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57 relations: Abelian integral, Angular momentum, Antipodes, Astroid, Azimuth, Barnaba Oriani, Beltrami identity, Calculus of variations, Caustic (optics), Clairaut's relation, Conjugate points, Cut locus, Double-precision floating-point format, Dynamical billiards, Ellipse, Ellipsoid, Ellipsoidal coordinates, Elliptic function, Elliptic integral, Equator, Evolute, Fédération Aéronautique Internationale, Federal Aviation Administration, Figure of the Earth, Friedrich Heinrich Albert Wangerin, Gauss–Bonnet theorem, Gaussian curvature, Geodesic, Geodesic curvature, Geodesy, Geodetic control network, Geographic information system, Geographical distance, Great circle, Great-circle navigation, Involute, Königsberg, Least squares adjustment, Line (geometry), Maritime boundary, Meridian (geography), Meridian arc, Ordinary differential equation, Orthogonality, Principal curvature, Principle of least action, PROJ.4, Quadrature (mathematics), Reference ellipsoid, Rhumb line, ..., Sphere, Spherical trigonometry, Spheroid, Triangulation (surveying), Umbilical point, Vincenty's formulae, World Geodetic System. Expand index (7 more) »
Abelian integral
In mathematics, an abelian integral, named after the Norwegian mathematician Niels Henrik Abel, is an integral in the complex plane of the form where R(x,w) is an arbitrary rational function of the two variables x and w, which are related by the equation where F(x,w) is an irreducible polynomial in w, whose coefficients \varphi_j(x), j.
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Angular momentum
In physics, angular momentum (rarely, moment of momentum or rotational momentum) is the rotational equivalent of linear momentum.
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Antipodes
In geography, the antipode of any spot on Earth is the point on Earth's surface diametrically opposite to it; the antipodes of a region similarly represent the area opposite it.
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Astroid
An astroid is a particular mathematical curve: a hypocycloid with four cusps.
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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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Barnaba Oriani
Barnaba Oriani FRS FRSE (17 July 1752 – 12 November 1832) was an Italian priest, geodesist, astronomer and scientist.
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Beltrami identity
The Beltrami identity, named after Eugenio Beltrami, is a simplified and less general version of the Euler–Lagrange equation in the calculus of variations.
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Calculus of variations
Calculus of variations is a field of mathematical analysis that uses variations, which are small changes in functions and functionals, to find maxima and minima of functionals: mappings from a set of functions to the real numbers.
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Caustic (optics)
In optics, a caustic or caustic network is the envelope of light rays reflected or refracted by a curved surface or object, or the projection of that envelope of rays on another surface.
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Clairaut's relation
Clairaut's relation, named after Alexis Claude de Clairaut, is a formula in classical differential geometry.
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Conjugate points
In differential geometry, conjugate points are, roughly, points that can almost be joined by a 1-parameter family of geodesics.
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Cut locus
The cut locus is a mathematical structure defined for a closed set S in a space X in which the length of every path is well defined.
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Double-precision floating-point format
Double-precision floating-point format is a computer number format, usually occupying 64 bits in computer memory; it represents a wide dynamic range of numeric values by using a floating radix point.
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Dynamical billiards
A billiard is a dynamical system in which a particle alternates between motion in a straight line and specular reflections from a boundary.
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Ellipse
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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Ellipsoid
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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Ellipsoidal coordinates
Ellipsoidal coordinates are a three-dimensional orthogonal coordinate system (\lambda, \mu, \nu) that generalizes the two-dimensional elliptic coordinate system.
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Elliptic function
In complex analysis, an elliptic function is a meromorphic function that is periodic in two directions.
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Elliptic integral
In integral calculus, elliptic integrals originally arose in connection with the problem of giving the arc length of an ellipse.
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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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Evolute
In the differential geometry of curves, the evolute of a curve is the locus of all its centers of curvature.
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Fédération Aéronautique Internationale
The Fédération aéronautique internationale (FAI; The World Air Sports Federation), is the world governing body for air sports.
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Federal Aviation Administration
The Federal Aviation Administration (FAA) of the United States is a national authority with powers to regulate all aspects of civil aviation.
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Figure of the Earth
The figure of the Earth is the size and shape of the Earth in geodesy.
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Friedrich Heinrich Albert Wangerin
Friedrich Heinrich Albert Wangerin (November 18, 1844 – October 25, 1933) was a German mathematician.
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Gauss–Bonnet theorem
The Gauss–Bonnet theorem or Gauss–Bonnet formula in differential geometry is an important statement about surfaces which connects their geometry (in the sense of curvature) to their topology (in the sense of the Euler characteristic).
