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	Torus - Wikipedia, the free encyclopedia
		In geometry, a torus (pl. tori) is a doughnut-shaped surface of revolution generated by revolving a circle about an axis coplanar with the circle.
		The sphere is a special case of the torus obtained when the axis of rotation is a diameter of the circle.
		Intuitively speaking, this means that a closed path that circles the torus' "hole" (say, a circle that traces out a particular latitude) and then circles the torus' "body" (say, a circle that traces out a particular longitude) can be deformed to a path that circles the body and then the hole.
	en.wikipedia.org /wiki/Torus (649 words)

	Torus article - Torus torus (nuclear physics) geometry doughnut solid revolution circle - What-Means.com (Site not responding. Last check: 2007-10-21)
		In geometry, a torus (pl. tori) is a doughnut shaped solid of revolution generated by revolving a circle about an axis coplanar with the circle.
		According to a broader definition, the generator of a torus need not be a circle but could also be an ellipse or any other conic section.
		This is due in part to the fact that in any compact Lie group one can always find a maximal torus; that is, a closed subgroup which is a torus of the largest possible dimension.
	www.what-means.com /encyclopedia/Torus (357 words)

	TORUS
		Cassinian oval is the intersection of a plane parallel to the torus' axis and a distant from it.
		Arbitrary slice of a torus are not Cassinian ovals.
		The Lemniscate of Bernoulli is the intersection of a plane tangent to the inner ring of a torus whose inner radius equals to its radius of generating circle.
	isolatium.uhh.hawaii.edu /m206L/student/torus/torus.htm (1515 words)

	Stanford torus - Wikipedia, the free encyclopedia
		It consists of a torus or doughnut-shaped ring that is one mile in diameter and rotates once per minute to provide Earth-normal gravity on the inside of the outer ring via centrifugal force.
		The interior space of the torus itself would be used as living space, and would be large enough that a "natural" environment could be simulated; the torus would appear similar to a long, narrow, straight glacial valley whose ends curved upward and eventually met overhead to form a complete circle.
		The Stanford Torus was proposed during the 1975 NASA Summer Study, conducted at Stanford University, with the purpose of speculating on designs for future space colonies.
	en.wikipedia.org /wiki/Stanford_torus (349 words)

	Surface -- Torus (Site not responding. Last check: 2007-10-21)
		The elliptical torus is formed by the rotation around the x' -axis of an ellipse defined in the (x', y') plane.
		This ellipse has its center on the y' -axis a distance r from the origin, a semi-axis parallel to the x' -axis equal to a, and a semi-axis along the y' -axis equal to b.
		Example of an elliptical TORUS, with a major radius r = 1.0, and ellipse semi-axes of 0.8 in x' and 0.5 in y'.
	www-phys.llnl.gov /N_Div/COG/Manual/Surface/Torus.html (131 words)

	Torus (Site not responding. Last check: 2007-10-21)
		In geometry, a torus is a solid of revolution generated by revolving a circle about an axis coplanar with the circle.
		According to the broadest definition, the generator of a torus need not be a circle but could also be an ellipse or any other conic section.
		In nuclear physics a torus is a large fusion reactor which is very roughly the shape of an elliptical torus.
	www.theezine.net /t/torus.html (212 words)

	TORUS - LoveToKnow Article on TORUS
		The earliest examples are found in Egypt, where it was carried up the angles of the pylon and temple walls and horizontally across the same.
		Its most frequent employment is in the bases of columns; in the Roman Doric order being the lowest moulding; in the Ionic orders there are generally two torus mouldings separated by a scotia with fillets.
		Both in Greek and Roman bases sometimes the torus is elaborately carved.
	www.1911encyclopedia.org /T/TO/TORUS.htm (110 words)

	Torus (Site not responding. Last check: 2007-10-21)
		The torus is perhaps the least used object in real modelling applications but it still appears as a standard form in modelling and rendering packages ahead of far more useful geometric primitives.
		The equation for the supertoroid is the same as that for the torus except that the sin and cosine terms are raised to powers.
		The value of n1 determines the shape of the torus ring, n2 determines the shape of the cross section of the ring.
	astronomy.swin.edu.au /~pbourke/surfaces/torus (415 words)

	Torus Maps (Site not responding. Last check: 2007-10-21)
		The torus is represented as a rectangle in which opposite sides have been identified, the "torus rectangle".
		Since the torus is an oriented surface, if the torus is "flipped" (ie, turned inside out), a graph X embedded on it may not be isomorphic to the result, as a torus map.
		Graphs embedded on the torus which are related by a Dehn twist are considered isomorphic, even though they may look quite different on the screen, and it may not be possible to transform one into the other by a continuous deformation of the torus.
	kohlrabi.cs.umanitoba.ca /G&G/TorusOverview.html (648 words)

