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# Topic: Spherical

###### In the News (Thu 15 Feb 18)

 Spherical trigonometry - Wikipedia, the free encyclopedia Spherical trigonometry is a part of spherical geometry that deals with polygons (especially triangles) on the sphere and explains how to find relations between the involved angles. Hence, a spherical triangle is specified as usual by its corner angles and its sides, but the sides are given not by their length, but by their arc angle. Spherical Trigonometry — for the use of colleges and schools by I. Todhunter, M.A., F.R.S. Historical Math Monograph posted by Cornell University Library. en.wikipedia.org /wiki/Spherical_trigonometry   (603 words)

 Spherical aberration Spherical aberration (SA) is an image imperfection that is due to the spherical lens shape. Spherical aberration is uniform over the field, in the sense that the longitudinal focus difference between the lens margins and center does not depend on the obliquity of the incident light. Spherical aberration is responsible for the rugged blur character at negative distances, and the transition to a smoother appearance at positive distances. www.vanwalree.com /optics/spherical.html   (1391 words)

 Encyclopedia article on Spherical geometry [EncycloZine]   (Site not responding. Last check: 2007-11-07) Spherical geometry is the geometry of the two-dimensional surface of a sphere. Thus, in spherical geometry angles are defined between great circles, resulting in a spherical trigonometry that differs from ordinary trigonometry in many respects (for example, the sum of the interior angles of a triangle can exceed 180 degrees). Spherical geometry is the simplest model of elliptic geometry, in which a line has no parallels through a given point. encyclozine.com /Spherical_geometry   (292 words)

 Sphere - Wikipedia, the free encyclopedia The sphere has the smallest surface area among all surfaces enclosing a given volume and it encloses the largest volume among all closed surfaces with a given surface area. For this reason, the sphere appears in nature: for instance bubbles and small water drops are roughly spherical, because the surface tension minimizes surface area. This terminology is also used for astronomical bodies such as the planet Earth, even though it is neither spherical nor even spheroidal (see geoid). en.wikipedia.org /wiki/Sphere   (883 words)

 SPHERICAL TO PLANAR TRANSFORMATION   (Site not responding. Last check: 2007-11-07) To illustrate the model, the icosehedral spherical triangle and the equilateral planar triangle are each divided into six similar triangles by projecting the three perpendicular bisectors. To transform a point P on the Icosahedral spherical triangle, multiply the distance of the point P from the centroid, (=Dg from Rotation 3, Step 5), by the Amplitude factor and add the Angle factor to the bearing of the point P, (=B"' from Rotation 3, Step 7), from the perpendicular bisector. This paper explained a scheme using spherical coordinate notation to transform the spherical facets of a regular icosahedron to planar facets suitable for plotting on an X-Y plotter. www.academic.marist.edu /~jwg9/dymaxion/sphere.htm   (924 words)

 SPHERICAL - Definition   (Site not responding. Last check: 2007-11-07) Of or pertaining to the heavenly orbs, or to the sphere or spheres in which, according to ancient astronomy and astrology, they were set. {Spherical geometry}, that branch of geometry which treats of spherical magnitudes; the doctrine of the sphere, especially of the circles described on its surface. {Spherical projection}, the projection of the circles of the sphere upon a plane. www.hyperdictionary.com /dictionary/spherical   (215 words)

 LaserMyEye :: Encyclopedia :: Spherical aberration Laser eye surgery for myopes is generally thought to cause spherical aberration in some amount. Depending on the amount, it may or may not be perceptible; moderate to large amounts may cause significant degradation of vision quality. Spherical aberration is most commonly associated with reduced vision quality in dim light, including reduction in contrast sensitivity and the appearance of point light source vision disturbances (starbursts, haloes). www.lasermyeye.org /encyclopedia/sphericalab.html   (137 words)

 Spherical Aberration The result is that the images of objects as seen in spherical mirrors are often blurry. Spherical aberration is most commonly corrected by use of a mirror with a different shape. Usually, a parabolic mirror is substituted for a spherical mirror. www.glenbrook.k12.il.us /gbssci/phys/Class/refln/u13l3g.html   (394 words)

 Spherical Stellarator Home Page Tokamaks have the best plasma confinement properties, and the low-aspect-ratio tokamaks (also called spherical tokamaks) could confine high pressure plasmas (or high beta plasmas, where beta is the ratio of the plasma pressure to the magnetic field pressure). The average plasma beta in spherical tokamaks was already experimentally demonstrated in the excess of 40%. For a spherical tokamak-reactor, it would be practically impossible to put inside a current generating transformer. www.highfactor.com /ss   (2600 words)

 Spherical Projection of Cube It is then from these spherical triangles that an actual model can be made up of the whole sphere. R) projecting from the common centre of the cube and the sphere to the vertices of the spherical triangle. The surface area of the triangle being projected onto the sphere is one eight of the total surface area of the top face which is broken into eight equal triangles each having a vertex at the centre of the face. www.ul.ie /~cahird/polyhedronmode/projecti.htm   (615 words)

