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Azimuthal Equal-area Projection
The Lambert azimuthal equal-area projection is a particular mapping from a sphere to a disk (mathematics), disk. It accurately represents area in all regions of the sphere, but it does not accurately represent angles. It is named for the Switzerland, Swiss mathematician Johann Heinrich Lambert, who announced it in 1772. "Zenithal" being synonymous with "azimuthal", the projection is also known as the Lambert zenithal equal-area projection. The Lambert azimuthal projection is used as a map projection in cartography. For example, the National Atlas of the United States, National Atlas of the US uses a Lambert azimuthal equal-area projection to display information in the online Map Maker application, and the European Environment Agency recommends its usage for European mapping for statistical analysis and display. It is also used in scientific disciplines such as geology for plotting the orientations of lines in three-dimensional space. This plotting is aided by a special kind of gr ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Lambert Azimuthal Equal-area Projection SW
Lambert may refer to People *Lambert (name), a given name and surname * Lambert, Bishop of Ostia (c. 1036–1130), became Pope Honorius II * Lambert, Margrave of Tuscany ( fl. 929–931), also count and duke of Lucca * Lambert (pianist), stage-name of German pianist and composer Paul Lambert Places United States * Lambert, Mississippi, a town * Lambert, Missouri, a village *St. Louis Lambert International Airport, St. Louis, Missouri *Lambert, Montana, a rural town in Montana * Lambert, Oklahoma, a town *Lambert Township, Red Lake County, Minnesota *Lambert Castle, a mansion in Paterson, New Jersey * Lambert Creek, San Mateo County, California Elsewhere * Lambert Gravitational Centre, the geographical centre of Australia * Lambert (lunar crater), named after Johann Heinrich Lambert *Lambert (Martian crater), named after Johann Heinrich Lambert Transportation *Lambert (automobile), a defunct American automobile brand *Lambert (cyclecar), British three-wheeled cyclecar *''Lambert' ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Antipodes
In geography, the antipode () of any spot on Earth is the point on Earth's surface diametrically opposite to it. A pair of points ''antipodal'' () to each other are situated such that a straight line connecting the two would pass through Earth's center. Antipodal points are as far away from each other as possible. The North and South Poles are antipodes of each other. In the Northern Hemisphere, "the Antipodes" may refer to Australia and New Zealand, and Antipodeans to their inhabitants. Geographically, the antipodes of Britain and Ireland are in the Pacific Ocean, south of New Zealand. This gave rise to the name of the Antipodes Islands of New Zealand, which are close to the antipode of London. With the exception of a part of the Perth metropolitan area near Baldivis and Rockingham that is antipodal to Bermuda, the antipodes of Australia are in the North Atlantic Ocean, while parts of Spain, Portugal, France and Morocco are antipodal to New Zealand. Approximately 15% of ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Isometry
In mathematics, an isometry (or congruence, or congruent transformation) is a distance-preserving transformation between metric spaces, usually assumed to be bijective. The word isometry is derived from the Ancient Greek: ἴσος ''isos'' meaning "equal", and μέτρον ''metron'' meaning "measure". Introduction Given a metric space (loosely, a set and a scheme for assigning distances between elements of the set), an isometry is a transformation which maps elements to the same or another metric space such that the distance between the image elements in the new metric space is equal to the distance between the elements in the original metric space. In a two-dimensional or three-dimensional Euclidean space, two geometric figures are congruent if they are related by an isometry; the isometry that relates them is either a rigid motion (translation or rotation), or a composition of a rigid motion and a reflection. Isometries are often used in constructions where one space i ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Surface Integral
In mathematics, particularly multivariable calculus, a surface integral is a generalization of multiple integrals to integration over surfaces. It can be thought of as the double integral analogue of the line integral. Given a surface, one may integrate a scalar field (that is, a function of position which returns a scalar as a value) over the surface, or a vector field (that is, a function which returns a vector as value). If a region R is not flat, then it is called a ''surface'' as shown in the illustration. Surface integrals have applications in physics, particularly with the theories of classical electromagnetism. Surface integrals of scalar fields Assume that ''f'' is a scalar, vector, or tensor field defined on a surface ''S''. To find an explicit formula for the surface integral of ''f'' over ''S'', we need to parameterize ''S'' by defining a system of curvilinear coordinates on ''S'', like the latitude and longitude on a sphere. Let such a parameterization be ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Infinitely Differentiable
In mathematical analysis, the smoothness of a function is a property measured by the number of continuous derivatives it has over some domain, called ''differentiability class''. At the very minimum, a function could be considered smooth if it is differentiable everywhere (hence continuous). At the other end, it might also possess derivatives of all orders in its domain, in which case it is said to be infinitely differentiable and referred to as a C-infinity function (or C^ function). Differentiability classes Differentiability class is a classification of functions according to the properties of their derivatives. It is a measure of the highest order of derivative that exists and is continuous for a function. Consider an open set U on the real line and a function f defined on U with real values. Let ''k'' be a non-negative integer. The function f is said to be of differentiability class ''C^k'' if the derivatives f',f'',\dots,f^ exist and are continuous on U. If f is k-differ ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Bijection
