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	Sphere - Wikipedia, the free encyclopedia
		A sphere is a perfectly symmetrical geometrical object.
		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.
		The circumscribed cylinder for a given sphere has a volume which is 3/2 times the volume of the sphere, and also a surface area which is 3/2 times the surface area of the sphere.
	en.wikipedia.org /wiki/Sphere (883 words)

	Sphere
		Sphere is the name of a book written by Michael Crichton, which was subsequently turned into a movie by the same name.
		More precisely, a sphere is the set of points in 3-dimensional Euclidean space which are at distance r from a fixed point of that space, where r is a positive real number called the radius of the sphere.
		For this reason, the sphere appears in nature: for instance bubbles and small water drops are spheres, because the surface tension tries to minimize surface area.
	www.brainyencyclopedia.com /encyclopedia/s/sp/sphere.html (617 words)

	Sphere - Wikipedia, the free encyclopedia (Site not responding. Last check: 2007-11-07)
		A sphere is, roughly speaking, a ball-shaped object.
		In non-mathematical usage, the term sphere is often used for something "solid" (which mathematicians call ball).
		But in mathematics, sphere refers to the boundary of a ball, which is "hollow".
	www.butte-silverbow.us /project/wikipedia/index.php/Sphere (946 words)

	Station Information - 3-sphere
		A sphere consists of all points an equal distance away from a single point in 3-dimensional Euclidean space.
		Whereas a sphere has dimension 2 and is therefore a 2-manifold (a surface), a 3-sphere has dimension 3 and is a 3-manifold.
		The unit quaternions form a 3-sphere, and since they are a group under multiplication, the 3-sphere can be regarded as a topological group, even a Lie group, in a natural fashion.
	www.stationinformation.com /encyclopedia/3/3_/3_sphere.html (203 words)

	3-sphere - Wikipedia, the free encyclopedia
		In mathematics, a 3-sphere is a higher-dimensional analogue of a sphere.
		Roughly speaking, a glome is to a sphere as a sphere is to a circle.
		A benefit of this correspondence is that geometric spheres in 3-space map to geometric spheres of the 3-sphere, and planes in 3-space map to spheres containing the Pole.
	www.wikipedia.org /wiki/3-sphere (2015 words)

	Sphere node (Site not responding. Last check: 2007-11-07)
		When a texture is applied to a sphere, the texture covers the entire surface, wrapping counterclockwise from the back of the sphere (i.e., longitudinal arc intersecting the -Z-axis) when viewed from the top of the sphere.
		Sphere nodes are specified in the geometry field of a Shape node; they may not be children of a Transform or Group node.
		They may choose to display very coarse-looking spheres to make scenes render faster, which is good if you want your world to display smoothly on a wide variety of machines, but is bad if you want to guarantee that your world maintains a certain image quality.
	archnt2.tamu.edu /tlarsen/ends370/index/Sphere.html (315 words)

	PRSG Tutorial, Basic Blob 1 (Site not responding. Last check: 2007-11-07)
		// 3 - this is the radius of the cylinder.
		// 1.5 - The radius of the sphere.
		In this example we must move // the red sphere to 1 on the y axis and on // the yellow we move it on the x axis to 4.
	users3.ev1.net /~povstudy/blob_1/blob1.htm (1565 words)

	pack.html: JEHS sphere packing page
		The centres of these spheres are then evenly spaced on a 'spherical surface' (again, in 2-d a circle).
		Similarly in higher dimensional sphere packings, the centres of all spheres touching a given one yield suitable nodes for numerical integration over a spherical surface.
		In particular, the densest 8-dimensional sphere packing yields a 240-node degree-7 integration rule, the densest known 16-dimensional sphere packing yields a 4320-node degree-7 rule, and the densest 24-dimensional sphere packing yields a 196560-node degree-11 rule (and also a 4600-node degree-7 rule for integrating over the surface of a sphere in 23 dimensions, see e.g.
	www.ewartshaw.co.uk /pack.html (305 words)

	Homology sphere (Site not responding. Last check: 2007-11-07)
		In algebraic topology, a homology sphere is a topological space X having the homology groups of an n-sphere, for some integer n ≥ 1.
		The Poincaré sphere, or Poincaré dodecahedral space, is a particular example of a homology sphere.
		Alternatively, the Poincaré sphere can be constructed as the quotient space SO(3)/I where I is the icosahedral group (i.e.
	www.tocatch.info /en/Poincar%C3%A9_sphere.htm (308 words)

	3-sphere (Site not responding. Last check: 2007-11-07)
		Whereas a 2-sphere is a smooth 2-dimensional surface a 3-sphere is an object with dimensions also known as 3- manifold.
		Some refer to an sphere in 3-dimensional Euclidean space as a The concept discussed here would then be a 4-sphere.
		It is a non abelian compact Lie group of dimension 3.
	www.freeglossary.com /3-sphere (1412 words)

