map projection

Stereographic projection - Polar coordinates. On a sphere, let φ be azimuth and θ be co-latitude (angular distance from the pole). Let R be the radius of the sphere. Let the points of the sphere be projected stereographically onto a plane which is tangent to the pole. Let the points of the projection have coordinates ρP (radial distance away from origin) and θP. Then the projection is If θL is, instead, the latitude, then the equation for ρP changes to < ...

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Stereographic projection, Stereographic projection - Notable properties, Stereographic projection - Formula, Stereographic projection - Polar coordinates, Stereographic projection - Cartesian coordinates, Stereographic projection - Loxodromes on a stereographic projection, Stereographic projection - External link

Read more here: » Stereographic projection: Encyclopedia II - Stereographic projection - Formula

A cone is a basic geometrical shape: see cone (solid). Several things have also been called "cones" on account of their shape: A volcanic cone is a mountain formed by material ejected from a volcanic vent. In relativity, the light cone of an event consists of all spacetime events that can interact with it. The scaly fruit-like reproductive bodies of certain plants, especially conifers and cycads, are called cones: see conifer cone. In vertebrate anatomy, a cone cel ...

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TM, Tm or tm may stand for: Tmoney, a Korea's first smart card.(Tm) .tm, the Internet domain code for Turkmenistan. melting temperature in shorthand Technical Machine (Pokémon) Telekom Malaysia (the largest telecommunication company in Malaysia) Terametre (Tm) Terra Mystica a german Ultima-Online Freeshard Texas Mexican Railway (AAR reporting mark TM) Thulium a radio-active element (69th Element) Timiş county (Romania)

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In mathematics, a conformal map is a function which preserves angles. More formally, a map w = f(z) is called conformal (or angle-preserving) at z0, if it preserves oriented angles between curves through z0, as well as their orientation, i.e. direction. Conformal maps preserve both angles and the shapes of infinitesi ...

Including:

• Conformal map - Cartography
• Conformal map - Complex analysis
• Conformal map - Riemannian geometry
• Conformal map - Euclidean space
• Conformal map - Uses

Read more here: » Conformal map: Encyclopedia - Conformal map

It is possible to find the equations of loxodromes on the stereographic projection. A loxodrome on a sphere is described by Substituting equation (1) we obtain Equation (3) can be solved for θL: Substitute equation (5) into equation (4), then simplify, Apply the following trigonometric identity to equation (6), yielding Let b = −1/a; then ...

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Stereographic projection, Stereographic projection - Notable properties, Stereographic projection - Formula, Stereographic projection - Polar coordinates, Stereographic projection - Cartesian coordinates, Stereographic projection - Loxodromes on a stereographic projection, Stereographic projection - External link

Read more here: » Stereographic projection: Encyclopedia II - Stereographic projection - Loxodromes on a stereographic projection

A globe is a three-dimensional scale model of a spheroid celestial body such as a planet, star or moon, in particular Earth, or, alternatively, a spherical representation of the sky with the stars (but without the Sun, Moon, or planets, because their positions vary relative to those of the stars; however, the "orbit" of the Sun is indicated). Globes are the only geographical representation of Earth that have no distortion. Spheres such as the Earth are mapped onto a flat surface using a map projection with an inherent degree of distortion. These projections can either enforce angle preservation or area preservation. A typica ...

Including:

• Globe - Notable large globes

Read more here: » Globe: Encyclopedia - Globe

The word projection has several uses. In digital identity, a transaction. See also link contracts In chemistry: Fischer projection Haworth projection Newman projection stereochemical projection In dentistry, enamel projection: focal apical extensions of the coronal enamel beyond the normally smooth cervical margin and on to the root of the tooth. In cartography, a map projection In psychology, psychological projection I

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The locations of points in three-dimensional space are most conveniently described by three cartesian or rectangular coordinates, X,Y and Z. Since the advent of satellite positioning, such coordinate sytems are typically geocentric: the Z axis is aligned with the Earth's (conventional or instantaneous) rotation axis. Before the satellite geodesy era, the coordinate systems associated with geodetic datums attempted ...

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Geodesy, Geodesy - Definition, Geodesy - Geoid and reference ellipsoid, Geodesy - Coordinate systems in space, Geodesy - Coordinate systems in the plane, Geodesy - Heights, Geodesy - Geodetic datums, Geodesy - A note on terminology, Geodesy - Point positioning, Geodesy - Geodetic problems, Geodesy - Geodetic observational concepts, Geodesy - Geodetic observing instruments, Geodesy - Units and measures on the ellipsoid, Geodesy - Temporal change, Geodesy - International organizations, Geodesy - University institutes, Geodesy - Governmental agencies

Read more here: » Geodesy: Encyclopedia II - Geodesy - Coordinate systems in space

An important family of examples of conformal maps comes from complex analysis. If U is an open subset of the complex plane, C, then a function f : U → C is conformal if and only if it is holomorphic and its derivative is everywhere non-zero on U. If f is antiholomorphic (that is, the conjugate to a holomorphic function), it still pr ...