In mathematics, a bijection, also known as a bijective function, one-to-one correspondence, or invertible function, 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. There are no unpaired elements. In mathematical terms, a bijective function is a one-to-one (injective) and onto (surjective) mapping of a set ''X'' to a set ''Y''. The term ''one-to-one correspondence'' must not be confused with ''one-to-one function'' (an injective function; see figures). A bijection from the set ''X'' to the set ''Y'' has an inverse function from ''Y'' to ''X''. If ''X'' and ''Y'' are finite sets, then the existence of a bijection means they have the same number of elements. For infinite sets, the picture is more complicated, leading to the concept of cardinal number—a way to distinguish the various sizes of infinite sets. ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Diffeomorphism
In mathematics, a diffeomorphism is an isomorphism of smooth manifolds. It is an invertible function that maps one differentiable manifold to another such that both the function and its inverse are differentiable. Definition Given two manifolds M and N, a differentiable map f \colon M \rightarrow N is called a diffeomorphism if it is a bijection and its inverse f^ \colon N \rightarrow M is differentiable as well. If these functions are r times continuously differentiable, f is called a C^r-diffeomorphism. Two manifolds M and N are diffeomorphic (usually denoted M \simeq N) if there is a diffeomorphism f from M to N. They are C^r-diffeomorphic if there is an r times continuously differentiable bijective map between them whose inverse is also r times continuously differentiable. Diffeomorphisms of subsets of manifolds Given a subset X of a manifold M and a subset Y of a manifold N, a function f:X\to Y is said to be smooth if for all p in X there is a neighbor ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
International Association Of Oil & Gas Producers
The International Association of Oil & Gas Producers (IOGP) is the petroleum industry's global forum in which members identify and share best practices to achieve improvements in health, safety, the environment, security, social responsibility, engineering and operations. The association was formed in London in 1974 to develop effective communications between the upstream industry and the network of international regulators. Originally called the ''E&P Forum'' (for oil and gas exploration and production), in 1999 the current name was adopted. Most of the world’s leading publicly traded, private and state-owned oil & gas companies, oil & gas associations and major upstream service companies are members. The IOGP claims its members produce 40% of the world’s oil and gas. Co-operation with other bodies IOGP also represent the interests of the upstream industry before international regulators and legislators in UN bodies such as the International Maritime Organization and the Com ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Cylindrical Coordinates
A cylindrical coordinate system is a three-dimensional coordinate system that specifies point positions by the distance from a chosen reference axis ''(axis L in the image opposite)'', the direction from the axis relative to a chosen reference direction ''(axis A)'', and the distance from a chosen reference plane perpendicular to the axis ''(plane containing the purple section)''. The latter distance is given as a positive or negative number depending on which side of the reference plane faces the point. The ''origin'' of the system is the point where all three coordinates can be given as zero. This is the intersection between the reference plane and the axis. The axis is variously called the ''cylindrical'' or ''longitudinal'' axis, to differentiate it from the ''polar axis'', which is the ray that lies in the reference plane, starting at the origin and pointing in the reference direction. Other directions perpendicular to the longitudinal axis are called ''radial lines''. The ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Polar Coordinates
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. The reference point (analogous to the origin of a Cartesian coordinate system) is called the ''pole'', and the ray from the pole in the reference direction is the ''polar axis''. The distance from the pole is called the ''radial coordinate'', ''radial distance'' or simply ''radius'', and the angle is called the ''angular coordinate'', ''polar angle'', or ''azimuth''. Angles in polar notation are generally expressed in either degrees or radians (2 rad being equal to 360°). Grégoire de Saint-Vincent and Bonaventura Cavalieri independently introduced the concepts in the mid-17th century, though the actual term "polar coordinates" has been attributed to Gregorio Fontana in the 18th century. The initial motivation for the introduction of the polar system was the study of circula ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Colatitude
In a spherical coordinate system, a colatitude is the complementary angle of a given latitude, i.e. the difference between a right angle and the latitude. Here Southern latitudes are defined to be negative, and as a result the colatitude is a non-negative quantity, ranging from zero at the North pole to 180° at the South pole. The colatitude corresponds to the conventional 3D polar angle in spherical coordinates, as opposed to the latitude as used in cartography. Examples Latitude and colatitude sum up to 90°. Astronomical use The colatitude is most useful in astronomy because it refers to the zenith distance of the celestial poles. For example, at latitude 42°N, Polaris (approximately on the North celestial pole) has an altitude of 42°, so the distance from the zenith (overhead point) to Polaris is . Adding the declination of a star to the observer's colatitude gives the maximum latitude of that star (its angle from the horizon at culmination or upper transit). For ex ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Spherical Coordinates
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 ''azimuthal 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. It can be seen as the three-dimensional version of the polar coordinate system. The radial distance is also called the ''radius'' or ''radial coordinate''. The polar angle may be called '' colatitude'', ''zenith angle'', '' normal angle'', or ''inclination angle''. When radius is fixed, the two angular coordinates make a coordinate system on the sphere sometimes called spherical polar coordinates. The use of symbols and the order of the coordinates differs among sources and disciplines. This article will us ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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