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Mean Diameter
In applied sciences, the equivalent radius (or mean radius) is the radius of a circle or sphere with the same perimeter, area, or volume of a non-circular or non-spherical object. The equivalent diameter (or mean diameter) (D) is twice the equivalent radius. Perimeter equivalent The perimeter of a circle of radius ''R'' is 2 \pi R. Given the perimeter of a non-circular object ''P'', one can calculate its perimeter-equivalent radius by setting :P = 2\pi R_\text or, alternatively: :R_\text = \frac For example, a square of side ''L'' has a perimeter of 4L. Setting that perimeter to be equal to that of a circle imply that :R_\text = \frac \approx 0.6366 L Applications: * US hat size is the circumference of the head, measured in inches, divided by pi (constant), pi, rounded to the nearest 1/8 inch. This corresponds to the 1D mean diameter. *Diameter at breast height is the circumference of tree trunk, measured at height of 4.5 feet, divided by pi. This corresponds to the 1D mean di ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Applied Science
Applied science is the use of the scientific method and knowledge obtained via conclusions from the method to attain practical goals. It includes a broad range of disciplines such as engineering and medicine. Applied science is often contrasted with basic science, which is focused on advancing scientific theories and laws that explain and predict events in the natural world. Applied science can also apply formal science, such as statistics and probability theory, as in epidemiology. Genetic epidemiology is an applied science applying both biological and statistical methods. Applied research Applied research is the practical application of science. It accesses and uses accumulated theories, knowledge, methods, and techniques, for a specific state-, business-, or client-driven purpose. Applied Research can be better understood in any area when contrasting it with, basic, or pure, research. Basic geography research strives to create new theories and methods that aid in the e ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Hydraulic Radius
The Manning formula or Manning's equation is an empirical formula estimating the average velocity of a liquid flowing in a conduit that does not completely enclose the liquid, i.e., open channel flow. However, this equation is also used for calculation of flow variables in case of flow in partially full conduits, as they also possess a free surface like that of open channel flow. All flow in so-called open channels is driven by gravity. It was first presented by the French engineer in 1867, and later re-developed by the Irish engineer Robert Manning in 1890. Thus, the formula is also known in Europe as the Gauckler–Manning formula or Gauckler–Manning–Strickler formula (after ). The Gauckler–Manning formula is used to estimate the average velocity of water flowing in an open channel in locations where it is not practical to construct a weir or flume to measure flow with greater accuracy. Manning's equation is also commonly used as part of a numerical step method, such ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Osculating Circle
In differential geometry of curves, the osculating circle of a sufficiently smooth plane curve at a given point ''p'' on the curve has been traditionally defined as the circle passing through ''p'' and a pair of additional points on the curve infinitesimally close to ''p''. Its center lies on the inner normal line, and its curvature defines the curvature of the given curve at that point. This circle, which is the one among all tangent circles at the given point that approaches the curve most tightly, was named ''circulus osculans'' (Latin for "kissing circle") by Leibniz. The center and radius of the osculating circle at a given point are called center of curvature and radius of curvature of the curve at that point. A geometric construction was described by Isaac Newton in his '' Principia'': Nontechnical description Imagine a car moving along a curved road on a vast flat plane. Suddenly, at one point along the road, the steering wheel locks in its present position. ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Solid Figure
In mathematics, solid geometry or stereometry is the traditional name for the geometry of three-dimensional, Euclidean spaces (i.e., 3D geometry). Stereometry deals with the measurements of volumes of various solid figures (or 3D figures), including pyramids, prisms and other polyhedrons; cylinders; cones; truncated cones; and balls bounded by spheres. History The Pythagoreans dealt with the regular solids, but the pyramid, prism, cone and cylinder were not studied until the Platonists. Eudoxus established their measurement, proving the pyramid and cone to have one-third the volume of a prism and cylinder on the same base and of the same height. He was probably also the discoverer of a proof that the volume enclosed by a sphere is proportional to the cube of its radius.Paraphrased and taken in part from the ''1911 Encyclopædia Britannica''. Topics Basic topics in solid geometry and stereometry include: * incidence of planes and lines * dihedral angle and solid a ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Surface Area
