|
Equidimensional (geology)
Equidimensional is an adjective applied to objects that have nearly the same size or spread in multiple directions. As a mathematical concept, it may be applied to objects that extend across any number of dimensions, such as equidimensional schemes. More specifically, it's also used to characterize the shape of three-dimensional solids. In geology The word ''equidimensional'' is sometimes used by geologists to describe the shape of three-dimensional objects. In that case it is a synonym for equant. Deviations from equidimensional are used to classify the shape of convex objects like rocks or particles. For instance, if ''a'', ''b'' and ''c'' are the long, intermediate, and short axes of a convex structure, and ''R'' is a number greater than one, then four ''mutually exclusive'' shape classes may be defined by:Th. Zingg (1935).Beitrag zur Schotteranalyse. ''Schweizerische Mineralogische und Petrographische Mitteilungen'' 15, 39–140. Table 1: Zingg's convex object shape clas ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Equidimensional Scheme
In algebraic geometry, the dimension of a scheme is a generalization of a dimension of an algebraic variety. Scheme theory emphasizes the relative point of view and, accordingly, the relative dimension of a morphism of schemes is also important. Definition By definition, the dimension of a scheme ''X'' is the dimension of the underlying topological space: the supremum of the lengths ''ℓ'' of chains of irreducible closed subsets: :\emptyset \ne V_0 \subsetneq V_1 \subsetneq \cdots \subsetneq V_\ell \subset X. In particular, if X = \operatorname A is an affine scheme, then such chains correspond to chains of prime ideals (inclusion reversed) and so the dimension of ''X'' is precisely the Krull dimension of ''A''. If ''Y'' is an irreducible closed subset of a scheme ''X'', then the codimension of ''Y'' in ''X'' is the supremum of the lengths ''ℓ'' of chains of irreducible closed subsets: :Y = V_0 \subsetneq V_1 \subsetneq \cdots \subsetneq V_\ell \subset X. An irreducible su ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Shape
A shape or figure is a graphics, graphical representation of an object or its external boundary, outline, or external Surface (mathematics), surface, as opposed to other properties such as color, Surface texture, texture, or material type. A plane shape or plane figure is constrained to lie on a ''plane (geometry), plane'', in contrast to ''solid figure, solid'' 3D shapes. A two-dimensional shape or two-dimensional figure (also: 2D shape or 2D figure) may lie on a more general curved ''surface (mathematics), surface'' (a non-Euclidean two-dimensional space). Classification of simple shapes Some simple shapes can be put into broad categories. For instance, polygons are classified according to their number of edges as triangles, quadrilaterals, pentagons, etc. Each of these is divided into smaller categories; triangles can be equilateral, isosceles, obtuse triangle, obtuse, Triangle#By internal angles, acute, Triangle, scalene, etc. while quadrilaterals can be rectangles, rho ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Convex Envelope
In geometry, the convex hull or convex envelope or convex closure of a shape is the smallest convex set that contains it. The convex hull may be defined either as the intersection of all convex sets containing a given subset of a Euclidean space, or equivalently as the set of all convex combinations of points in the subset. For a bounded subset of the plane, the convex hull may be visualized as the shape enclosed by a rubber band stretched around the subset. Convex hulls of open sets are open, and convex hulls of compact sets are compact. Every compact convex set is the convex hull of its extreme points. The convex hull operator is an example of a closure operator, and every antimatroid can be represented by applying this closure operator to finite sets of points. The algorithmic problems of finding the convex hull of a finite set of points in the plane or other low-dimensional Euclidean spaces, and its dual problem of intersecting half-spaces, are fundamental problems of com ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Sphere
A sphere () is a Geometry, geometrical object that is a solid geometry, three-dimensional analogue to a two-dimensional circle. A sphere is the Locus (mathematics), set of points that are all at the same distance from a given point in three-dimensional space.. That given point is the centre (geometry), centre of the sphere, and is the sphere's radius. The earliest known mentions of spheres appear in the work of the Greek mathematics, ancient Greek mathematicians. The sphere is a fundamental object in many fields of mathematics. Spheres and nearly-spherical shapes also appear in nature and industry. Bubble (physics), Bubbles such as soap bubbles take a spherical shape in equilibrium. spherical Earth, The Earth is often approximated as a sphere in geography, and the celestial sphere is an important concept in astronomy. Manufactured items including pressure vessels and most curved mirrors and lenses are based on spheres. Spheres rolling, roll smoothly in any direction, so mos ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Equant
