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Topic: Solid angle

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	Solid angle - Wikipedia, the free encyclopedia
		Thus the solid angle of a sphere measured at its center is 4π steradians, and the solid angle subtended at the center of a cube by one of its sides is one-sixth of this, that is, 2π/3 steradians.
		A solid angle is the three dimensional analogue of the ordinary angle, and the steradian is similarly analogous to the radian.
		A spherical angle is a particular dihedral angle; it is the angle between two intersecting arcs on a sphere, and is measured by the angle between the planes containing the arcs and the centre of the sphere.
	en.wikipedia.org /wiki/Solid_angle (496 words)

	Encyclopedia article on Angle [EncycloZine] (Site not responding. Last check: 2007-11-06)
		Angles provide a means of expressing the difference in slope between two rays meeting at a vertex without the need to explicitly define the slopes of the two rays.
		The degree measure of the angle is the length of the arc, divided by the circumference of the circle, and multiplied by 360.
		The angle between a line and a curve (mixed angle) or between two intersecting curves (curvilinear angle) is defined to be the angle between the tangents at the point of intersection.
	encyclozine.com /Angle (1209 words)

	Danzer Tile Characteristics (Site not responding. Last check: 2007-11-06)
		The solid angle is the area on the surface of the unit sphere which is subtended by a surface.
		The total solid angle is the area of the unit sphere, 4*pi.
		Thus the sum of the solid angles of all of the vertices involved in a vertex configuration is always 4*pi = 720 degrees.
	www.cs.williams.edu /~98bcc/tiling/danztable.html (216 words)

	Tom's Combinatorial Geometry Class
		The area of the gray spherical triangle is the measure of the solid angle.
		You measure the dihedral angle between two planes, P1 and P2, of a solid angle by inserting a plane that is perpendicular to the edge between P1 and P2, and then measuring the 2D angle that's cut out on this plane between P1 and P2.
		Plane angles are used to measure the deficiency of a solid angle.
	www.merrimack.edu /~thull/combgeom/convex/convexnotes.html (1109 words)

	Solid Angle \| Steradian
		The value of the solid angle is numerically equal to the size of that area divided by the square of the radius of the sphere.
		The solid angle is the quantitative aspect of the conical slice of space, that has the center of the sphere as its peak, the area on the surface of the sphere as one of its spherical cross sections, and extends to infinity.
		The maximum solid angle is ~12.57, corresponding to the full area of the unit sphere, which is 4*Pi.
	www.schorsch.com /kbase/glossary/solid_angle.html (226 words)

	How Does a Liquid Wet a Solid? Hydrodynamics of Dynamic Contact Angles
		The contact angle, the angle formed at the intersection of the solid and the fluid-fluid interfaces, is a key material property needed to determine the shape of the fluid-fluid interface.
		This suggests that, in contrast to the static contact angle (see the first graph, preceding page), the dynamic contact angle is not a well-defined quantityit is not at all clear where on the interface one should apply the slope condition in order to calculate the interface shape.
		Nevertheless, a dynamic contact angle is still necessary to calculate the interface shape in dynamic conditions, the pressure drop necessary to move a meniscus in a capillary tube, and the spreading dynamics of small droplets.
	www.lerc.nasa.gov /WWW/RT2000/6000/6712rame.html (1245 words)

	Radiometry and Photometry
		A radian is the angle subtended at the center of a circle of radius r by a section of its circumference of length equal to r.
		A steradian is the solid angle subtended at the center of a sphere of radius r by a section of its surface area of magnitude equal to r
		When determining the brightness of a small source we measure the energy that falls on a detector subtending a given solid angle at the source and then divide by the apparent size (area) of the source.
	electron9.phys.utk.edu /optics421/modules/m4/radiometry.htm (1197 words)

	Math Forum - Ask Dr. Math
		A tall narrow cone has a small solid angle at the tip; a broad flat cone has a large solid angle at the tip.
		The solid angle doesn't have to be "round" though.
		For instance, the peak of a triangular pyramid is sort of a "triangular" solid angle, and the peak of a square pyramid is sort of a "square" solid angle.
	mathforum.org /library/drmath/view/55358.html (682 words)

	Basic geometric relationships (Site not responding. Last check: 2007-11-06)
		A solid angle is the 3D analog to the familiar 2D concept of angle.
		The solid angle of a cone of directions is defined as the area cut out by the cone on the unit sphere.
		The solid angle is measured in steradians (sr).
	www.cs.technion.ac.il /Labs/Isl/Project/Projects_done/VisionClasses/Vision/3D_Photometry/node4.html (395 words)

	SoVRMLSpotLight class Reference (Site not responding. Last check: 2007-11-06)
		This point is the apex of the solid angle which bounds light emission from the given light source.
		The radius field specifies the radial extent of the solid angle and the maximum distance from location than may be illuminated by the light source - the light source does not emit light outside this radius.
		(Note: Not implemented) Specifies the radial extent of the solid angle and the maximum distances from location that may be illuminated by the light source.
	www.tgs.com /support/java_api_doc/api_cpp/html/classSoVRMLSpotLight.html (686 words)

