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Topic: Hyperboloid of one sheet

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	Hyperboloid structure - Wikipedia, the free encyclopedia
		The hyperboloid roofs of the exhibition pavilions of the 1896 All-Russian Industrial and Handicrafts Exposition in Nizhny Novgorod were the first publicly prominent examples of Shukhov’s new system.
		A hyperboloid tower in the port of Kobe, Japan.
		The world’s first hyperboloid tower is located in Polibino of the Lipetsk region of Russia.
	en.wikipedia.org /wiki/Hyperboloid_structures (724 words)

	A hyperboloid of one sheet
		A drawing of the hyperboloid in which some of these lines are explicitly shown.
		A drawing of the hyperboloid and one of its tangent planes
		Note that the intersection of the hyperboloid and the tangent plane is a reducible plane conic -- accordingly, the union of two lines in the tangent plane.
	www.math.umn.edu /~roberts/java.dir/JGV/hyperboloid1a.html (190 words)

	Hyperboloid - Wikipedia, the free encyclopedia
		Alternatively, a hyperboloid of two sheets of axis AB is obtained as the set of points P such that AP−BP is a constant, AP being the distance between A and P. Points A and B are then called the foci of the hyperboloid.
		A hyperboloid of two sheets can be obtained by revolving a hyperbola around its focal axis.
		A hyperboloid of one sheet is a doubly ruled surface; if it is a hyperboloid of revolution, it can also be obtained by revolving a line about a skew line.
	en.wikipedia.org /wiki/Hyperboloid (216 words)

	hyperboloid
		A quadratic surface of which there are two basic forms: a hyperboloid of one sheet, generated by spinning a hyperbola around its conjugate axis, and a hyperboloid of two sheets produced by rotating a hyperbola about its transverse axis.
		This fact enables a close approximation to a hyperboloid to be made in the form of a string model.
		Hyperboloids are seen in the manmade world in the form of cooling towers at power stations and, most strikingly, in the shape of the McDonnell Planetarium in St. Louis, Missouri (shown above).
	www.daviddarling.info /encyclopedia/H/hyperboloid.html (323 words)

	The Hyperboloid (Site not responding. Last check: 2007-10-23)
		The hyperboloid is a well-known quadratic surface that comes in two varieties: the hyperboloid of one sheet (above) and the hyperboloid of two sheets (below).
		It is interesting to note that the hyperboloid of one sheet is asymptotic to a cone, as shown below.
		The hyperboloid of one sheet is also a ruled surface.
	www.math.hmc.edu /faculty/gu/curves_and_surfaces/surfaces/hyperboloid.html (129 words)

	References on Computational Geometry on Object Representations
		We show that all hyperboloids of one sheet and hyperbolic paraboloids can be represented by two lines.
		This representation makes it easier to use the hyperboloid of one sheet as a fundamental primitive like the sphere, including input, display and computations (such as rigid transformation and point classification).
		We extend to the bisector and weighted bisector of two skew lines with respect to a plane, and show that they exactly represent the hyperboloid of one sheet and the hyperbolic paraboloid.
	www.lems.brown.edu /vision/people/leymarie/Refs/CompGeom/Representations.html (954 words)

	IGQS: Hyperboloid of One Sheet
		The hyperboloid of one sheet is possibly the most complicated of all the quadric surfaces.
		For one thing, its equation is very similar to that of a hyperboloid of two sheets, which is confusing.
		A hyperboloid of one sheet looks an awful lot like a cooling tower at the Springfield Nuclear Power Plant.
	www.joma.org /images/upload_library/4/vol5/quadric/hyper1.html (489 words)

	Math 281 Animations
		The hyperboloid of one sheet and its horizontal traces
		The hyperboloid of one sheet and its vertical traces
		Hyperboliods of two sheets, a cone, and Hyperboloids of one sheet.
	grossmont.gcccd.cc.ca.us /jennyvandeneynden/archive/M281_links.htm (823 words)

