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Topic: Surface of revolution

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	PlanetMath: area of surface of revolution
		A surface of revolution is a 3D surface, generated when an arc is rotated fully around a straight line.
		The general surface of revolution is obtained when the arc is rotated about an arbitrary axis.
		This is version 6 of area of surface of revolution, born on 2006-02-26, modified 2006-06-03.
	www.planetmath.org /encyclopedia/SurfaceOfRevolution.html (258 words)

	PlanetMath: surface of revolution
		of the surface of revolution and therefore it is the equation of the whole surface of revolution.
		surface of revolution, axis of revolution, circle of latitude, meridian curve, 0-meridian, cone of revolution, asymptote cone
		This is version 5 of surface of revolution, born on 2007-06-20, modified 2007-06-28.
	planetmath.org /encyclopedia/MeridianCurve.html (284 words)

	Surface of revolution - Wikipedia, the free encyclopedia
		A surface of revolution is a surface created by rotating a curve lying on some plane (the generatrix) around a straight line (the axis of rotation) that lies on the same plane.
		Examples of surfaces generated by a straight line are the cylindrical and conical surfaces.
		Applications of surfaces of revolution The use of surface of revolutions is essential in many fields in physics and engineering.
	en.wikipedia.org /wiki/Surface_of_revolution (260 words)

	Rotating surface of revolution reactor with feed and collection mechanisms - Patent 7014820
		A surface of the impeller or fan facing the rotating surface of the support element may be provided with blades or vanes such that rotation of the impeller or fan serves to suck the gaseous phase component from a periphery of the surface and the impeller or fan towards the centre of the surface.
		Reference herein to a rotating surface is to any continuous or discrete planar or three-dimensional surface or assembly which rotates approximately or truly about an axis, and preferably is reference to an approximate or true rotating surface of revolution.
		The facing surfaces of the support elements may be provided with at least one generally circular wall defined about the axis of rotation, and preferably a plurality of concentric walls, the walls being divergent with respect to the axis of rotation of their respective support element.
	www.freepatentsonline.com /7014820.html (6531 words)

	Surfaces of Revolution
		At a radial distance of r, the surface is restricted to a thin band with circumference 2πr.
		The surface area is multiplied by the length of the upward vector, which has components 1,f′(r).
		There are other formulas for surfaces of revolution that are based on the centroid.
	www.mathreference.com /ca-surf,rot.html (380 words)

	Area - Wikipedia, the free encyclopedia
		Area is a physical quantity expressing the size of a part of a surface.
		Surface area is the summation of the areas of the exposed sides of an object.
		Surface area of a sphere of radius r or diameter d
	en.wikipedia.org /wiki/Surface_area (298 words)

	[No title] (Site not responding. Last check: 2007-10-19)
		A second helical surface of revolution is defined between the secondary and tertiary flights, and a third helical surface of revolution is defined between the primary and tertiary flights.
		In the preferred embodiment of the present invention, the first surface of revolution cooperates with the primary and secondary flights to form a melt channel for conveying the resinous material in a molten state, along the barrier section of the extruder screw.
		The second solids channel 50 is defined by the cooperation of a third retreating surface 68 of the tertiary flight 62, the second advancing surface 54 of the secondary flight 48 and a second helical surface of revolution 70 defined by the screw body 38 and located between the third retreating and second advancing surfaces.
	www.wipo.int /cgi-pct/guest/getbykey5?KEY=01/17750.010315&ELEMENT_SET=DECL (3672 words)

	Surfaces of Revolution
		A surface of revolution is generated by revolving a given curve about an axis.
		Note that the intersection point of the profile curve and the axis of revolution becomes the vertex (or apex) of the cone.
		The torus is another well-known surface of revolution and is generated by revolving a circle about an axis.
	www.cs.mtu.edu /~shene/COURSES/cs3621/LAB/surface/rev-surf.html (636 words)

	Creating a revolution surface (Site not responding. Last check: 2007-10-19)
		By default, a revolution is a rounded shape, but you can change it to an angled surface by reducing the number of subdivisions.
		This is true as long as the revolution's geometry is not altered, for example by moving points or manipulating the revolution's center, in which case the original curve loses its influence.
		When you choose Other axis for the Revolution around parameter, this is the axis that the curve revolves around to create a surface.
	www.mindavenue.com /en/support/onlineHelp/04_mod23.htm (477 words)