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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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Geodesic
In differential geometry, a geodesic is a generalization of the notion of a "straight line" to "curved spaces".
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Geodesic curvature
In Riemannian geometry, the geodesic curvature k_g of a curve \gamma measures how far the curve is from being a geodesic.
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Geodesy
Geodesy, also known as geodetics, is the earth science of accurately measuring and understanding three of Earth's fundamental properties: its geometric shape, orientation in space, and gravitational field.
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Geodetic control network
A geodetic control network (also geodetic network, reference network, control point network, or control network) is a network, often of triangles, which are measured exactly by techniques of terrestrial surveying or by satellite geodesy.
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Geographic information system
A geographic information system (GIS) is a system designed to capture, store, manipulate, analyze, manage, and present spatial or geographic data.
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Geographical distance
Geographical distance is the distance measured along the surface of the earth.
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Great circle
A great circle, also known as an orthodrome, of a sphere is the intersection of the sphere and a plane that passes through the center point of the sphere.
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Great-circle navigation
Great-circle navigation or orthodromic navigation (related to orthodromic course; from the Greek ορθóς, right angle, and δρóμος, path) is the practice of navigating a vessel (a ship or aircraft) along a great circle.
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Involute
In the differential geometry of curves, an involute (also known as evolvent) is a curve obtained from another given curve by one of two methods.
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Königsberg
Königsberg is the name for a former German city that is now Kaliningrad, Russia.
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Least squares adjustment
Least squares adjustment is a model for the solution of an overdetermined system of equations based on the principle of least squares of observation residuals.
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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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Maritime boundary
A maritime boundary is a conceptual division of the Earth's water surface areas using physiographic or geopolitical criteria.
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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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Meridian arc
In geodesy, a meridian arc measurement is the distance between two points with the same longitude, i.e., a segment of a meridian curve or its length.
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Ordinary differential equation
In mathematics, an ordinary differential equation (ODE) is a differential equation containing one or more functions of one independent variable and its derivatives.
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Orthogonality
In mathematics, orthogonality is the generalization of the notion of perpendicularity to the linear algebra of bilinear forms.
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Principal curvature
In differential geometry, the two principal curvatures at a given point of a surface are the eigenvalues of the shape operator at the point.
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Principle of least action
The principle of least action – or, more accurately, the principle of stationary action – is a variational principle that, when applied to the action of a mechanical system, can be used to obtain the equations of motion for that system.
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PROJ.4
PROJ.4 (or proj) is a library for performing conversions between cartographic projections.
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Quadrature (mathematics)
In mathematics, quadrature is a historical term which means determining area.
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Reference ellipsoid
In geodesy, a reference ellipsoid is a mathematically defined surface that approximates the geoid, the truer figure of the Earth, or other planetary body.
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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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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 trigonometry
Spherical trigonometry is the branch of spherical geometry that deals with the relationships between trigonometric functions of the sides and angles of the spherical polygons (especially spherical triangles) defined by a number of intersecting great circles on the sphere.
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Spheroid
A spheroid, or ellipsoid of revolution, is a quadric surface obtained by rotating an ellipse about one of its principal axes; in other words, an ellipsoid with two equal semi-diameters.
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Triangulation (surveying)
In surveying, triangulation is the process of determining the location of a point by measuring only angles to it from known points at either end of a fixed baseline, rather than measuring distances to the point directly as in trilateration.
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Umbilical point
In the differential geometry of surfaces in three dimensions, umbilics or umbilical points are points on a surface that are locally spherical.
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Vincenty's formulae
Vincenty's formulae are two related iterative methods used in geodesy to calculate the distance between two points on the surface of a spheroid, developed by Thaddeus Vincenty (1975a).
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World Geodetic System
The World Geodetic System (WGS) is a standard for use in cartography, geodesy, and satellite navigation including GPS.
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Redirects here:
Earth geodesic, Earth geodesics, Earth's geodesic, Ellipsoid geodesic, Ellipsoidal geodesic, Ellipsoidal geodesics, Ellipsoidal trigonometry, Geodesics on a spheroid, Geodesics on a triaxial ellipsoid, Geodesics on an ellipsoid of revolution, Geodesics on ellipsoids, Geodesics on spheroids, Geodesics on the ellipsoid, Inverse geodetic problem, Spheroidal geodesic, Spheroidal geodesics, Spheroidal trigonometry.
References
[1] https://en.wikipedia.org/wiki/Geodesics_on_an_ellipsoid
