ellipsoid

Birefringence, or double refraction, is the decomposition of a ray of light into two rays (the ordinary ray and the extraordinary ray) when it passes through certain types of material, such as calcite crystals, depending on the polarization of the light. This effect can occur only if the structure of the material is anisotropic. If the material has a single axis of anisotropy, (i.e. it is uniaxial,) birefringence can be formalised by assigning two different refractive indices to the material for diff ...

Including:

• Birefringence - Electromagnetic waves in an anisotropic material
• Birefringence - Examples of birefringent materials
• Birefringence - Biaxial birefringence
• Birefringence - Measuring birefringence
• Birefringence - Birefringence in fiber optics

Read more here: » Birefringence: Encyclopedia - Birefringence

Area is a quantity expressing the size of a figure in the Euclidean plane or on a 2-dimensional surface. Points and lines have zero area. Depending on the particular definition taken, a figure may have infinite area, for example the entire Euclidean plane. In three dimensions, the analog of area is called a volume. Area geometry - How to define area. Although area seems to be one of the basic notions in geometry, it is not at all easy to define even in the Euclidean plane. Most textbooks avoid defining an a ...

Including:

• Area geometry - How to define area
• Area geometry - Formulae
• Area geometry - Areas of 2-dimensional figures
• Area geometry - Surface area of 3-dimensional figures

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The Fullerenes are recently-discovered allotropes of carbon. They are molecules composed entirely of carbon, which take the form of a hollow sphere, ellipsoid, or tube. Spherical fullerenes are sometimes called buckyballs, while cylindrical fullerenes are called buckytubes or nanotubes. Fullerene - Naming. The molecule was named for Richard Buckminster Fuller, a noted architect who popularized the geodesic dome. Since buckminsterfullerenes have a similar shape to that sort of dome, the ...

Including:

• Fullerene - Naming
• Fullerene - Buckminsterfullerene
• Fullerene - Prediction and discovery
• Fullerene - Properties
• Fullerene - Possible dangers
• Fullerene - Fullerene extract mixture C₆₀/C₇₀ solubility
• Fullerene - Diffraction of fullerene
• Fullerene - Notes
• Fullerene - Mathematics of Fullerenes
• Fullerene - Media

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Volume, also called capacity, is a quantification of how much space an object occupies. The international unit for volume is the cubic meter. The volume of a solid object is a numerical value given to describe the three-dimensional concept of how much space it occupies. One-dimensional objects (such as lines) and two-dimensional objects (such as squares) are assigned zero volume in the three-dimensional space. Mathematically, volumes are defined by means of integral calculus, by approximating the giv ...

Including:

• Volume - Volume formula
• Volume - Volume measures: other metric units
• Volume - Volume measures: USA
• Volume - Volume measures: UK
• Volume - Volume measures: cooking
• Volume - Relationship to density
• Volume - Volume comparisons

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A whispering gallery is a gallery beneath a dome or vault or enclosed in a circular or elliptical area in which whispers can be heard clearly in other parts of the building. A whispering gallery is usually constructed in the form of an ellipsoid, with an accessible point at each focus. When a visitor stands at one focus and whispers, the line of sound emanating from this focus reflects directly to the dish/focus at the other end of the room, and to the other person. Circular whispering galleries may provide "communication" from any part on the circumference ...

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Alexis Claude Clairault (or Clairaut) (May 3, 1713 – May 17, 1765) was a French mathematician. He was born in Paris, France, where his father taught mathematics. He was a prodigy - at the age of twelve he wrote a memoir on four geometrical curves and under his father's tuition he made such rapid progress in the subject that in his thirteenth year he read before the Académie française an account of the properties of four curves which he had discovered. When only sixteen he finished a treatise on tortuous curves, Re ...

Including:

• Alexis Clairault - External link

Read more here: » Alexis Clairault: Encyclopedia - Alexis Clairault

The term above mean sea level (AMSL) refers to the elevation (on the ground) or altitude (in the air) of any object, relative to the average sea level. AMSL is used extensively in radio (both in broadcasting and other telecommunications uses) by engineers to determine the coverage area a station will be able to reach. It is also used in aviation, all heights are recorded and re ...