	Surfaces of revolution (Site not responding. Last check: 2007-10-19)
		It is a plane curve (a pair of plane curves) symmetric with respect to the axis of the surface of revolution.
		Tangent cylindrical surface is tangent to the surface of revolution in the parallel circle, in the points of which there exist common tangent planes to both surfaces parallel to the axis o of the surface of revolution.
		Ground view of the surface of revolution appears as the part of the plane inbetween two concentric circles, which are views of the surface parallel circles of the extremal radii (minimal and maximal), Fig.
	www.km.sjf.stuba.sk /Geometria/PREDNASKY/lecture7.htm (1610 words)

	Surface Construction Schemes
		A ruled surface interpolates to two boundary curves -a rectangular surface, however, has four boundary curves, and that is precisely what a Coons patch interpolates to.
		The idea behind the construction of this Gordon surface g is the same as for the Coons patch: find a surface g1 that interpolates to one family of isoparametric curves, for instance to the g(ui, v).
		A sweep surface of this curve should contain all the curves generated by rotating this curve, and its horizontal cross sections should always be circles.
	www.math.hmc.edu /~gu/math142/mellon/Application_to_CAGD/Surface_Construction_Schem.html (2564 words)

	15 Surfaces of Revolution. The Torus (Site not responding. Last check: 2007-10-19)
		A surface of revolution is formed by the rotation of a planar curve C about an axis in the plane of the curve and not cutting the curve.
		The volume bounded by the surface of revolution on a simple closed curve C is equal to the product of the area bounded by C and the length of the path traced by the centroid of the area bounded by C.
		When C is a circle, the surface obtained is a circular torus or torus of revolution (Figure 1).
	www.geom.uiuc.edu /docs/reference/CRC-formulas/node60.html (174 words)

	Surface of Revolution (Site not responding. Last check: 2007-10-19)
		This is our “intuitive” result and there could be other ways to find the surface area of a object; or this method might fail to apply on some cases. Thus, we need to think about the condition that every step can hold. The simplest conjecture is that
		b]. Then the surface generated by rotating the curve y= f(x) along x-axis is with area
		, r > 0. Find the surface area by rotating E along x-axis.
	www.scienceoxygen.com /mathnote/calculus224.html (187 words)

	16 Quadrics
		Surfaces with equations (9) --(17) are cylinders over the planes curves of the same equation (Section 13.2).
		A surface with equation (5) can be regarded as a cone (Section 13.3) over a conic C (any ellipse, parabola or hyperbola can be taken as the directrix; there is a two-parameter family of essentially distinct cones over it, determined by the position of the vertex with respect to C).
		The surfaces with equations (1) --(6) are central quadrics; in the form given, the center is at the origin.
	www.geom.uiuc.edu /docs/reference/CRC-formulas/node61.html (363 words)

	Isosurface Tutorial: i_algbr Library part 2
		The 2d version of the Lemniscate can be extruded in the Z direction, or used as a surface of revolution to generate the equivalent of the 3d version, or revolved in different ways.
		I've cut the surface in half so that you can see the figure-of-eight curve that sweeps round the Y axis to generate this surface of revolution.
		The 2d version of the Piriform can be extruded in the Z direction, or used as a surface of revolution to generate the equivalent of the 3d version, or revolved in different ways.
	www.econym.demon.co.uk /isotut/builtin3.htm (783 words)

	math lessons - Surface of revolution
		A surface of revolution is a surface created by rotating a curve lying on some plane (the generatrix) around a straight line (the axis of revolution) that lies on the same plane.
		Examples of surfaces generated by a straight line are the cylindrical and conical surfaces.
		For example, the spherical surface with unit radius is generated by the curve x(t)=sin(t), y(t)=cos(t), when t ranges over [0,π].
	www.mathdaily.com /lessons/Surface_of_revolution (137 words)

	Isosurface Tutorial: i_nfunc library part 1
		The f_blob2 surface is similar to a CSG blob with two spherical components.
		The f_cross_ellipsoids surface is like the union of three crossed ellipsoids, one oriented along each axis.
		This function can be used to generate the surface of revolution of any polynomial up to degree 4.
	www.econym.demon.co.uk /isotut/nfunc.htm (542 words)

	Gallery - Geometric Surface Models
		The surface is known for the presence of 2 of more folds formed by the application of a cylindrical equation to the line during this rotation.
		The ruled hyperboloid is a surface of revolution formed by rotating a line about the perpendicular axis.
		The ellipsoid is a quadratic surface that is composed of a number of elliptic curves swept along a given axis, usually z.
	www.btinternet.com /~krys1/gallery/vrml_geo1.html (634 words)

	Solid of revolution: Facts and details from Encyclopedia Topic (Site not responding. Last check: 2007-10-19)
		This is used when the slice that was drawn is perpendicular to the axis of revolution.
		This is used when the slice that was drawn is parallel to the axis of revolution.
		A surface of revolution is a surface created by rotating a curve lying on some plane (the generatrix) around a straight line (the axis of revolution)...
	www.absoluteastronomy.com /encyclopedia/s/so/solid_of_revolution.htm (1425 words)

