), Rational number, Rational point, Rational variety, Real projective plane, Rhumb line, Riemann sphere, Riemannian manifold, Rumold Mercator, Schlegel diagram, Slickenside, Smoothness, Sphere, Spherical coordinate system, Star chart, Statistics, Stereographic projection, Structural geology, Surface (topology), Tissot's indicatrix, Tom M. Apostol, Topology, Transmission electron microscopy, Transversality (mathematics), Unit circle, Unit sphere, Western Hemisphere, X-ray crystallography, Zenith. Expand index (70 more) »

Alexandroff extension

In the mathematical field of topology, the Alexandroff extension is a way to extend a noncompact topological space by adjoining a single point in such a way that the resulting space is compact.

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Algebraic geometry

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

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American Mathematical Society

The American Mathematical Society (AMS) is an association of professional mathematicians dedicated to the interests of mathematical research and scholarship, and serves the national and international community through its publications, meetings, advocacy and other programs.

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Ancient Egypt

Ancient Egypt was a civilization of ancient Northeastern Africa, concentrated along the lower reaches of the Nile River - geographically Lower Egypt and Upper Egypt, in the place that is now occupied by the countries of Egypt and Sudan.

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Angle

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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Antipodal point

In mathematics, the antipodal point of a point on the surface of a sphere is the point which is diametrically opposite to it — so situated that a line drawn from the one to the other passes through the center of the sphere and forms a true diameter.

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Astrolabe

An astrolabe (ἀστρολάβος astrolabos; ٱلأَسْطُرلاب al-Asturlāb; اَختِرِیاب Akhteriab) is an elaborate inclinometer, historically used by astronomers and navigators to measure the inclined position in the sky of a celestial body, day or night.

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Astronomical clock

An astronomical clock is a clock with special mechanisms and dials to display astronomical information, such as the relative positions of the sun, moon, zodiacal constellations, and sometimes major planets.

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Azimuth

An azimuth (from the pl. form of the Arabic noun "السَّمْت" as-samt, meaning "the direction") is an angular measurement in a spherical coordinate system.

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Beam compass

A beam compass is a compass with a beam and sliding sockets or cursors for drawing and dividing circles larger than those made by a regular pair of compasses.

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Bernhard Riemann

Georg Friedrich Bernhard Riemann (17 September 1826 – 20 July 1866) was a German mathematician who made contributions to analysis, number theory, and differential geometry.

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Bijection

In mathematics, a bijection, bijective function, or one-to-one correspondence is a function between the elements of two sets, where each element of one set is paired with exactly one element of the other set, and each element of the other set is paired with exactly one element of the first set.

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Calculus

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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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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Cartography

Cartography (from Greek χάρτης chartēs, "papyrus, sheet of paper, map"; and γράφειν graphein, "write") is the study and practice of making maps.

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Central angle

Central angles are subtended by an arc between those two points, and the arc length is the central angle of a circle of radius one (measured in radians).

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Circle of a sphere

A circle of a sphere is a circle that lies on a sphere.

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Circle of latitude

A circle of latitude on Earth is an abstract east–west circle connecting all locations around Earth (ignoring elevation) at a given latitude.

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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 number

A complex number is a number that can be expressed in the form, where and are real numbers, and is a solution of the equation.

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Computer

A computer is a device that can be instructed to carry out sequences of arithmetic or logical operations automatically via computer programming.

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Conformal geometry

In mathematics, conformal geometry is the study of the set of angle-preserving (conformal) transformations on a space.

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Conformal map

In mathematics, a conformal map is a function that preserves angles locally.

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Contour line

A contour line (also isocline, isopleth, isarithm, or equipotential curve) of a function of two variables is a curve along which the function has a constant value, so that the curve joins points of equal value.

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Crystal

A crystal or crystalline solid is a solid material whose constituents (such as atoms, molecules, or ions) are arranged in a highly ordered microscopic structure, forming a crystal lattice that extends in all directions.

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Crystallography

Crystallography is the experimental science of determining the arrangement of atoms in crystalline solids (see crystal structure).

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Cut-the-Knot

Cut-the-knot is a free, advertisement-funded educational website maintained by Alexander Bogomolny and devoted to popular exposition of many topics in mathematics.

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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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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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Eastern Hemisphere

The Eastern Hemisphere is a geographical term for the half of Earth which is east of the prime meridian (which crosses Greenwich, London, UK) and west of the antimeridian (which crosses the Pacific Ocean and relatively little land from pole to pole).