	Steradian - Wikipedia, the free encyclopedia (Site not responding. Last check: 2007-11-06)
		The name is partly derived from the Greek stereos for solid.
		The steradian is defined as "the solid angle subtended at the center of a sphere of radius r by a portion of the surface of the sphere having an area r
		A steradian is also equal to the spherical area of a polygon having an angle excess of 1 radian, to 1/4π of a complete sphere, or to (180/π)
	en.wikipedia.org /wiki/Steradian (218 words)

	A Method for Calculating the Average Solid Angle Subtended by a Circular Disk From Uniformly Distributed Points within ...
		Methods for calculating the solid angles subtended at a point by closed contours of some given objects are required in manu areas of optical and nuclear physics to estimate the fluxes or particle beams of radiation.
		It is therefore of interest to derive solid angle equations for various closed contours and the location of such contours with respect to a single point or some points.
		In the second method this formula was used to derive another formula for calculating the average solid angle subtended by a circular disk from uniformly distributed multiple points lying on the planar circular surface coaxial to the disk.
	library.wolfram.com /infocenter/Articles/1573 (348 words)

	steradian - a Whatis.com definition (Site not responding. Last check: 2007-11-06)
		The steradian (symbolized sr) is the Standard International (SI) unit of solid angular measure.
		The solid (conical) angle q, representing one steradian, is such that the area A of the subtended portion of the sphere is equal to r
		Imagine a cone with its apex P at the center of the sphere, and that intersects the surface in a circle (shown as a red ellipse, the upper half of which is dashed).
	whatis.techtarget.com /definition/0,,sid9_gci528813,00.html (295 words)

	README (Site not responding. Last check: 2007-11-06)
		The Tolman cone angle is thereafter a simple average of the vertex angles of the separate parts of the ligand.
		As the radius of the sphere is increased from a minimum (normally zero) to a maximum (normally encompassing all atoms of interest), the data that represent the intersection of the sphere with the atomic data is used in the steric calculation.
		For example, a solid angle profile of a ligand would give the solid angle of that slice of the ligand at each radial distance from the metal, and is a measure of the radial dependence of the ligands angular steric size.
	www.ccl.net /cca/software/SOURCES/C/steric/README.shtml (1990 words)

	All Elementary Mathematics - Study Guide - Geometry - Solid angles...
		A solid angle is a part of a space, concluded inside of one part of a conic surface with a closed directrix.
		A measure of a solid angle is a ratio of an area ABCDEF to a square of radius of the ball:
		This measure of solid angles is similar to the radian measure of plane angles.
	www.bymath.com /studyguide/geo/sec/geo20.htm (116 words)

	Tetrahedra Classified by Bad Angles (Site not responding. Last check: 2007-11-06)
		The sphere is (d-k-1)-dimensional and lies in a (d-k)-dimensional subspace perpendicular to the k-face; its center is the projection of the face onto the subspace.
		No small angle at a 0-face (no small solid angle) implies no small angle at a 1-face, which implies no small angle at a 2-face, and so forth up to no small angle at a (d-2)-face.
		In the opposite direction, a large solid angle implies a small dihedral, and hence bad angles of all types.
	www.ics.uci.edu /~eppstein/junkyard/tetraqual.html (389 words)

	Euclid's Elements, Book XI, Proposition 26
		To construct a solid angle equal to a given solid angle on a given straight line at a given point on it.
		It is required to construct at the point A on the straight line AB a solid angle equal to the solid angle at D.
		Then, since FG is at right angles to the plane of reference, therefore it is also at right angles with all the straight lines which meet it and are in the plane of reference.
	aleph0.clarku.edu /~djoyce/java/elements/bookXI/propXI26.html (430 words)

	3.2.1 Local Spherical System-Directional Distribution (Site not responding. Last check: 2007-11-06)
		A solid angle is two-dimensional by virtue of having no radial position, i.e., the solid angle remains fixed independent of radius.
		As particles originate inside the solid, their probability of escaping from the solid and being emitted is inversely proportional to the path length
		(normal to the surface), the solid angle tends to 0, and as
	csep1.phy.ornl.gov /pt/node16.html (653 words)

	College Mathematics Journal, The: Solid Angle Subtended by a Circular Disk with Application to Roadsigns, The (Site not responding. Last check: 2007-11-06)
		The Solid Angle Subtended by a Circular Disk with Application to Roadsigns, I. Jones.
		The apparent size of a roadsign can be measured by the solid angle it subtends at the observer's eye.
		For signs of a fixed area, the maximum apparent size as one approaches the sign is a function of its shape, height, and distance from the road.
	www.findarticles.com /p/articles/mi_qa3773/is_199803/ai_n8794041 (306 words)

	solid. The American Heritage® Dictionary of the English Language: Fourth Edition. 2000.
		A substance having a definite shape and volume; one that is neither liquid nor gaseous.
		As a whole; unanimously: The committee voted solid for the challenger.
		Without a break or opening; completely or continuously: The theater was booked solid for a month.
	www.bartleby.com /61/85/S0548500.html (179 words)

