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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]

116 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, Diffeomorphism, 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, Glossary of arithmetic and Diophantine geometry, Graph paper, Hipparchus, Homeomorphism, Homogeneous coordinates, ..., Hyperbolic geometry, Hyperplane, Integral, Isaac Newton, Isometry, 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, Mineralogy, N-sphere, Nadir, Navigation, Orientation (vector space), Panorama Tools, Parametrization, Photography, Plane (geometry), Planisphaerium, Planisphere, Poincaré disk model, 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, Russians, Saint-Dié-des-Vosges, Schlegel diagram, Slickenside, Smoothness, Sphere, Spherical coordinate system, Star chart, Statistics, Stereographic projection, Structural geology, Surface, Tom M. Apostol, Topology, Transmission electron microscopy, Transversality (mathematics), Unit circle, Unit sphere, Western Hemisphere, X-ray crystallography, Zenith. Expand index (66 more) »

Alexandroff extension

In 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 in what is now the modern country of Egypt.

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In planar 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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An astrolabe (ἀστρολάβος astrolabos, "star-taker"), Oxford English Dictionary 2nd ed.

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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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An azimuth (from Arabic al-sumūt, meaning "the directions") 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 (September 17, 1826 – July 20, 1866) was an influential German mathematician who made lasting and revolutionary contributions to analysis, number theory, and differential geometry.

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

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Calculus is the mathematical study of change, in the same way that geometry is the study of shape and algebra is the study of operations and their application to solving equations.

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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 from the point to two fixed perpendicular directed lines, measured in the same unit of length.

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

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Central angle

A central angle is an angle whose apex (vertex) is the center O of a circle and whose legs (sides) are radii intersecting the circle in two distinct points A and B thereby subtending an arc between those two points whose angle is (by definition) equal to that of the central angle itself.

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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 the Earth is an imaginary east-west circle connecting all locations (ignoring elevation) with 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 the imaginary unit, that satisfies the equation.

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A computer is a general-purpose device that can be programmed to carry out a set of arithmetic or logical operations automatically.

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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 isoline, isopleth, or isarithm) of a function of two variables is a curve along which the function has a constant value.

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

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

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Eastern Hemisphere

The Eastern Hemisphere is a geographical term for the half of the Earth that is east of the Prime Meridian (which crosses Greenwich, England, United Kingdom) and west of 180° longitude.

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Edmond Halley

Edmond (or Edmund) Halley, FRS (pronounced; 8 November 1656 – 14 January 1742) was an English astronomer, geophysicist, mathematician, meteorologist, and physicist who is best known for computing the orbit of the eponymous Halley's Comet.

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Electron diffraction

Electron diffraction refers to the wave nature of electrons.

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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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An equator is the intersection of a sphere's surface with the plane perpendicular to the sphere's axis of rotation and midway between the poles.

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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 construct 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, complex projective space CPn endowed with a Hermitian form.

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Function (mathematics)

In mathematics, a function is a relation between a set of inputs and a set of permissible outputs with the property that each input is related to exactly one output.

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Gaussian curvature

In differential geometry, the Gaussian curvature or Gauss curvature of a surface at a point is the product of the principal curvatures, κ1 and κ2, at the given point.

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

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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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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, graphing paper, or millimeter paper is writing paper that is printed with fine lines making up a regular grid.

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

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

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The integral is an important concept in mathematics.

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Isaac Newton

Sir Isaac Newton (25 December 164220 March 1726/7) was an English physicist and mathematician (described in his own day as a "natural philosopher") who is widely recognised as one of the most influential scientists of all time and as a key figure in the scientific revolution.

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In mathematics, an isometry is a distance-preserving injective map between metric spaces.

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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 at what they are looking.

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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/table provides an overview of significant map projections, including those described by articles in Wikipedia.

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List of trigonometric identities

In mathematics, trigonometric identities are equalities that involve trigonometric functions and are true for every single value of the occurring variables.

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

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Map projection

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

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

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Möbius transformation

In geometry and complex analysis, a Möbius transformation of the 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 meridian (or line of longitude) is any great circle line on the Earth's surface, passing through the North Pole and the South Pole.

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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 D except a set of isolated points (the poles of the function), at each of which the function must have a Laurent series.

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Miller index

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

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Mineralogy is a subject of geology specializing in the scientific study of chemistry, crystal structure, and physical (including optical) properties of minerals.

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

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The nadir (from نظير / ALA-LC: naẓīr, meaning "opposite") 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 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 the German physics and mathematics professor Helmut Dersch.

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Parametrization (or parameterization; also parameterisation, parametrisation) is the process of deciding and defining the parameters necessary for a complete or relevant specification of a model or geometric object.

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Photography is the science, art 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.

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The Planisphaerium is a work by Ptolemy.

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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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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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In elementary geometry, a polytope is a geometric object with flat sides, and may exist in any general number of dimensions n as an n-dimensional polytope or n-polytope.

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Projective geometry

In mathematics, projective geometry is the study of geometric properties that are invariant under projective transformations.

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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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Claudius Ptolemy (Κλαύδιος Πτολεμαῖος, Klaúdios Ptolemaîos,; Claudius Ptolemaeus) was a Greco-Egyptian writer of Alexandria, known as a 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 a, b, and c, such that.

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In mathematics, a quadric, or quadric surface, is any D-dimensional hypersurface in -dimensional space defined as the locus of zeros of a quadratic polynomial.

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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 p/q of two integers, p and q, with the denominator q not equal to zero.

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Rational point

In number theory, a rational point is a point in space each of whose coordinates are rational; that is, the coordinates of the point are elements of the field of rational numbers, as well as being elements of larger fields that contain the rational numbers, such as the real numbers and the complex numbers.

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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, that is, a one-sided surface.

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Rhumb line

In navigation, a rhumb line (or loxodrome) is an arc crossing all meridians of longitude at the same angle, i.e. 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 the 19th century mathematician 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 vector fields on M, then p \mapsto g_p(X(p),Y(p)) is a smooth function.

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Russians (русские, russkiye) are an East Slavic ethnic group native to Russia, who speak the Russian language and primarily live in Russia. They are the most numerous ethnic group in Russia constituting more than 80% of the country's population according to the census of 2010, and the most numerous ethnic group in Europe.

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Saint-Dié-des-Vosges, commonly referred to as Saint-Dié, is a commune in the Vosges department in Lorraine in northeastern France.

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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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Rt 322 northeast of State College, Pennsylvania fault in quartzite in the Alpujarras 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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In mathematical analysis, smoothness has to do with how many derivatives of a function exist and are continuous.

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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 a circular object in two dimensions).

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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 is a map of the night sky.

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Statistics is the study of 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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In mathematics, specifically, in topology, a surface is a two-dimensional, topological manifold.

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Tom M. Apostol

Tom Mike Apostol is an American analytic number theorist and professor at the California Institute of Technology.

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In mathematics, topology (from the Greek τόπος, place, and λόγος, study), is the study of topological spaces.

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Transmission electron microscopy

Transmission electron microscopy (TEM) is a microscopy technique in which a beam of electrons is transmitted through an ultra-thin specimen, interacting with the specimen as it passes through.

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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 the Earth that lies west of the Prime Meridian (which crosses Greenwich, London, United Kingdom) and east of the Antimeridian, the other half being called the Eastern Hemisphere.

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X-ray crystallography

X-ray crystallography is a tool used for identifying 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 refers to an imaginary point directly "above" a particular location, on the imaginary celestial sphere.

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Azimuthal conformal projection, George Wulff, Stereographic chart, Stereographic net, Stereonet, Wolff net, Wulff net, Wulff plot.


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

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