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Angular Eccentricity
Angular eccentricity is one of many parameters which arise in the study of the ellipse or ellipsoid. It is denoted here by α (alpha). It may be defined in terms of the eccentricity, ''e'', or the aspect ratio, ''b/a'' (the ratio of the semi-minor axis and the semi-major axis In geometry, the major axis of an ellipse is its longest diameter: a line segment that runs through the center and both foci, with ends at the two most widely separated points of the perimeter. The semi-major axis (major semiaxis) is the long ...): :\alpha=\sin^\!e=\cos^\left(\frac\right). \,\! Angular eccentricity is not currently used in English language publications on mathematics, geodesy or map projections but it does appear in older literature. Any non-dimensional parameter of the ellipse may be expressed in terms of the angular eccentricity. Such expressions are listed in the following table after the conventional definitions.Rapp, Richard H. (1991). ''Geometric Geodesy, Part I'', Dept. o ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Angular Eccentricity And Linear Eccentricity
Angular may refer to: Anatomy * Angular artery, the terminal part of the facial artery * Angular bone, a large bone in the lower jaw of amphibians and reptiles * Angular incisure, a small anatomical notch on the stomach * Angular gyrus, a region of the brain in the parietal lobe * Angular vein, formed by the junction of the frontal vein and supraorbital vein Other uses * Angular (web framework), an open-source web platform **AngularJS, the first incarnation of Angular * Angle, having an angle or angles * Angular diameter, describing how large a sphere or circle appears from a given point of view ** Angular diameter distance, used in astronomy * Angular Recording Corporation Angular Recording Corporation was an independent record label founded in New Cross, South East London. It was established in June 2003 by two ex-Goldsmiths College students, Joe Daniel and Joe Margetts, who reclaimed a local Ordnance Survey Tr ..., a British independent record label See also * Angle (dis ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Ellipse
In mathematics, an ellipse is a plane curve surrounding two focus (geometry), focal points, such that for all points on the curve, the sum of the two distances to the focal points is a constant. It generalizes a circle, which is the special type of ellipse in which the two focal points are the same. The elongation of an ellipse is measured by its eccentricity (mathematics), eccentricity e, a number ranging from e = 0 (the Limiting case (mathematics), limiting case of a circle) to e = 1 (the limiting case of infinite elongation, no longer an ellipse but a parabola). An ellipse has a simple algebraic solution for its area, but only approximations for its perimeter (also known as circumference), for which integration is required to obtain an exact solution. Analytic geometry, Analytically, the equation of a standard ellipse centered at the origin with width 2a and height 2b is: : \frac+\frac = 1 . Assuming a \ge b, the foci are (\pm c, 0) for c = \sqrt. The standard parametric e ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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. An ellipsoid is a quadric surface; that is, a surface that may be defined as the zero set of a polynomial of degree two in three variables. Among quadric surfaces, an ellipsoid is characterized by either of the two following properties. Every planar cross section is either an ellipse, or is empty, or is reduced to a single point (this explains the name, meaning "ellipse-like"). It is bounded, which means that it may be enclosed in a sufficiently large sphere. An ellipsoid has three pairwise perpendicular axes of symmetry which intersect at a center of symmetry, called the center of the ellipsoid. The line segments that are delimited on the axes of symmetry by the ellipsoid are called the ''principal axes'', or simply axes of the ellipsoid. If the three axes have different lengths, the figure is a triaxial ellipsoid (r ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Eccentricity (mathematics)
In mathematics, the eccentricity of a conic section is a non-negative real number that uniquely characterizes its shape. More formally two conic sections are similar if and only if they have the same eccentricity. One can think of the eccentricity as a measure of how much a conic section deviates from being circular. In particular: * The eccentricity of a circle is zero. * The eccentricity of an ellipse which is not a circle is greater than zero but less than 1. * The eccentricity of a parabola is 1. * The eccentricity of a hyperbola is greater than 1. * The eccentricity of a pair of lines is \infty Definitions Any conic section can be defined as the locus of points whose distances to a point (the focus) and a line (the directrix) are in a constant ratio. That ratio is called the eccentricity, commonly denoted as . The eccentricity can also be defined in terms of the intersection of a plane and a double-napped cone associated with the conic section. If the cone is oriented ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Semi-minor Axis
In geometry, the major axis of an ellipse is its longest diameter: a line segment that runs through the center and both focus (geometry), foci, with ends at the two most widely separated points of the perimeter. The semi-major axis (major wikt:semiaxis, semiaxis) is the longest semidiameter or one half of the major axis, and thus runs from the centre, through a focus (geometry), focus, and to the perimeter. The semi-minor axis (minor semiaxis) of an ellipse or hyperbola is a line segment that is at right angles with the semi-major axis and has one end at the center of the conic section. For the special case of a circle, the lengths of the semi-axes are both equal to the radius of the circle. The length of the semi-major axis of an ellipse is related to the semi-minor axis's length through the eccentricity (mathematics), eccentricity and the semi-latus rectum \ell, as follows: The semi-major axis of a hyperbola is, depending on the convention, plus or minus one half of the ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Semi-major Axis
In geometry, the major axis of an ellipse is its longest diameter: a line segment that runs through the center and both foci, with ends at the two most widely separated points of the perimeter. The semi-major axis (major semiaxis) is the longest semidiameter or one half of the major axis, and thus runs from the centre, through a focus, and to the perimeter. The semi-minor axis (minor semiaxis) of an ellipse or hyperbola is a line segment that is at right angles with the semi-major axis and has one end at the center of the conic section. For the special case of a circle, the lengths of the semi-axes are both equal to the radius of the circle. The length of the semi-major axis of an ellipse is related to the semi-minor axis's length through the eccentricity and the semi-latus rectum \ell, as follows: The semi-major axis of a hyperbola is, depending on the convention, plus or minus one half of the distance between the two branches. Thus it is the distance from the center ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Flattening
Flattening is a measure of the compression of a circle or sphere along a diameter to form an ellipse or an ellipsoid of revolution (spheroid) respectively. Other terms used are ellipticity, or oblateness. The usual notation for flattening is and its definition in terms of the semi-axes of the resulting ellipse or ellipsoid is :: \mathrm = f =\frac . The ''compression factor'' is \frac\,\! in each case; for the ellipse, this is also its aspect ratio. Definitions There are three variants of flattening; when it is necessary to avoid confusion, the main flattening is called the first flattening.Torge, W. (2001). ''Geodesy'' (3rd edition). de Gruyter. and online web textsOsborne, P. (2008). The Mercator Projections'' Chapter 5.Rapp, Richard H. (1991). ''Geometric Geodesy, Part I''. Dept. of Geodetic Science and Surveying, Ohio State Univ., Columbus, Ohio/ref> In the following, is the larger dimension (e.g. semimajor axis), whereas is the smaller (semiminor axis). All flatt ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Geodesy
Geodesy ( ) is the Earth science of accurately measuring and understanding Earth's figure (geometric shape and size), orientation in space, and gravity. The field also incorporates studies of how these properties change over time and equivalent measurements for other planets (known as '' planetary geodesy''). Geodynamical phenomena, including crustal motion, tides and polar motion, can be studied by designing global and national control networks, applying space geodesy and terrestrial geodetic techniques and relying on datums and coordinate systems. The job title is geodesist or geodetic surveyor. History Definition The word geodesy comes from the Ancient Greek word ''geodaisia'' (literally, "division of Earth"). It is primarily concerned with positioning within the temporally varying gravitational field. Geodesy in the German-speaking world is divided into "higher geodesy" ( or ), which is concerned with measuring Earth on the global scale, and "practical geodes ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