	NEA-1688: SACALC2, Calculates the average solid angle for source-detector geometries
		The values of solid angle are calculated to accuracies of typically better than 0.1%.
		Whitcher, R. Calculation of the average solid angle subtended by a detector to source in a parallel plane by a Monte Carlo method.
		The use of a Monte Carlo method to calculate the average solid angle subtended by a detector to source in a non-parallel plane.
	www.nea.fr /abs/html/nea-1688.html (429 words)

	Euclid's Elements, Book XI, Proposition 20
		If a solid angle is contained by three plane angles, then the sum of any two is greater than the remaining one.
		Therefore, if a solid angle is contained by three plane angles, then the sum of any two is greater than the remaining one.
		The angle BAE is constructed in one plane to equal a given angle BAE in a different plane.
	aleph0.clarku.edu /~djoyce/java/elements/bookXI/propXI20.html (598 words)

	Math Forum - Ask Dr. Math (Site not responding. Last check: 2007-11-06)
		Date: 2/14/96 at 10:1:27 From: Doctor Ethan Subject: Re: question Much like radian measure, which is a unitless description of the size of an angle in two dimensions, steradians are a similar measure of 'solid angles' in three dimensions.
		Similarly, steradians relate solid angles (which you can imagine as cones radiating out from a point) to an angles that subtend an entire sphere (4*Pi).
		If dU is the solid angle subtended by da, we therefore have: R * da dU = ------- r^2 where * is being used as the _dot product_ (not multiplication).
	mathforum.org /dr.math/problems/scaffidi2.8.96.html (274 words)

	1996 Fire Publications - Effect of Liquid-Solid Contact Angle on Droplet Evaporation. (Site not responding. Last check: 2007-11-06)
		The effect of varying initial liquid-solid contact angle on the evaporation of single droplets of water deposited on a stainless steel surface is studied using both experiments and numerical modeling.
		The evolution of contact angle and liquid-solid contact diameter is measured from a video record of droplet evaporation.
		Reducing contact angle increases contact area between the droplet and solid surface, and also reduces droplet thickness, enhancing heat conduction through the droplet.
	fire.nist.gov /bfrlpubs/fire96/art166.html (205 words)

	SOLID CLOUD COVER
		angle of solid cloud cover, such as is indicated in figure
		elevation angle at the center of the solid band.
		angle at the left side of the solid band, and then add the
	www.tpub.com /content/aerographer/14269/css/14269_114.htm (268 words)

	Mathematical Modeling of the Solid Angle Function, Part II: Transmission Through Refractive Media -- from Mathematica ...
		Previously, we developed a classical solid angle function that is valid only when the light is traveling within a homogeneous medium.
		A different approach must be used if one is to include refraction effects in the solid angle formulation.
		The final refracted solid angle formula also includes the expression of Fresnel's transmission coefficient.
	library.wolfram.com /infocenter/Articles/1724 (109 words)

	Golf Digest: Frank talk: how to identify the proper lie angle; comparing solid-core balls to wound balls - Equipment: ...
		The lie angle is the angle between the shaft and the ground when the club is in the normal address position.
		If the mark is toward the heel, then the angle is too upright (and the ball will likely go to the left).
		A launch angle of about 12 degrees and a spin rate of 2,000 revolutions per minute is ideal for an above-average swing speed.
	www.findarticles.com /p/articles/mi_m0HFI/is_2004_Jan/ai_112104102 (734 words)

	Merriam-Webster Online
		1 a : being without an internal cavity solid ball of rubber> b (1) : printed with minimum space between lines (2) : joined without a hyphen solid compound> c : not interrupted by a break or opening solid wall>
		b : possessing or characterized by the properties of a solid : neither gaseous nor liquid
		solid support of the party> c : intimately friendly or associated with the boss>
	www.m-w.com /cgi-bin/dictionary?book=Dictionary&va=solid (248 words)

	ANS : Publications : Journals : Nuclear Science and Engineering : Volume 132 : Derivations of the Solid Angle Subtended ...
		An analytic study of the solid angle subtended at a point by objects of first and second algebraic order has been made.
		It is shown that the derived solid angle for all such objects is in the form of a general elliptic integral, which can be written as a linear combination of elliptic integrals of the first and third kind and elementary functions.
		Approximate and degenerate forms of the equations are shown, and methods for the evaluation of the solid angle of a torus are outlined.
	www.ans.org /pubs/journals/nse/va-132-2-217-258 (290 words)

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