Equant (or punctum aequans) is a mathematical concept developed by Claudius Ptolemy in the 2nd century AD to account for the observed motion of the planets. The equant is used to explain the observed speed change in different stages of the planetary orbit. This planetary concept allowed Ptolemy to keep the theory of uniform circular motion alive by stating that the path of heavenly bodies was uniform around one point and circular around another point. Placement The equant point (shown in the diagram by the large • ), is placed so that it is directly opposite to Earth from the deferent's center, known as the ''eccentric'' (represented by the × ). A planet or the center of an epicycle (a smaller circle carrying the planet) was conceived to move at a constant angular speed with respect to the equant. In other words, to a hypothetical observer placed at the equant point, the epicycle's center (indicated by the small · ) would appear to move at a st ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Oblate Spheroid
A spheroid, also known as an ellipsoid of revolution or rotational ellipsoid, 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. A spheroid has circular symmetry. If the ellipse is rotated about its major axis, the result is a ''prolate spheroid'', elongated like a rugby ball. The American football is similar but has a pointier end than a spheroid could. If the ellipse is rotated about its minor axis, the result is an ''oblate spheroid'', flattened like a lentil or a plain M&M. If the generating ellipse is a circle, the result is a sphere. Due to the combined effects of gravity and rotation, the figure of the Earth (and of all planets) is not quite a sphere, but instead is slightly flattened in the direction of its axis of rotation. For that reason, in cartography and geodesy the Earth is often approximated by an oblate spheroid, known as the reference ellipsoid, instead of a spher ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Prolate Spheroid
A spheroid, also known as an ellipsoid of revolution or rotational ellipsoid, 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. A spheroid has circular symmetry. If the ellipse is rotated about its major axis, the result is a ''prolate spheroid'', elongated like a rugby ball. The American football is similar but has a pointier end than a spheroid could. If the ellipse is rotated about its minor axis, the result is an ''oblate spheroid'', flattened like a lentil or a plain M&M. If the generating ellipse is a circle, the result is a sphere. Due to the combined effects of gravity and rotation, the figure of the Earth (and of all planets) is not quite a sphere, but instead is slightly flattened in the direction of its axis of rotation. For that reason, in cartography and geodesy the Earth is often approximated by an oblate spheroid, known as the reference ellipsoid, instead of a sphere ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Shape Analysis (digital Geometry)
This article describes shape analysis to analyze and process geometric shapes. Description ''Shape analysis'' is the (mostly) automatic analysis of geometric shapes, for example using a computer to detect similarly shaped objects in a database or parts that fit together. For a computer to automatically analyze and process geometric shapes, the objects have to be represented in a digital form. Most commonly a boundary representation is used to describe the object with its boundary (usually the outer shell, see also 3D model). However, other volume based representations (e.g. constructive solid geometry) or point based representations (point clouds) can be used to represent shape. Once the objects are given, either by modeling (computer-aided design), by scanning (3D scanner) or by extracting shape from 2D or 3D images, they have to be simplified before a comparison can be achieved. The simplified representation is often called a ''shape descriptor'' (or fingerprint, signature). The ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Sedimentology
Sedimentology encompasses the study of modern sediments such as sand, silt, and clay, and the processes that result in their formation (erosion and weathering), transport, deposition and diagenesis. Sedimentologists apply their understanding of modern processes to interpret geologic history through observations of sedimentary rocks and sedimentary structures. Sedimentary rocks cover up to 75% of the Earth's surface, record much of the Earth's history, and harbor the fossil record. Sedimentology is closely linked to stratigraphy, the study of the physical and temporal relationships between rock layers or strata. The premise that the processes affecting the earth today are the same as in the past is the basis for determining how sedimentary features in the rock record were formed. By comparing similar features today to features in the rock record—for example, by comparing modern sand dunes to dunes preserved in ancient aeolian sandstones—geologists reconstruct past environmen ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