	PlanetMath: torus
		Informally, we take a rectangle, identify two edges to form a cylinder, and then identify the two ends of the cylinder to form the torus.
		This is version 9 of torus, born on 2002-08-07, modified 2003-09-12.
		It is a bit confusing to think about 0 \times 1, for it feels as if you were referring to 0 and 1 as sets (which they are, but only if we're talking about set theory and ordinals).
	planetmath.org /encyclopedia/Torus.html (306 words)

	The Torus (Site not responding. Last check: 2007-10-21)
		The torus is the orientable surface with Euler characteristic = 0.
		The torus is easily seen to be a surface of revolution: a planar curve is revolved about an axis.
		The next image of the torus is obtained as follows: an ellipse centered at the origin in the xy-plane is tilted 45 degrees.
	www.geom.umn.edu /zoo/toptype/torus (156 words)

	Concerning Steady State Corotation of the Io Plasma Torus
		The absolute angular velocity of the torus and the Alfven waves velocity relative to the middle line of the torus are the main parameters of the problem.
		Figure 1 presents the kinematic picture of the partial corotation of the torus corresponding to the described model for the mean values of the torus parameters related to its central line.
		Five positions of the Io torus, Io and Jupiter in the inertial medium corresponding to one rotation of Jupiter around its axis (the scale is distorted for clarity).
	www.iki.rssi.ru /vprokhor/papers/iotor/iotor.htm (1121 words)

	Glossary: Torus (Site not responding. Last check: 2007-10-21)
		A torus is an orientable surface of genus one.
		It can be made from a rectangular piece of plane by identifying the top and bottom edges (i.e., rolling it into a tube) and then identifying the left and right edges (that is, bending the tube around so that the ends meet).
		An n-handled torus is a sphere with n handles; it has Euler characteristic equal to 2 - 2 n.
	www.math.union.edu /~dpvc/papers/RP2/Glossary/Torus.html (93 words)

	SB3D (Tour/Torus): Movies of In- and Outside the Torus
		The torus shown in "In- and Outside the Torus" is the projection of a torus on the three-sphere in four-space projected into three-space.
		The region in "front" of the torus is congruent to the region "behind" it.
		The initial image is a torus of revolution, but as the torus rotates in four dimensions, it seems to expand on one side (the side that moves closer to the projection point) and contract on the other.
	www.maa.org /cvm/1998/01/sbtd/article/tour/torus/torus-movies.html (319 words)

	Stanford Torus Space Colony
		The Stanford Torus was the principal design considered by the 1975 NASA Summer Study, which was conducted in conjunction with Stanford University (and published as Space Settlements: A Design Study, NASA Publication SP-413).
		It consists of a torus or donut-shaped ring that is one mile in diameter, rotates once per minute to provide Earth-normal gravity on the inside of the outer ring, and which can house 10,000 people.
		Stanford Torus agriculture, conducted on multiple tiers for efficient use of space.
	www.l5news.org /stanfordtorus.htm (145 words)

	The Torus (Site not responding. Last check: 2007-10-21)
		The torus shown above is known as a ring torus, because its wheel radius a exceeds its tube radius b.
		When a and b are equal, the torus is called a spindle torus, and when b > a, it is referred to as either an inside-out torus or a horn torus.
		Note that the curvature depends only on whether you are "inside" or "outside" the torus, not on your position around the rim.
	www.math.hmc.edu /faculty/gu/curves_and_surfaces/surfaces/torus.html (95 words)

	Spiral on Torus (Site not responding. Last check: 2007-10-21)
		This is because the torus is able to 'remember' its shape and holographic memory is created as a result of this ability.
		At the very centre of each mandala (the centre of the three rings) is a key glyph, the Hebrew letter that is controlling energy of the mandala and the 'hidden' gate within it.
		These three spinning gyroscopes within the torus give it complete stability, which is why it is the best geometric shape for holding light memory.
	www.lightofisis.com /alphabet2.htm (458 words)

	Paper strip
		I hope to return to the topic of shredding the torus at a later date.
		Living on a torus is not the same as living on a plane or even on a sphere.
		Other games on torus are available at http://www.northnet.org/weeks/TorusGames/TorusGames.shtml.
	www.cut-the-knot.org /do_you_know/paper_strip.shtml (1581 words)

	Torus Doubling (Site not responding. Last check: 2007-10-21)
		In the torus doubling route to chaos, our original torus (which is a closed curve in cross section) appears to split into two circles at the torus doubling bifurcation point [24].
		The torus doubling route to chaos is reminiscent of the period doubling route to chaos.
		Second, the torus doubling route to chaos is a higher-dimensional phenomenon, requiring at least a four-dimensional flow, or a three-dimensional map.
	www.drchaos.net /drchaos/Book/node81.html (265 words)