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Edmond Halley

Edmond (or Edmund) Halley, FRS (–) was an English astronomer, geophysicist, mathematician, meteorologist, and physicist.

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Electron diffraction

Electron diffraction refers to the wave nature of electrons.

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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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Equator

An equator of a rotating spheroid (such as a planet) is its zeroth circle of latitude (parallel).

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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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Ewald's sphere

The Ewald sphere is a geometric construction used in electron, neutron, and X-ray crystallography which demonstrates the relationship between: It was conceived by Paul Peter Ewald, a German physicist and crystallographer.

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Fault (geology)

In geology, a fault is a planar fracture or discontinuity in a volume of rock, across which there has been significant displacement as a result of rock-mass movement.

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Fisheye lens

A fisheye lens is an ultra wide-angle lens that produces strong visual distortion intended to create a wide panoramic or hemispherical image.

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Foliation (geology)

Foliation in geology refers to repetitive layering in metamorphic rocks.

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François d'Aguilon

François d'Aguilon (also d'Aguillon or in Latin Franciscus Aguilonius) (4 January 1567 – 20 March 1617) was a Belgian Jesuit mathematician, physicist and architect.

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Fubini–Study metric

In mathematics, the Fubini–Study metric is a Kähler metric on projective Hilbert space, that is, on a complex projective space CPn endowed with a Hermitian form.

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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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Gaussian curvature

In differential geometry, the Gaussian curvature or Gauss curvature Κ of a surface at a point is the product of the principal curvatures, κ1 and κ2, at the given point: For example, a sphere of radius r has Gaussian curvature 1/r2 everywhere, and a flat plane and a cylinder have Gaussian curvature 0 everywhere.

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Geology

Geology (from the Ancient Greek γῆ, gē, i.e. "earth" and -λoγία, -logia, i.e. "study of, discourse") is an earth science concerned with the solid Earth, the rocks of which it is composed, and the processes by which they change over time.

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Geometry

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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George Wulff

George (Yuri Viktorovich) Wulff (Георгий (Юрий) Викторович Вульф) (22 June 1863, Nizhyn (Russian Empire, nowadays Ukraine) – 25 December 1925, Moscow) was a Russian crystallographer.

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Glossary of arithmetic and diophantine geometry

This is a glossary of arithmetic and diophantine geometry in mathematics, areas growing out of the traditional study of Diophantine equations to encompass large parts of number theory and algebraic geometry.

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Graph paper

Graph paper, coordinate paper, grid paper, or squared paper is writing paper that is printed with fine lines making up a regular grid.

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Hemispheres of Earth

In geography and cartography, the hemispheres of Earth refer to any division of the globe into two hemispheres (from Ancient Greek ἡμισφαίριον hēmisphairion, meaning "half of a sphere").

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Hipparchus

Hipparchus of Nicaea (Ἵππαρχος, Hipparkhos) was a Greek astronomer, geographer, and mathematician.

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Homeomorphism

In the mathematical field of topology, a homeomorphism or topological isomorphism or bi continuous function is a continuous function between topological spaces that has a continuous inverse function.

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Homogeneous coordinates

In mathematics, homogeneous coordinates or projective coordinates, introduced by August Ferdinand Möbius in his 1827 work Der barycentrische Calcül, are a system of coordinates used in projective geometry, as Cartesian coordinates are used in Euclidean geometry.

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Hyperbolic geometry

In mathematics, hyperbolic geometry (also called Bolyai–Lobachevskian geometry or Lobachevskian geometry) is a non-Euclidean geometry.

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Hyperplane

In geometry, a hyperplane is a subspace whose dimension is one less than that of its ambient space.

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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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Isaac Newton

Sir Isaac Newton (25 December 1642 – 20 March 1726/27) was an English mathematician, astronomer, theologian, author and physicist (described in his own day as a "natural philosopher") who is widely recognised as one of the most influential scientists of all time, and a key figure in the scientific revolution.

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Isometry

In mathematics, an isometry (or congruence, or congruent transformation) is a distance-preserving transformation between metric spaces, usually assumed to be bijective.

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Jean Roze

Jean Roze is a traditional textile producer in Saint-Avertin, Indre-et-Loire, France founded in 1470.

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Kikuchi line

Kikuchi lines pair up to form bands in electron diffraction from single crystal specimens, there to serve as "roads in orientation-space" for microscopists not certain what they are looking at.