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Conformal map, Conformal map - Cartography, Conformal map - Complex analysis, Conformal map - Riemannian geometry, Conformal map - Euclidean space, Conformal map - Uses

Read more here: » Conformal map: Encyclopedia II - Conformal map - Complex analysis

The "Peters projection map" was featured in the television drama, The West Wing (season 2, episode 16), in which the (fictitious) "Organisation of Cartographers for Social Equality" is given access to the White House Press Secretary due to Big Block of Cheese Day. Dr. John Fallow (actor John Billingsley) explains why the President of the United States of America should champion the use of this map in schools, because it correctly represents the size of the countries and therefore gives due prominence to countries in less developed par ...

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Gall-Peters projection, Gall-Peters projection - On the screen

Read more here: » Gall-Peters projection: Encyclopedia II - Gall-Peters projection - On the screen

Finé wrote on astronomical instruments and astronomy. On how to determine the longitude of places, he suggested that eclipses of the moon could be used to determine it, and described an instrument he called a méthéoroscope, an astrolabe modified by adding a compass. In 1542 appeared his De mundi sphaera (On the Heavenly Spheres), a popular astronomy textbook whose woodcut illustrations Finé also produced. He also invented a heart-shaped map projection, frequently utilized by other cartographers, such as Peter ...

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Oronce Finé, Oronce Finé - Mathematics, Oronce Finé - Astronomy and geography, Oronce Finé - Death and legacy

Read more here: » Oronce Finé: Encyclopedia II - Oronce Finé - Astronomy and geography

In geodesy, temporal change can be studied by a variety of techniques. Points on the Earth's surface change their location due to a variety of mechanisms: Continental plate motion, plate tectonics Episodic motion of tectonic origin, esp. close to fault lines Periodic effects due to Earth tides Postglacial land uplift due to isostatic adjustment Various anthropogenic movements due to, e.g., petroleum or water ...

See also:

Geodesy, Geodesy - Definition, Geodesy - Geoid and reference ellipsoid, Geodesy - Coordinate systems in space, Geodesy - Coordinate systems in the plane, Geodesy - Heights, Geodesy - Geodetic datums, Geodesy - A note on terminology, Geodesy - Point positioning, Geodesy - Geodetic problems, Geodesy - Geodetic observational concepts, Geodesy - Geodetic observing instruments, Geodesy - Units and measures on the ellipsoid, Geodesy - Temporal change, Geodesy - International organizations, Geodesy - University institutes, Geodesy - Governmental agencies

Read more here: » Geodesy: Encyclopedia II - Geodesy - Temporal change

As a fortifications expert (in keeping with his training in mathematics), Finé worked on the fortifications of Milan. He gave the value of pi to be (22 2/9)/7 in 1544. Later, he gave 47/15 and, in De rebus mathematicis (1556), he gave 3 11/78. ...

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Oronce Finé, Oronce Finé - Mathematics, Oronce Finé - Astronomy and geography, Oronce Finé - Death and legacy

Read more here: » Oronce Finé: Encyclopedia II - Oronce Finé - Mathematics

Geographical latitude and longitude are stated in the units degree, minute of arc, and second of arc. They are angles, not metric measures, and describe the direction of the local normal to the reference ellipsoid of revolution. This is approximately the same as the direction of the plumbline, i.e., local gravity, which is also the normal to the geoid surface. For this reason, astronomical position determination, measuring the direction of the plumbline by astronomical means, works fairly well pr ...

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Geodesy, Geodesy - Definition, Geodesy - Geoid and reference ellipsoid, Geodesy - Coordinate systems in space, Geodesy - Coordinate systems in the plane, Geodesy - Heights, Geodesy - Geodetic datums, Geodesy - A note on terminology, Geodesy - Point positioning, Geodesy - Geodetic problems, Geodesy - Geodetic observational concepts, Geodesy - Geodetic observing instruments, Geodesy - Units and measures on the ellipsoid, Geodesy - Temporal change, Geodesy - International organizations, Geodesy - University institutes, Geodesy - Governmental agencies

Read more here: » Geodesy: Encyclopedia II - Geodesy - Units and measures on the ellipsoid

In geodesy, point or terrain heights are "above sea level", an irregular, physically defined surface. Therefore a height should ideally not be referred to as a coordinate. It is more like a physical quantity, and though it can be tempting to treat height as the vertical coordinate z, in addition to the horizontal coordinates x and y, and though this actually is a good approximation of physical reality in small areas, it becom ...