	Cassini "sees" invisible gas doughnut around Jupiter
		The torus was detected in the 1970s, but almost all of its light is invisible to the human eye.
		The torus apparently gets its ingredients and shape when some of the neutral oxygen and sulfur atoms around Io become ionized by exposure to radiation from the Sun or from a radiation belt that surrounds Jupiter.
		The torus material apparently dissipates and cools over time, to be replenished and re-energized by the next episode of volcanic activity from Io.
	www.jpl.nasa.gov /releases/2001/torus010124.html (674 words)

	Knots and Surfaces: Torus Knots (Site not responding. Last check: 2007-10-21)
		Recall that a torus may be parametrized by rotating a circle of radius r about another circle of radius R.
		This curve wraps around the torus once in the "long" direction while it wraps around the torus two times in the "short" direction, as indicted in Figure 1.
		If either m=0 or n=0, then the definition changes slightly: a torus knot of type (1,0) is the image of the line t=constant whereas a knot of type (0,1) is the image of a line s=constant.
	www.geom.uiuc.edu /~thurman/calcIII/Lab18/Knots.html (377 words)

	life on torus (Site not responding. Last check: 2007-10-21)
		To do so, I find an isomorphic system in which each column in a torus is labeled with a number that is the total number of filled cells in that column and in the two adjacent columns.
		A common object in the shape of a torus is a donut.
		The only difference is that the torus is made up of a finite face that wraps around to reconnect with itself, and the plane continues infinitely in all directions.
	www.goshen.edu /~andrewjh/writings/lifeontorus.htm (1657 words)

	POV-Ray: Documentation: 2.4.1.14 Torus
		The major radius extends from the center of the hole to the mid-line of the rim while the minor radius is the radius of the cross-section of the rim.
		The torus is centered at the origin and lies in the x-z-plane with the y-axis sticking through the hole.
		The torus is internally bounded by two cylinders and two rings forming a thick cylinder.
	winupdate.povray.org /documentation/view/3.6.1/288 (186 words)

	The Torus -- The 4th Dimension (Site not responding. Last check: 2007-10-21)
		The horn torus has no hole in the middle, rather the point (0,0,0) is tangent to itself.
		The torus plays an important role in knot theory, as it can be knotted both internally or externally.
		However, since the torus is a closed surface it cannot be simultaneously knotted both internally and externally.
	www.uta.edu /optics/sudduth/4d/orientable/torus/torus.htm (312 words)

	POV-Ray: Documentation: 1.2.2.5 Torus Object
		The syntax for a torus is so simple that it makes it a very easy shape to work with once we learn what the two float values mean.
		With such a simple syntax, there is not much else we can do to a torus besides change its texture...
		This may seem like a wasteful way to make a complete torus, but we are really going to move each half apart to make room for the cylinders.
	www.povray.org /documentation/view/3.6.0/26 (943 words)

	Disentangling Electron Temperature and Density in the Io Plasma Torus (Site not responding. Last check: 2007-10-21)
		One of the torus characteristics of most interest for understanding torus energization is its electron temperature (T_e).
		Because of the lack of information available on the collision strengths of important lines between 350 and 600 AA, we have attempted to simultaneously deduce both the unknown collision strengths and also the time-varying torus characteristics by fitting analytic models which exploit the both the commonalities and the variations among the observations.
		The anti-correlation of N_e and T_e suggests that torus luminosity may be primarily determined by a relatively constant power-limited energy supply, so that as N_e increases (decreases), T_e sags (surges) in response.
	www.cea.berkeley.edu /~euve/sci/Resources_pubs_abstracts_torus_herbe.html (267 words)

	Torus Attractor (Site not responding. Last check: 2007-10-21)
		Although this map is not a true Poincaré map, it is easy to obtain experimentally and will be useful in explaining the notion of a torus attractor (see section 3.8.1).
		and a torus attractor naturally arises whenever quasiperiodic motion is encountered in a dissipative dynamical system.
		The torus is an attractor because it is an invariant set and an attracting limit set.
	www.drchaos.net /drchaos/Book/node79.html (247 words)

	Shredding the torus
		We have considered several examples of cutting the torus along the lines parallel to the fundamental square of its plane model.
		The problem of shredding a torus along such a line has two distinct solutions depending on whether the slope of the cut is rational or not.
		Since the torus has two sides we are going to end up with a closed serpentine band that might be thought of as having been wrapped around the torus to start with.
	www.cut-the-knot.org /do_you_know/shredding.shtml (1076 words)

	SPACE.com -- Swirling Dust Near Black Hole Too Thick for Theory
		Astronomers long ago speculated that this and similar fl holes might be shrouded in a disk of dust that partially hides the tremendous luminosity that a fl hole's sloppy eating habits generate.
		The torus of dust is about room temperature at the outer edge, and about 1,832 degrees Fahrenheit (1,000 Celsius) on the inner edge.
		The torus is composed of tiny dust particles similar to rock minerals on the Earth, including silicon, oxygen, and probably aluminum and magnesium, Jaffe said.
	www.space.com /scienceastronomy/blackhole_vlt_040507.html (601 words)

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