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Lambert azimuthal equal-area projection

The Lambert azimuthal equal-area projection is a particular mapping from a sphere to a disk (that is, a region bounded by a circle).

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Lineation (geology)

Lineations in structural geology are linear structural features within rocks.

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List of map projections

This list provides an overview of some of the significant or common map projections.

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List of trigonometric identities

In mathematics, trigonometric identities are equalities that involve trigonometric functions and are true for every value of the occurring variables where both sides of the equality are defined.

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Logarithmic spiral

A logarithmic spiral, equiangular spiral or growth spiral is a self-similar spiral curve which often appears in nature.

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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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Map projection

A map projection is a systematic transformation of the latitudes and longitudes of locations from the surface of a sphere or an ellipsoid into locations on a plane.

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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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Möbius transformation

In geometry and complex analysis, a Möbius transformation of the complex plane is a rational function of the form of one complex variable z; here the coefficients a, b, c, d are complex numbers satisfying ad − bc ≠ 0.

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Meridian (geography)

A (geographical) meridian (or line of longitude) is the half of an imaginary great circle on the Earth's surface, terminated by the North Pole and the South Pole, connecting points of equal longitude.

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Meromorphic function

In the mathematical field of complex analysis, a meromorphic function on an open subset D of the complex plane is a function that is holomorphic on all of D except for a discrete set of isolated points, which are poles of the function.

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Miller index

Miller indices form a notation system in crystallography for planes in crystal (Bravais) lattices.

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N-sphere

In mathematics, the n-sphere is the generalization of the ordinary sphere to spaces of arbitrary dimension.

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Nadir

The nadir (from نظير / ALA-LC: naẓīr, meaning "counterpart") is the direction pointing directly below a particular location; that is, it is one of two vertical directions at a specified location, orthogonal to a horizontal flat surface there.

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Navigation

Navigation is a field of study that focuses on the process of monitoring and controlling the movement of a craft or vehicle from one place to another.

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Orientation (vector space)

In mathematics, orientation is a geometric notion that in two dimensions allows one to say when a cycle goes around clockwise or counterclockwise, and in three dimensions when a figure is left-handed or right-handed.

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Panorama Tools

Panorama Tools (also known as PanoTools) are a suite of programs and libraries originally written by German physics and mathematics professor Helmut Dersch.

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Parametrization

Parametrization (or parameterization; also parameterisation, parametrisation) is the process of finding parametric equations of a curve, a surface, or, more generally, a manifold or a variety, defined by an implicit equation.

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Photography

Photography is the science, art, application and practice of creating durable images by recording light or other electromagnetic radiation, either electronically by means of an image sensor, or chemically by means of a light-sensitive material such as photographic film.

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Plane (geometry)

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

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PlanetMath

PlanetMath is a free, collaborative, online mathematics encyclopedia.

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Planisphaerium

The Planisphaerium is a work by Ptolemy.

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Planisphere

In astronomy, a planisphere is a star chart analog computing instrument in the form of two adjustable disks that rotate on a common pivot.

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Poincaré disk model

In geometry, the Poincaré disk model, also called the conformal disk model, is a model of 2-dimensional hyperbolic geometry in which the points of the geometry are inside the unit disk, and the straight lines consist of all segments of circles contained within that disk that are orthogonal to the boundary of the disk, plus all diameters of the disk.

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Point at infinity

In geometry, a point at infinity or ideal point is an idealized limiting point at the "end" of each line.

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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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Polytope

In elementary geometry, a polytope is a geometric object with "flat" sides.

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Projective geometry

Projective geometry is a topic in mathematics.

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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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Ptolemy

Claudius Ptolemy (Κλαύδιος Πτολεμαῖος, Klaúdios Ptolemaîos; Claudius Ptolemaeus) was a Greco-Roman mathematician, astronomer, geographer, astrologer, and poet of a single epigram in the Greek Anthology.

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Pythagorean triple

A Pythagorean triple consists of three positive integers,, and, such that.

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Quadric

In mathematics, a quadric or quadric surface (quadric hypersurface in higher dimensions), is a generalization of conic sections (ellipses, parabolas, and hyperbolas).

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Quotient space (topology)

In topology and related areas of mathematics, a quotient space (also called an identification space) is, intuitively speaking, the result of identifying or "gluing together" certain points of a given topological space.

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Rational number

In mathematics, a rational number is any number that can be expressed as the quotient or fraction of two integers, a numerator and a non-zero denominator.

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Rational point

In number theory and algebraic geometry, a rational point of an algebraic variety is a solution of a set of polynomial equations in a given field.