The surface area of a solid object is a measure of the total area that the surface of the object occupies. The mathematical definition of surface area in the presence of curved surfaces is considerably more involved than the definition of arc length of one-dimensional curves, or of the surface area for polyhedra (i.e., objects with flat polygonal faces), for which the surface area is the sum of the areas of its faces. Smooth surfaces, such as a sphere, are assigned surface area using their representation as parametric surfaces. This definition of surface area is based on methods of infinitesimal calculus and involves partial derivatives and double integration. A general definition of surface area was sought by Henri Lebesgue and Hermann Minkowski at the turn of the twentieth century. Their work led to the development of geometric measure theory, which studies various notions of surface area for irregular objects of any dimension. An important example is the Minkows ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Authalic Radius
Earth radius (denoted as ''R''🜨 or R_E) is the distance from the center of Earth to a point on or near its surface. Approximating the figure of Earth by an Earth spheroid, the radius ranges from a maximum of nearly (equatorial radius, denoted ''a'') to a minimum of nearly (polar radius, denoted ''b''). A ''nominal Earth radius'' is sometimes used as a unit of measurement in astronomy and geophysics, which is recommended by the International Astronomical Union to be the equatorial value. A globally-average value is usually considered to be with a 0.3% variability (±10 km) for the following reasons. The International Union of Geodesy and Geophysics (IUGG) provides three reference values: the ''mean radius'' (R) of three radii measured at two equator points and a pole; the ''authalic radius'', which is the radius of a sphere with the same surface area (R); and the ''volumetric radius'', which is the radius of a sphere having the same volume as the ellipsoid (R). All three ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Physics Of The Earth And Planetary Interiors
''Physics of the Earth and Planetary Interiors'', established in October 1967, is a biweekly peer-reviewed scientific journal published by Elsevier. The co-editors are A. Ferreira (University College London), K. Hirose (Tokyo Institute of Technology), D. Jault (Grenoble Alpes University), and C. Michaut ( Ecole normale superieure de Lyon). The journal covers the physical and chemical processes of planetary interiors. Topical coverage broadly encompasses planetary physics, geodesy, and geophysics. Publishing formats include original research papers, review articles, short communications and book reviews on a regular basis. Occasional special issues are set aside for proceedings of conferences. The journal has a 2020 impact factor of 2.261. Abstracting and indexing This journal is indexed in the following bibliographic databases: * Science Citation Index * Current Contents/Physical, Chemical & Earth Sciences * Chemical Abstracts Service – CASSI * AGI's Bibliography and I ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Earth
Earth is the third planet from the Sun and the only astronomical object known to harbor life. While large volumes of water can be found throughout the Solar System, only Earth sustains liquid surface water. About 71% of Earth's surface is made up of the ocean, dwarfing Earth's polar ice, lakes, and rivers. The remaining 29% of Earth's surface is land, consisting of continents and islands. Earth's surface layer is formed of several slowly moving tectonic plates, which interact to produce mountain ranges, volcanoes, and earthquakes. Earth's liquid outer core generates the magnetic field that shapes the magnetosphere of the Earth, deflecting destructive solar winds. The atmosphere of the Earth consists mostly of nitrogen and oxygen. Greenhouse gases in the atmosphere like carbon dioxide (CO2) trap a part of the energy from the Sun close to the surface. Water vapor is widely present in the atmosphere and forms clouds that cover most of the planet. More sola ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Rotational Ellipsoid
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] |
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 ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Astronomy & Astrophysics
''Astronomy & Astrophysics'' is a monthly peer-reviewed scientific journal covering theoretical, observational, and instrumental astronomy and astrophysics. The journal is run by a Board of Directors representing 27 sponsoring countries plus a representative of the European Southern Observatory. The journal is published by EDP Sciences and the editor-in-chief is . History Origins ''Astronomy and Astrophysics'' (A&A) was created as an answer to the publishing scenario found in Europe in the 1960s. At that time, multiple journals were being published in several countries around the continent. These journals usually had a limited number of subscribers, and published articles in languages other than English, resulting in a small number of citations compared to American and British journals. Starting in 1963, conversations between astronomers from European countries assessed the need for a common astronomical journal. On 8 April 1968, leading astronomers from Belgium, Denmark, Fran ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Tri-axial Ellipsoid
An ellipsoid is a surface that may be obtained from a sphere by deforming it by means of directional Scaling (geometry), scalings, or more generally, of an affine transformation. An ellipsoid is a quadric surface; that is, a Surface (mathematics), 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 (geometry), 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 set, bounded, which means that it may be enclosed in a sufficiently large sphere. An ellipsoid has three pairwise perpendicular Rotational symmetry, axes of symmetry which intersect at a Central symmetry, 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 ax ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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