	ICEM \| products \| ICEM Style \| functionality \| modelling
		Surface creation tools that quickly allow the designer to experiment and build geometry, with history support and bookmark capability.
		Create a surface fillet between multiple surfaces and use ICEM Style's powerful tools to control all aspects of the resultant surface.
		Create surfaces by sweeping numbers of curves along rails and controlling the start end points and the level of continuity.
	www.icem.com /text.asp?PageId=428 (701 words)

	SSD - Revolution, Niche, or Revolutionary Niche - Midwest Printed Circuit Services, Inc.
		Originally SSD was touted as a revolution that was to shift the solder paste process from the printed circuit assembler to the fabricator.
		The surface mount component land pattern pitch was a minimum of 0.035 and the connector was 0.020" pitch.
		If both side surface mount parts can be placed at once using glue or in many cases, the bottom side parts are small and can be supported by the flux adhesive, then double-sided boards can benefit from SSD.
	www.midwestpcb.com /sales/kehoe/Niche.html (1731 words)

	[No title]
		Therefore, the circumference of this surface is C = 2
		The width of this rectangle is the length of the plane curve.
		As you can see, the integral for finding the surface area of a solid of revolution is based on the integral to find the length of a plane curve.
	faculty.eicc.edu /bwood/math150supnotes/supplemental29.html (290 words)

	Intersections of elementary surfaces (Site not responding. Last check: 2007-10-19)
		Intersections of these lines on one surface and related edges on the other one, all located in one of the auxhiliary vertex plane are vertices of the intersection polygon.
		Orthogonal axonometric view of the total intersection of the conical surface of revolution and cylindrical surface of revolution is illustrated in obr.
		Intersection of sphere and conical or cylindrical surface, which is not the surface of revolution, BR> can be determined as a set of intersection points of lines on the concerned surface with the sphere by means of the system of auxhiliary planes.
	www.km.sjf.stuba.sk /Geometria/PREDNASKY/eleminter.htm (1619 words)

	The Eight Surface (Site not responding. Last check: 2007-10-19)
		The surface pictured above is called an eight surface because it is a surface of revolution of a figure eight.
		The surface comes to a point at its very center, which causes problems in the VRML version of the surface (you may receive a series of warnings when you view it).
		Note also that the mean curvature becomes infinitely large at the center of the surface, and the surface can thus not be colored by mean curvature.
	www.math.hmc.edu /faculty/gu/math142/mellon/curves_and_surfaces/surfaces/eightsurf.html (139 words)

	Surface Logix, Inc.
		Surface Logix Inc. uses its expertise in biophysical chemistry to create new small molecule drugs that are optimized to meet the challenges of human physiology.
		Surface Logix Commences Phase I Trial for Novel Gastrointestinal-Specific MTP Inhibitor.
		Surface Logix appoints Steven Gillis, Ph.D. to Board of Directors.
	www.surfacelogix.com (73 words)

	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 surface area and interior volume of this torus are given by
		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.
	en.wikipedia.org /wiki/Torus (719 words)

	LESSON 27 (Site not responding. Last check: 2007-10-19)
		A surface of revolution is the lateral boundary of a solid of revolution.
		The area of this surface can be computed using the same principle that we used to measure the length of arc.
		The strip of surface corresponding to this subinterval is approximated by the frustum of cone that results from rotating the line segment from
	www.msri.org /people/members/ljuan/teaching/calc2/92app.htm (216 words)

	Surfaces of Revolution (Site not responding. Last check: 2007-10-19)
		A surface of revolution is a surface generated by revolving a plane curve C about a line L lying in the same plane as the curve.
		In order to construct a surface of revolution using a parametric equation, it is important to first understand how a circle is constructed in the plane since the surface is made up of a series of circles at various heights.
		In a surface of revolution, the radius may be different at each height, so if the radius at height v is r(v), then the equation of the surface is
	www.math.union.edu /research/student/1998/tolin/surf-rev.htm (174 words)

	Revolution - Dictionary Definition and Meaning of Revolution
		The space measured by the regular return of a revolving body; the period made by the regular recurrence of a measure of time, or by a succession of similar events.
		The violence of revolutions is generally proportioned to the degree of the maladministration which has produced them.
		Note: When used without qualifying terms, the word is often applied specifically, by way of eminence, to: (a) The English Revolution in 1689, when William of Orange and Mary became the reigning sovereigns, in place of James II.
	www.wordiq.com /reference/revolution (438 words)

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