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Rational variety

In mathematics, a rational variety is an algebraic variety, over a given field K, which is birationally equivalent to a projective space of some dimension over K. This means that its function field is isomorphic to the field of all rational functions for some set \ of indeterminates, where d is the dimension of the variety.

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Real projective plane

In mathematics, the real projective plane is an example of a compact non-orientable two-dimensional manifold; in other words, a one-sided surface.

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Rhumb line

In navigation, a rhumb line, rhumb, or loxodrome is an arc crossing all meridians of longitude at the same angle, that is, a path with constant bearing as measured relative to true or magnetic north.

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Riemann sphere

In mathematics, the Riemann sphere, named after Bernhard Riemann, is a model of the extended complex plane, the complex plane plus a point at infinity.

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Riemannian manifold

In differential geometry, a (smooth) Riemannian manifold or (smooth) Riemannian space (M,g) is a real, smooth manifold M equipped with an inner product g_p on the tangent space T_pM at each point p that varies smoothly from point to point in the sense that if X and Y are differentiable vector fields on M, then p \mapsto g_p(X(p),Y(p)) is a smooth function.

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Rumold Mercator

Rumold Mercator (1545–1599) was a cartographer and the son of cartographer Gerardus Mercator.

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Schlegel diagram

In geometry, a Schlegel diagram is a projection of a polytope from R^d into R^ through a point beyond one of its facets or faces.

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Slickenside

Rt 322 northeast of State College, Pennsylvania In geology, a slickenside is a smoothly polished surface caused by frictional movement between rocks along the two sides of a fault.

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Smoothness

In mathematical analysis, the smoothness of a function is a property measured by the number of derivatives it has that are continuous.

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Sphere

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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Star chart

A star chart or star map, also called a sky chart or sky map, is a map of the night sky.

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Statistics

Statistics is a branch of mathematics dealing with the collection, analysis, interpretation, presentation, and organization of data.

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Stereographic projection

In geometry, the stereographic projection is a particular mapping (function) that projects a sphere onto a plane.

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Structural geology

Structural geology is the study of the three-dimensional distribution of rock units with respect to their deformational histories.

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Surface (topology)

In topology and differential geometry, a surface is a two-dimensional manifold, and, as such, may be an "abstract surface" not embedded in any Euclidean space.

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Tissot's indicatrix

In cartography, a Tissot's indicatrix (Tissot indicatrix, Tissot's ellipse, Tissot ellipse, ellipse of distortion) (plural: "Tissot's indicatrices") is a mathematical contrivance presented by French mathematician Nicolas Auguste Tissot in 1859 and 1871 in order to characterize local distortions due to map projection.

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Tom M. Apostol

Tom Mike Apostol (August 20, 1923 – May 8, 2016) was an American analytic number theorist and professor at the California Institute of Technology, best known as the author of widely used mathematical textbooks.

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Topology

In mathematics, topology (from the Greek τόπος, place, and λόγος, study) is concerned with the properties of space that are preserved under continuous deformations, such as stretching, crumpling and bending, but not tearing or gluing.

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Transmission electron microscopy

Transmission electron microscopy (TEM, also sometimes conventional transmission electron microscopy or CTEM) is a microscopy technique in which a beam of electrons is transmitted through a specimen to form an image.

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Transversality (mathematics)

In mathematics, transversality is a notion that describes how spaces can intersect; transversality can be seen as the "opposite" of tangency, and plays a role in general position.

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Unit circle

In mathematics, a unit circle is a circle with a radius of one.

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Unit sphere

In mathematics, a unit sphere is the set of points of distance 1 from a fixed central point, where a generalized concept of distance may be used; a closed unit ball is the set of points of distance less than or equal to 1 from a fixed central point.

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Western Hemisphere

The Western Hemisphere is a geographical term for the half of Earth which lies west of the prime meridian (which crosses Greenwich, London, United Kingdom) and east of the antimeridian.

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X-ray crystallography

X-ray crystallography is a technique used for determining the atomic and molecular structure of a crystal, in which the crystalline atoms cause a beam of incident X-rays to diffract into many specific directions.

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Zenith

The zenith is an imaginary point directly "above" a particular location, on the imaginary celestial sphere.

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Azimuthal conformal projection, Little planet effect, Stereographic chart, Stereographic net, Stereonet, Tiny Planet, Tiny planet, Wolff net, Wulff net, Wulff plot.

References

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

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