Read more here: » Above mean sea level: Encyclopedia - Above mean sea level

The Moon as seen from Earth Ammonia Carbon dioxide The Moon is the planet Earth's only natural satellite. It has no formal name other than "The Moon", although in English it is occasionally called Luna (Latin for moon), or Selene, to distinguish it from the generic "moon" (natural satellites of other planets are also called moons). Its symbol is a crescent (Unicode: ☾). The terms lunar, selene/seleno-, and cynthion (from the Lunar deities Selene and Cynthia) refer to the Moon (apo ...

Including:

• Moon - The two sides
• Moon - Orbit
• Moon - Earth & Moon
• Moon - Origin and history
• Moon - Physical characteristics
• Moon - Composition
• Moon - Selenography
• Moon - Presence of water
• Moon - Magnetic field
• Moon - Atmosphere
• Moon - Eclipses
• Moon - Occultation of stars
• Moon - Observation of the Moon
• Moon - Exploration of the Moon
• Moon - Human understanding of the Moon
• Moon - Myth and folk culture
• Moon - The Moon as muse
• Moon - Astrology
• Moon - Scientific understanding
• Moon - Meteor impact on the Moon
• Moon - Legal status
• Moon - Satellites
• Moon - Surface installations
• Moon - Lunar location listings

Read more here: » Moon: Encyclopedia - Moon

The lunar landscape is characterized by impact craters, their ejecta, a few volcanoes, hills, lava flows and depressions filled by magma. Geology of the Moon - Lunar highlands and lowlands. The most distinctive aspect of the Moon is the constract between its light and dark zones. Lighter surfaces are the lunar highlands, which receive the name of terrae (singular terra, from the Latin for Earth) and darker plains which are called maria (singular mare, from the latin for sea), after Johannes Kepler, who introduced the name in the 1600's. < ...

See also:

Geology of the Moon, Geology of the Moon - Formation, Geology of the Moon - Lunar capture, Geology of the Moon - Fission hypothesis, Geology of the Moon - Accretion hypothesis, Geology of the Moon - Giant impact theory, Geology of the Moon - Geologic history, Geology of the Moon - Lunar landscape, Geology of the Moon - Lunar highlands and lowlands, Geology of the Moon - Impact cratering, Geology of the Moon - Highlands and craters, Geology of the Moon - Volcanism, Geology of the Moon - Maria, Geology of the Moon - Rilles, Geology of the Moon - Wrinkle-ridges, Geology of the Moon - Lunar domes, Geology of the Moon - Composition, Geology of the Moon - Surface, Geology of the Moon - Lunar surface, Geology of the Moon - Lunar rocks, Geology of the Moon - Highlands and lunar magma, Geology of the Moon - Mineral composition of lunar rocks, Geology of the Moon - Lunar minerals, Geology of the Moon - Study of lunar rocks, Geology of the Moon - Interior, Geology of the Moon - Interior and moonquakes

Read more here: » Geology of the Moon: Encyclopedia II - Geology of the Moon - Lunar landscape

Spherical harmonics are often used to approximate the shape of the geoid. The current best such set of spherical harmonic coefficients is EGM96 (Earth Gravity Model 1996), determined in an international collaborative project led by NIMA. It contains a full set of coefficients to degree and order 360, describing details in the global geoid as small as 55 km. The mathematical description of this model is where and are geocentric latitude and longitude respectively, are the fully normalized Legendre ...

See also:

Geoid, Geoid - Spherical harmonics representation

Read more here: » Geoid: Encyclopedia II - Geoid - Spherical harmonics representation

The historical sequence of events now brings us to the discovery of the achromatic telescope. The first person who succeeded in making achromatic refracting telescopes seems to have been Chester Moor Hall, a gentleman of Essex. He argued that the different humours of the human eye so refract rays of light as to produce an image on the retina which is free from colour, and he reasonably argued that it might be possible to produce a like result by combining lenses composed of different refracting media. After devoting some time to the i ...