 Spherical Bearings Reference Center - Spherical Bearings Spherical bearings offer an unequaled combination of high load capacity, high tolerance to shock loads, and self-aligning ability, but they are speed limited. Accordingly, spherical bearings are used in vibrators, shakers, conveyors, speed reducers, transmissions, and other heavy machinery. The spherical bearing retainer is usually a stamped assembly piloted on the inner ring. bearings.machinedesign.com /guiEdits/Content/BDE_6_4/bdemech6_31.aspx   (365 words)

 spherical aberration on Encyclopedia.com   (Site not responding. Last check: 2007-11-07) Electron microscopes stand corrected: correction for the spherical aberration of lenses in electron microscopes is allowing scientists to push the resolution into the sub-angstrom range, opening the doors to new... Wavefront-guided ablations reduce spherical aberrations: both low-and high-order aberrations must be minimized to achieve good visual acuity. Wavefront-guided LASIK effective for higher-order aberrations: overall reduction seen in higher-order aberrations as well as in coma and spherical aberration. www.encyclopedia.com /html/x/x-spherica.asp   (396 words)

 Tech Notes 067 - Starnet Proprietary Spherical Plywood Panels Starnet has developed two types of proprietary spherical panel systems to create a complete spherical exterior plywood surface that may be clad in a number of materials and methods. The Type A panels are spherical on both the outside and interior surface. This provides an interior surface that has been a spherical form that can be finished with sheet rock or sprayed on cladding. www.starnetint.com /Business/Tech/Tn067a.html   (277 words)

 Spherical Trigonometry   (Site not responding. Last check: 2007-11-07) One of the primary concerns in astronomy throughout history was the positioning of the heavenly bodies, for which spherical trigonometry was required. The spherical triangle in the diagram above is the same as the trihedral, except that the sides a, b and c are great circle paths on the surface of the sphere centred at V rather than straight lines (as in the trihedral). To solve a spherical triangle problem, known values are substituted into the equations, which are then solved for the remaining unknown values. www.hps.cam.ac.uk /starry/sphertrig.html   (567 words)

 Headlines@Hopkins: Johns Hopkins University News Releases Image B. The spherical motor consists of a globe filled with permanent magnets, resting atop a "saddle" of electromagnets that can be activated by a computer. With further refinement, the inventors say, the spherical motor could replace the conventional motors that are now used to move robotic arms in three dimensions. As a result, Chirikjian says, three spherical motors could give a robotic arm a greater range of motion than arms that have six traditional motors. www.jhu.edu /~news_info/news/home01/jan01/motor.html   (809 words)

 Spherical Harmonic Discrete Ordinate Method (SHDOM) The angular part of the source function is represented with a spherical harmonic expansion. The other reason for using spherical harmonics is that the scattering integral is more efficiently computed than in discrete ordinates. The system consist of make_mie_table.f90 and make_ice_table.f90 for creating single scattering tables for spherical particles and eight shapes of ice crystals, and propgen.f90 for producing property files with mixtures of particles at each grid point. nit.colorado.edu /~evans/shdom.html   (1058 words)

 Spherical Waves from a Point Source Furthermore, the sound from any radiating surface can be computed as the sum of spherical wave contributions from each point on the surface (including any relevant reflections). It is also an example of an inverse square law which is found repeatedly in the physics of conserved quantities in three-dimensional space. The sound-pressure amplitude of a traveling wave is proportional to the square-root of its energy per unit area. ccrma-www.stanford.edu /~jos/waveguide/Spherical_Waves_Point_Source.html   (361 words)

 SPHERICAL PROCESSORS   (Site not responding. Last check: 2007-11-07) One of the main reasons for this is because the spherical processor is cheaper as compared to other processors being used right now. The production speed of the spherical processor is much faster than the production of other processors. The spherical processor is also a lot smaller and lighter than present processors and also has lower energy consumption. www.wiu.edu /users/mfdmd/Sphere/Sph-Wimp.htm   (84 words)

 Egypt Bearings, Bearings Egypt, IKO SPHERICAL BUSHINGS These bushing have an outer ring split into halves, Asnap ring is fixed to the groove around the outer periphery of the outer ring and this holds the inner and outer rings. The radial clearance values for IKO SPHERICAL BUSHINGS are the values before splitting the outer ring,and are shown. Spherical bushings with other clearancees can also be manufactured. www.iko.net /ikosb.html   (624 words)

 A Primer on Spherical Geometry   (Site not responding. Last check: 2007-11-07) While it is messier than planar trigonometry, spherical trigonometry is conceptually no more complicated than what you've all done in high school. The astronomical (or navigational) use for spherical trigonometry is to solve triangles on a spherical surface - either on the celestial sphere or on the surface of the Earth. While spherical trig may seen either old fashioned or arcane, and it isn't taught much anymore, it is the basis of navigation. www.ess.sunysb.edu /fwalter/AST443/sphgeo.html   (499 words)