	Index: Ruled Surfaces
		Some quadratic surfaces are ruled: hyperboloids of one sheet, hyperbolic paraboloids, and quadratic cones and cylinders.
		A general way to form a ruled surface is to take three curves in space, and move a straight line so that it intersects all three curves at all times.
		This procedure, applied to the three lines in one of the rulings of a hyperboloid of one sheet or a hyperbolic paraboloid, will give the other ruling.
	math.arizona.edu /~models/Ruled_Surfaces (194 words)

	Calculus II (Math 2414) - 3-Dimensional Space - Quadric Surfaces (Site not responding. Last check: 2007-10-23)
		Here is a sketch of a typical hyperboloid of one sheet.
		Here is a sketch of a typical hyperboloid of two sheets.
		Notice that the only difference between the hyperboloid of one sheet and the hyperboloid of two sheets is the signs in front of the variables. They are exactly the opposite signs.
	tutorial.math.lamar.edu /AllBrowsers/2414/QuadricSurfaces.asp (578 words)

	Quadratic Surfaces (1-14) (Site not responding. Last check: 2007-10-23)
		An elliptic hyperboloid is a solid or surface, some of whose plane sections are hyperbolas, while others are ellipses.
		If one of the elliptical cross-sections goes around the conjugate axis of one of the hyperbolic cross-sections, the hyperboloid has one sheet.
		The cross-sections in the coordinate planes may be seen by removing the octant.
	math.arizona.edu /~models/QuadraticSurfaces/source/6.html (63 words)

	Animated Demonstrations for Multivariable Calculus (Site not responding. Last check: 2007-10-23)
		The most difficult of the quadric surfaces for students to visualize, and certainly to draw, is the hyperbolic paraboloid.
		Like the hyperboloid of one sheet, the traces in certain planes are hyperbolas that change orientation after a point.
		whose level surface, f (x, y, z) = k, is a hyperboloid of two sheets when k < 0, a hyperboloid of one sheet when k > 0, and an elliptic cone when k = 0.
	archives.math.utk.edu /ICTCM/EP-10/C9/html/paper.html (1055 words)

	MAT 240 Calculus III Summer 2005
		Elliptic paraboloid.mw--aMaple worksheet that shows you how to plot an elliptic hyperboloid along with its cross sections in the coordinate planes and its level curves.
		Hyperboloid of one sheet.mw, Hyperboloid of two sheets.mw.
		Hyperboloid of one sheet.html, Hyperboloid of two sheets.html.
	glory.gc.maricopa.edu /~wkehowsk/240-Calculus-III-04-05-Su (190 words)

	Surgery Obstruction Groups
		this happens when a hyperboloid of one sheet passes trough a cone and becomes a hyperboloid of two sheets.
		D^1 x S^1, giving a hyperboloid of one sheet, or sew in a disjoint union of two discs,
		thus the process of a complex curve, or hyperboloid of one sheet, acquiring a singular point (vertex) then being desingularized by separating that vertex into two nappes, coulod be achieved by a simple surgery.
	www.physicsforums.com /showthread.php?referrerid=35074&t=68933 (975 words)

	St. Louis Science Center Planetarium Hyperboloid (Site not responding. Last check: 2007-10-23)
		The St. Louis Science Center Planetarium's HYPERBOLOID OF ONE SHEET exterior curved surface was conceived by Mr.
		His wife played an integral part in the early design concept when she held parts of the model in the air while the design sketches were completed.
		A mathematical model of a hyperboloid of revolution of one sheet is a hyperboloid of one sheet where a cross section perpendicular to the axis of revolution is a circular region and a cross section through the axis is a hyperbola of the form x
	www.jug.net /wt/slscp/pprob5.htm (372 words)

	Screenshots (Site not responding. Last check: 2007-10-23)
		This is the first development of a Hyperboloid of One Sheet model.
		In the middle screenshot, the cylinder has been twisted to a degree to illustrate a hyperboloid of one sheet.
		In the rightmost screenshot, the cylinder has been twisted 180 degrees, to show the transformation from a hyperboloid to a conoid.
	www.vu.union.edu /~pinchg/seniorproject/documentation/screenshots.html (462 words)