See also:

History of telescopes, History of telescopes - Refracting telescopes, History of telescopes - Reflecting telescopes, History of telescopes - Achromatic Telescope, History of telescopes - Related links

Read more here: » History of telescopes: Encyclopedia II - History of telescopes - Achromatic Telescope

List of geometry topics - Euclidean plane geometry. 2D computer graphics 2D geometric model Curve of constant width Coordinate notation Brahmagupta's formula Equilateral triangle Pythagorean triangle Pedal triangle Symmedian Altitude (triangle) Pons Asinorum Euler's line Trapezoid, trapezium Isosceles trapezoid Golden angle Complex geometry Conic section ...

See also:

List of geometry topics, List of geometry topics - Types methodologies and terminologies of geometry, List of geometry topics - Euclidean geometry foundations, List of geometry topics - Euclidean plane geometry, List of geometry topics - 3-dimensional Euclidean geometry solid geometry, List of geometry topics - n-dimensional Euclidean geometry, List of geometry topics - Non-Euclidean geometry, List of geometry topics - Numerical geometry, List of geometry topics - Geometric algorithms, List of geometry topics - Mathematical morphology, List of geometry topics - Generalizations, List of geometry topics - Various, List of geometry topics - Applications

Read more here: » List of geometry topics: Encyclopedia II - List of geometry topics - Euclidean geometry foundations

Once a clean, smooth geopotential field U has been constructed matching the known GRS80 reference ellipsoid with an equipotential surface -- we call such a field a normal potential -- we can subtract it from the true potential W of the real Earth. The result is the disturbing potential: which is numerically a whole lot smaller, and captures the detailed, complex variations of the gravity field of the really existing Earth, as distinguished f ...

See also:

Physical geodesy, Physical geodesy - Definition, Physical geodesy - The geopotential, Physical geodesy - Units of gravity and geopotential, Physical geodesy - The normal potential, Physical geodesy - Disturbing potential and geoid, Physical geodesy - Gravity anomalies

Read more here: » Physical geodesy: Encyclopedia II - Physical geodesy - Disturbing potential and geoid

A Transverse Mercator projection is an adaptation of the Mercator projection. Both projections are cylindrical and conformal . However, in a Transverse Mercator projection, the cylinder is rotated 90° (transverse) relative to the equator so that projected surface is aligned with a meridian (or line of longitude) rather than the equator, as is the case with the regular Mercator projection. In both the regular and transverse form of the Mercator projection, there is very little distortion of scale in the narrow region near where ...

See also:

Transverse Mercator projection, Transverse Mercator projection - Transverse Mercator Projection, Transverse Mercator projection - Forms of the Transverse Mercator Projection

Read more here: » Transverse Mercator projection: Encyclopedia II - Transverse Mercator projection - Transverse Mercator Projection

For a given (externally generated) gravitational field, the tidal acceleration at a point with respect to a body is obtained by vectorially subtracting the gravitational acceleration at the center of the body from the actual gravitational acceleration at the point. Correspondingly, the term tidal force is used to describe the forces due to tidal acceleration. Note that for these purposes the only gravitational field considered is the external one; the gravitational field ...

See also:

Tidal force, Tidal force - Mathematical treatment, Tidal force - Additional effect of rotation

Read more here: » Tidal force: Encyclopedia II - Tidal force - Mathematical treatment

The Moon makes a complete orbit about the Earth approximately once every 28 days. Each hour the Moon moves relative to the stars by an amount roughly equal to its angular diameter, or by about 0.5°. The Moon differs from most satellites of other planets in that its orbit is close to the plane of the ecliptic and not in the Earth's equatorial plane. Several ways to consider a complete orbit are detailed in the table below, but the two most familiar are: the sidereal month being the time it takes to make a complete orbit with respect t ...