 Spherical Earth - Wikipedia, the free encyclopedia The idea of a spherical Earth was espoused by Pythagoras apparently on aesthetic grounds, as he also held all other celestial bodies to be spherical. This idea probably replaced widespread belief in a flat Earth: In early Mesopotamian thought the world was portrayed as a flat disk floating in the ocean, and this forms the premise for early Greek maps like those of Anaximander and Hecataeus. Higher-order features of Earth's geoid's shape are often represented as spherical harmonics. en.wikipedia.org /wiki/Spherical_earth   (341 words)

 KryssTal : Spherical Trigonometry The small latters (a, b, c) represent the lengths of the great circle arcs measured as angles from the centre of the sphere. A spherical triangle, differs from a plane triangle in that the sum of the angles is more than 180 degrees. The Cosine Rule allows the length of one of the arcs of a spherical triangle to be evaluated if the other two arcs and the angle opposite the arc are known. www.krysstal.com /sphertrig.html   (4252 words)

 Spherical Speakers   (Site not responding. Last check: 2007-11-07) Because these speakers emit sound in a highly directional manner, the sounds produced have a quality that is very different from acoustic instruments, which radiate sound in all directions and engage their environment more completely. Spherical speakers allow electronic instruments to take on the characteristic intimacy of acoustic instruments, changing the experience of the performer and audience, and improving the viability of hybrid performances which mix acoustic and electronic sounds. The spherical speaker revolution has begun, and commercial versions are becoming available, though most are still very expensive and specialized. www.oddnoise.com /spheres.html   (686 words)

 Emerging Technologies - SIGGRAPH 2003 Basically a "spherical monitor," the OmniGlobe can be used as an interactive display for presenting spherical data in its natural format. Two-dimensional projections of spherical data have always represented a bad compromise, stretching some areas and compressing others to try to "squash" the curved data down onto a flat surface. It presents spherical information in its natural form, in a way that is instantly comprehended by even the smallest child. www.siggraph.org /s2003/conference/etech/omniglobe.html   (534 words)

 Spherical Mirrors The concave spherical mirror is the simplest image-forming optical system, and it has many applications. Glass correcting plates can correct the spherical aberration of a spherical mirror, and this is often a better solution than the use of a parabolic mirror, since it is very difficult to produce a good parabolic surface. The geometry for a concave mirror is shown at the left, and the formulas for finding the reflection angle i in terms of the ray height h, and the point at which a ray of angle i crosses the axis; the distance from this point to the vertex V is x. www.du.edu /~jcalvert/optics/mirror.htm   (3195 words)

 Spherical Aberration   (Site not responding. Last check: 2007-11-07) For lenses made with spherical surfaces, rays which are parallel to the optic axis but at different distances from the optic axis fail to converge to the same point. For a single lens, spherical aberration can be minimized by bending the lens into its best form. Although spherical aberration cannot be eliminated for a single lens, it can be minimized by the appropriate bending of the lens into its best form. hyperphysics.phy-astr.gsu.edu /hbase/geoopt/aber.html   (154 words)

 Spherical motor The ball-joint-like spherical motor has significant potentials in applications such as coordinate-measuring, high-speed plasma, laser and water cutting where the end-effector is required to orient quickly, continuously, and isotropically. Unlike the popular three-consecutive-rotational-joints wrist or spherical motors of other types where the solutions to the forward and inverse kinematics are unique, the VR spherical motor is characterized by its multiple independent inputs and the direction-varying and orientation dependent torque output. In order to characterize the torque specifications of the three DOF VR spherical motor which is significantly different from the traditional one DOF actuators, paper [2] derives the maximum torque-to-input power ratio to describe explicitly the relationship between the torque and the power input. www.me.gatech.edu /aimrl/motor.html   (770 words)

 Timesheets and Time Tracking Timesheet Software - Spherical Technology - 10/16/2005 Spherical Technology is an innovator in the field of timesheet technology. Spherical Top 10 is a personal time management tool that shows you an accurate summary of your PC-based work, helping you and your staff improve personal time management and boost productivity. Spherical Top 10 now available: Spherical Top 10 is an inexpensive tool for helping staff improve their time management. www.sphericaltech.com   (655 words)

 Sphere FAQ   (Site not responding. Last check: 2007-11-07) There is a page with a few short pieces concerning basic issues of spherical geometry, e.g. Similarly the organization and analysis of statistical data taken from the surface of the sphere would be in Statistics. Spherical harmonics are listed among the special functions. www.math.niu.edu /~rusin/known-math/index/spheres.html   (856 words)

 spherical geometry   (Site not responding. Last check: 2007-11-07) of the early geometry of the Babylonians, Arabs, and Greeks was spherical geometry--the study of... This section is supposed to be for "spherical and hyperbolic convexity" but it appears to be the only geometric area focusing on things spherical! Spherical Geometry -- from MathWorld Spherical Geometry -- from MathWorld The study of figures on the surface of a sphere (such as the spherical triangle and spherical polygon), as opposed to the type of geometry studied in plane geometry or... learning-gd.com /articles/275/spherical-geometry.html   (227 words)

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