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Geodesy, Geodesy - Definition, Geodesy - Geoid and reference ellipsoid, Geodesy - Coordinate systems in space, Geodesy - Coordinate systems in the plane, Geodesy - Heights, Geodesy - Geodetic datums, Geodesy - A note on terminology, Geodesy - Point positioning, Geodesy - Geodetic problems, Geodesy - Geodetic observational concepts, Geodesy - Geodetic observing instruments, Geodesy - Units and measures on the ellipsoid, Geodesy - Temporal change, Geodesy - International organizations, Geodesy - University institutes, Geodesy - Governmental agencies

Read more here: » Geodesy: Encyclopedia II - Geodesy - Heights

Geodesy is primarily concerned with positioning and the gravity field and geometrical aspects of their temporal variations, although it can also include the study of the Earth's magnetic field. Especially in the German speaking world, geodesy is divided in geomensuration ("Erdmessung" or "höhere Geodäsie"), which is concerned with measuring the earth on a global scale, and surveying ("Ingenieurgeodäsie"), which is concerne ...

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Geodesy, Geodesy - Definition, Geodesy - Geoid and reference ellipsoid, Geodesy - Coordinate systems in space, Geodesy - Coordinate systems in the plane, Geodesy - Heights, Geodesy - Geodetic datums, Geodesy - A note on terminology, Geodesy - Point positioning, Geodesy - Geodetic problems, Geodesy - Geodetic observational concepts, Geodesy - Geodetic observing instruments, Geodesy - Units and measures on the ellipsoid, Geodesy - Temporal change, Geodesy - International organizations, Geodesy - University institutes, Geodesy - Governmental agencies

Read more here: » Geodesy: Encyclopedia II - Geodesy - Definition

In Riemannian geometry, two Riemannian metrics g and h on smooth manifold M are called conformally equivalent if for g=uh for some positive function u on M. The function u is called conformal factor. A diffeomorphism between two Riemannian manifolds is called a conformal map if the pulled back metric is conformally equivalent to the original one. One can also define a conformal structure on a smooth manifold, as a class of conformally equivalent Riemannian metrics. For example, stereographic projection of a sphere onto the plane a ...

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Conformal map, Conformal map - Cartography, Conformal map - Complex analysis, Conformal map - Riemannian geometry, Conformal map - Euclidean space, Conformal map - Uses

Read more here: » Conformal map: Encyclopedia II - Conformal map - Riemannian geometry

In cartography, a conformal map projection is a map projection that preserves the angles at all but a finite number of points. The scale depends on location, but not on direction. Examples include the Mercator projection and the stereographic projection. ...

See also:

Conformal map, Conformal map - Cartography, Conformal map - Complex analysis, Conformal map - Riemannian geometry, Conformal map - Euclidean space, Conformal map - Uses

Read more here: » Conformal map: Encyclopedia II - Conformal map - Cartography

The geoid is essentially the figure of the Earth abstracted from its topographic features. It is an idealized equilibrium surface of sea water, the mean sea level surface in the absence of currents, air pressure variations etc. and continued under the continental masses. The geoid, unlike the ellipsoid, is irregular and too complicated to serve as the computational surface on which to solve geometrical problems like point positioning. The geometrical separation between it and the reference ellipsoid is called the geoidal undulation Wiktionar ...

See also:

Geodesy, Geodesy - Definition, Geodesy - Geoid and reference ellipsoid, Geodesy - Coordinate systems in space, Geodesy - Coordinate systems in the plane, Geodesy - Heights, Geodesy - Geodetic datums, Geodesy - A note on terminology, Geodesy - Point positioning, Geodesy - Geodetic problems, Geodesy - Geodetic observational concepts, Geodesy - Geodetic observing instruments, Geodesy - Units and measures on the ellipsoid, Geodesy - Temporal change, Geodesy - International organizations, Geodesy - University institutes, Geodesy - Governmental agencies

Read more here: » Geodesy: Encyclopedia II - Geodesy - Geoid and reference ellipsoid

Because geodetic point coordinates (and heights) are always obtained in a system that has been constructed itself using real observations, we have to introduce the concept of a geodetic datum: a physical realization of a coordinate system used for describing point locations. The realization is the result of choosing conventional coordinate values for one or more datum points. In the case of height datums, it suffices to choose one datum point: the reference bench mark, typically a tide gauge at the shore. T ...

See also:

Geodesy, Geodesy - Definition, Geodesy - Geoid and reference ellipsoid, Geodesy - Coordinate systems in space, Geodesy - Coordinate systems in the plane, Geodesy - Heights, Geodesy - Geodetic datums, Geodesy - A note on terminology, Geodesy - Point positioning, Geodesy - Geodetic problems, Geodesy - Geodetic observational concepts, Geodesy - Geodetic observing instruments, Geodesy - Units and measures on the ellipsoid, Geodesy - Temporal change, Geodesy - International organizations, Geodesy - University institutes, Geodesy - Governmental agencies

Read more here: » Geodesy: Encyclopedia II - Geodesy - Geodetic datums