	SPHEREPACK 3.1: A Model Development Facility
		This eliminates a number of computational difficulties associated with solving partial differential equations on the sphere including the accuracy and stability problems that can be created by the clustering of points near the pole.
		transfers scalar data on the sphere between an equally spaced grid that is offset by a half grid increment in both longitude and latitude (which excludes the poles) and an equally spaced grid that includes the poles.
		transfers vector data on the sphere between an equally spaced grid that is offset by a half grid increment in both longitude and latitude (which excludes the poles) and an equally spaced grid that includes the poles.
	www.scd.ucar.edu /css/software/spherepack (3038 words)

	[No title] (Site not responding. Last check: 2007-11-07)
		The SPHERE of radius r in R^n is the set of points whose coordinates satisfy x1^2+...+xn^2=r^2; the unit sphere is the sphere of radius 1.
		The interior of the sphere is called the BALL in R^n; it is the set of points of distance less than r from the origin.
		The difficulty is that a sphere packing implies a distribution of arbitrarily many points on the sphere, and gives these distributions in a coherent way, whereas an individual distribution is done with just one fixed number of points.
	www.math.niu.edu /~rusin/known-math/95/sphere.faq (4423 words)

	Crystal Spheres of Labradorite, Rose Quartz, Aventurine, Hematite, Tiger's Eye, and Snowflake Obsidian, and Fluorite ...
		To carve a sphere one must cut away a mass of crystal which can be as much as ten times the finished creation.
		A sphere is also the perfect centerpiece for a crystal arrangement or for an altar.
		In feng shui, the ancient art of creating optimal energy flow in an environment, a sphere is ideal to place in the center of a room for its balancing abilities.
	www.rainbowcrystal.com /crystal/sphere1.html (792 words)

	9.3.2 Sphere Mapping (Site not responding. Last check: 2007-11-07)
		Sphere mapping is a type of environment mapping in which the irradiance image is equivalent to that which would be seen in a perfectly reflective hemisphere when viewed using an orthographic projection.[35] This concept is illustrated in Figure 27.
		The width and height of the plane are equal to the diameter of the sphere.
		Note that since the sphere map computes the irradiance at a single point, the sphere is infinitely small.
	www.opengl.org /resources/tutorials/advanced/advanced97/notes/node93.html (496 words)

	Sphere Powers Our World
		Sphere version 51a and lower can only use UP TO client 2.0.0, for those I recommend 1.26.4.
		Sphere version 55i can only use clients 2.0.0 to 3.0.0g, for it I recommend 2.0.3.
		SPHERE is expecting numbers from an old prof.txt and therefore thinks someone is cheating when they make a character with a newer patched prof.txt.
	www.sphereserver.net /documentation/sphereconnectingerrors.htm (306 words)

	Brass Stands, Egg Stands and other Display items.
		The circle which holdes the sphere is 1 1/2" and it sets 1/2" in height.
		The circle which holds the sphere is 1 5/8" and it sets 1 7/8" in height.
		It measures 3" in width from trunk to trunk and 3 1/4" in diameter at the feet.
	www.therockshed.com /Display.html (483 words)

	The Poincare conjecture
		The Poincare Conjecture is essentially the first conjecture ever made in topology; it asserts that a 3-dimensional manifold is the same as the 3-dimensional sphere precisely when a certain algebraic condition is satisfied.
		Poincare himself found the first counterexample, a space which is now known as the Poincare homology sphere.
		A 3-manifold with trivial fundamental group is homotopy equivalent to the 3-sphere (hence the name "homotopy 3-sphere"), and so the Poincare Conjecture can be stated as the assertion that every 3-manifold homotopy equivalent to the 3-sphere is homeomorphic to the 3-sphere.
	www.math.unl.edu /~mbrittenham2/ldt/poincare.html (2822 words)

	Sphere Extension Service for Afghanistan, Evaluation
		The SESA Team is responsible for conducting trainings, discussing applications of Sphere and meeting with NGOs and government departments in order to disseminate and explain the Sphere concept, the Humanitarian Charter, standards and indicators.
		A Sphere Master Trainer was engaged as a consultant to provide support and technical assistance during the course of the project.
		The Sphere Master Trainer returned to adapt the training materials to the 2004 version of the handbook and co-facilitated a Sphere workshop.
	www.sphereproject.org /practice/sesa_eval.htm (800 words)

	INFLUENCE OF BONE THICKNESS ON SURFACE POTENTIALS USING A 3-SPHERE HEAD MODEL BASED ON RESISTOR MESHING ELEMENTS. (Site not responding. Last check: 2007-11-07)
		As they are not easy to measure, standard values are used with the classical three sphere head model [1], that is to say 0.33 S.m-1 for scalp and brain and 0.0042 S.m-1 for bone.
		We then calculated the potentials at all nodes of the 3D sphere for different radial dipoles corresponding to eccentricity of 0.24, 0.47, 0.66, and 0.81.
		[3] Meijs JW et al.(1988): Relative influence of model assumptions and measurement procedures in the analysis of the MEG.
	208.164.121.55 /hbm2003/abstract/abstract828.htm (500 words)