See also:

Moon, Moon - The two sides of the Moon, Moon - Orbit, Moon - Earth & Moon, Moon - Tidal Effects, Moon - Double-planet hypotheses, Moon - Origin and history, Moon - Physical characteristics, Moon - Composition, Moon - Selenography, Moon - Presence of water, Moon - Magnetic field, Moon - Atmosphere, Moon - Eclipses, Moon - Occultation of stars, Moon - Observation of the Moon, Moon - Exploration of the Moon, Moon - Human understanding of the Moon, Moon - Myth and folk culture, Moon - The Moon as muse, Moon - Astrology, Moon - Scientific understanding, Moon - Meteor impact on the Moon, Moon - Legal status, Moon - Satellites, Moon - Surface installations, Moon - Lunar location listings

Read more here: » Moon: Encyclopedia II - Moon - Orbit

The early Greeks, in their speculation and theorizing, ranged from the flat disc advocated by Homer to Pythagoras spherical figure-an idea supported one hundred years later by Aristotle. Pythagoras was a mathematician and to him the most perfect figure was a sphere. He reasoned that the gods would create a perfect figure and therefore the earth was created to be spherical in shape. Anaximenes, an early Greek scientist, bel ...

See also:

History of geodesy, History of geodesy - Early concepts of the figure of the Earth, History of geodesy - Classical Greece, History of geodesy - From Greece to the Middle Ages, History of geodesy - Scientific revolution, History of geodesy - 19th century, History of geodesy - About this article

Read more here: » History of geodesy: Encyclopedia II - History of geodesy - Classical Greece

There is another more abstract (but often useful) way of characterizing tensor fields on a manifold M which turns out to actually make tensor fields into honest tensors (i.e. single multilinear mappings), though of a different type (and this is not usually why one often says "tensor" when one really means "tensor field"). First, we may consider the set of all smooth (C∞) vector fields on M, (see the section on notation above) as a single space — a module over the ring of smooth functions, C< ...

See also:

Tensor field, Tensor field - Geometric introduction, Tensor field - The vector bundle explanation, Tensor field - Notation, Tensor field - The C^∞M module explanation, Tensor field - Applications, Tensor field - Tensor calculus, Tensor field - Twisting by a line bundle, Tensor field - The flat case, Tensor field - Cocycles and chain rules

Read more here: » Tensor field: Encyclopedia II - Tensor field - The C^∞M module explanation

After an extensive effort extending over a period of approximately three years, the Department of Defense World Geodetic System 1972 was completed. Selected satellite, surface gravity and astrogeodetic data available through 1972 from both DoD and non-DoD sources were used in a Unified WGS Solution (a large scale least squares adjustment). The results of the adjustment consisted of corrections to initial station coordinates and coefficients of the gravitational field. The largest collection of data ever used for WGS purposes was assem ...

See also:

World Geodetic System, World Geodetic System - History of the World Geodetic System, World Geodetic System - The Department of Defense World Geodetic System 1966, World Geodetic System - The Department of Defense World Geodetic System 1972, World Geodetic System - A new World Geodetic System: WGS84, World Geodetic System - Longitudes on WGS84, World Geodetic System - External link

Read more here: » World Geodetic System: Encyclopedia II - World Geodetic System - The Department of Defense World Geodetic System 1972

The deflections are connected with the local and regional undulations of the geoid — and also with gravity anomalies — for they are functionals of the gravity field and its inhomogeneities. VDs are usually determined astronomically. The true zenith is observed astronomically with respect to the stars, and the ellipsoidal zenith (theoretical vertical) by geodetic network computation, which always takes place on a reference ellipsoid. Additionally, the very local variations of the VD can be computed from gravimetric survey data and by means of digital ...

See also:

Vertical deflection, Vertical deflection - Determination of vertical deflections, Vertical deflection - Application of deflection data

Read more here: » Vertical deflection: Encyclopedia II - Vertical deflection - Determination of vertical deflections