	Sphere Packing in Curved 3D Space
		The densest possible packing of four spheres in flat 3D space is given by the tetrahedral arrangement, but this arrangement can't be used to fill space because tetrahedrons don't quite "fit together".
		This is because if five tetrahedrons share a common edge, they take up only 97.96% of the total 2pi arc about that axis, leaving a small gap.
		Then, if the tetrahedrons are to fit snugly together, we should be able to determine point 7 again, this time being equidistant from 1,2,6 and opposite 4, and it should coincide with the coordinates for point 7 determined previously.
	www.mathpages.com /home/kmath349.htm (616 words)

	Poincare Homology 3-Sphere (Site not responding. Last check: 2007-11-07)
		Their description of the Poincaré sphere as the spherical dodecahedron space is based on the solid dodecahedron where opposite pentagons on the boundary are identified by a coherent twist of pi/5 radians; see Threlfall and Seifert [17] or Weber and Seifert [19].
		For triangulations of Z_2-homology 3-spheres, other than the standard sphere, Bagchi and Datta [3] have shown recently that at least 12 vertices are necessary.
		Triangulations of Seifert homology spheres are constructed in [6].
	www.eg-models.de /models/Discrete_Mathematics/Simplicial_Manifolds/2003.04.001/_preview.html (1191 words)

	week164
		The Poincare homology sphere is actually the boundary of a 4-manifold, and it's not hard to say what this 4-manifold is. I just gave you a recipe for cutting out 8 solid tori from the 3-sphere and gluing them back in with a twist.
		Now, exotic spheres of a given dimension form an abelian group G under connected sum (see "week141").
		This matrix is important because it also describes the "intersection form" on the 2nd homology group of a simply-connected 4-manifold M whose boundary dM is the 3-manifold we're describing.
	math.ucr.edu /home/baez/week164.html (2840 words)

	3-sphere (Site not responding. Last check: 2007-11-07)
		En hecho, la 4ta dimensión se puede pensar en como campo escalar contínua, una función de los coordenadas de 3 dimensiones del 3-ball, similares a la "temperatura".
		Un 3-sphere es un acuerdo, múltiple de 3 dimensiones sin límite.
		3) es cíclico de la orden 3 y continúa como ése sin ningún patrón discernable.
	www.yotor.net /wiki/es/3s/3sphere.htm (1275 words)

	3-Sphere with a 3-edged knot (Site not responding. Last check: 2007-11-07)
		What he showed is the fact that if a triangulation of a 3-sphere contain a knot made of 3 edges in the 1-skeleton, then it is not shellable.
		Then we take a cone over the boundary of the ball, then we have a triangulated 3-sphere with a knot made of 3 edges.
		Lickorish's original theorem asserts that the triangulation is non-shellable if the knot embedded is "complex enough", but in fact, it is not shellable (even not constructible) if the knot is nontrivial.
	infoshako.sk.tsukuba.ac.jp /~hachi/math/library/nc_sphere_eng.html (149 words)

	Properties of Hyperspheres (Site not responding. Last check: 2007-11-07)
		Clearly circles and spheres fall into this definition as the two- and three-dimensional hyperspheres.
		The planar cross-sections of a sphere are circles whose radii progress from 0 to r, the radius of the sphere, and back to 0.
		The volume enclosed by a sphere, now, is found by integrating the areas of its composite circles:
	people.ucsc.edu /~erowland/hyperspheres.html (358 words)

	Geometry of the Sphere 3.
		The area of a sphere of radius R is 4
		If you can visualize the configuration of these six lunes on the sphere, you will be on the way to a solution.
		The previous section discusses incidence on the sphere.
	math.rice.edu /~pcmi/sphere/gos3.html (696 words)

	SPHERE Stabilizer System (Site not responding. Last check: 2007-11-07)
		Enter the new age of lightweight, shock absorbing, vibration dampening for the archer with the SPHERE Stabilizer System.
		The innovative SPHERE is made of a flexible rubber material that is designed with radially spaced cavities that absorb energy from every direction.
		The air cushion design and material work together to absorb shock and vibration instantly after the release for a smoother and more pleasant shooting experience.
	www.rockymtbroadheads.com /05sphere.html (119 words)

	Sphere Newsletter # 10
		Based on the practical experiences of individuals who use the Sphere handbook in their humanitarian work, the handbook will be revised over a 12-month period starting in June 2002.
		The twenty agencies piloting the implementation of Sphere into their organisations met over four days in May. During this meeting, practical experiences were shared, findings were debated, and trends were proposed.
		Module 3, Sphere and the Project Cycle, explores how the Sphere handbook can be used throughout the disaster response project cycle.
	www.sphereproject.org /about/nl10.htm (767 words)

	Examples of Constant Mean Curvature Immersions of the 3-Sphere into Euclidean 4-Space -- Hsiang et al. 79 (12): 3931 -- ...
		Therefore, closed hypersurfaces of constant mean curvature in euclidean spaces of high dimension are basic objects of fundamental importance in global differential geometry.
		Before the examples of this paper, the only known example was the obvious one of the round sphere.
		Examples of this paper seem surprising and are constructed in the framework of equivariant differential geometry.
	www.pnas.org /cgi/content/abstract/79/12/3931 (208 words)

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