	IGQS: Hyperboloid of Two Sheets
		The hyperboloid of two sheets looks an awful lot like two (elliptic) paraboloids facing each other.
		Here's a hint about telling the two kinds of hyperboloids apart: look at the cross sections x=0, y=0, and z=0.
		If they exist, then it's a hyperboloid of one sheet.
	www.joma.org /images/upload_library/4/vol5/quadric/hyper2.html (309 words)

	Hyperboloid Through the Three Tangent Lines (Site not responding. Last check: 2007-10-23)
		The lines meeting these three lines form a ruling of the quadric (here a hyperboloid of one sheet) through the three lines.
		Each intersection of this hyperboloid with a fourth line gives a line meeting all four.
		Any line tangent to the rational normal curve at a real point meets the hyperboloid in two real points.
	www.math.tamu.edu /~sottile/talks/04/TARAG/9.html (84 words)

	Mathematical Experiment 2 (Site not responding. Last check: 2007-10-23)
		Construct the hyperboloid of one sheet by rotating the line segment joining the point [cos t, sin t, 1] with the point [cos (a+t), sin(a+t), -1] about the z-axis, Here a is some given constant.
		Decompose the hyperboloid of one sheet into two disjoint, symmetric parts with the straight line as boundary.
		Construct the hyperboloid of two sheets given by the equations
	steiner.math.nthu.edu.tw /disk3/exp01/work/x37/Exp.02.htm (119 words)

	Surface -- Hyperboloid of One Sheet (Site not responding. Last check: 2007-10-23)
		A hyperboloid of one sheet is specified by:
		HYP1 (or H1) is the keyword identifying the surface type;
		The hyperboloid axis is coincident with the x' axis.
	www-phys.llnl.gov /N_Div/COG/Manual/Surface/HyperboloidOfOneSheet.html (199 words)

	The Fitful Flog » 2005 » August (Site not responding. Last check: 2007-10-23)
		This one has a one-sheet hyperboloid at the top and an iris closure.
		That’s kind of a pun, you know - a one-sheet hyperboloid made with just one sheet of paper.
		This is the same in construction - see the hints sheet below - and is actually rather easier to collapse, as the overlap in the middle is graspable.
	origami.oschene.com /archives/2005/08 (1450 words)

	Ruled Surfaces
		A variation of the cylinder yields a hyperboloid of one sheet.
		What we need to do is rotating one of the two circles about the z-axis some degree.
		After sending this design to the surface system, we shall see the following hyperboloid of one sheet on the drawing canvas.
	www.cs.mtu.edu /~shene/COURSES/cs3621/LAB/surface/ruled.html (638 words)

	[No title] (Site not responding. Last check: 2007-10-23)
		In three-dimensional Euclidean space, there are 16 such normalized forms, and the most interesting are the following:
		In real projective space, the ellipsoid, the elliptic paraboloid and the hyperboloid of two sheets are equivalent to each other up to a projective transformation; the two hyperbolic paraboloids are not different from each other ; the cone and the cylinder are not different from each other (these are "degenerate" quadrics, since their
		In complex projective space all of the nondegenerate quadrics become indistinguishable from each other.
	www.brujula.net /english/wiki/Quadric.html (172 words)

	Eigenspaces of the Laplace-Beltrami operator on a hyperboloid, Jirō Sekiguchi
		Eigenspaces of the Laplace-Beltrami operator on a hyperboloid, Jirō Sekiguchi
		Eigenspaces of the Laplace-Beltrami operator on a hyperboloid
		[10] S. Matsumoto, K. Hiraoka and K. Okamoto, Eigenfunctions of the laplacian on a real hyperboloid of one sheet, Hiroshima Math.
	projecteuclid.org /getRecord?id=euclid.nmj/1118786176 (269 words)

	lesson09.html
		Any surface given by the equation q=0 belongs to one of the following 14 types:
		ellipsoid, hyperboloid of one sheet, hyperboloid of two sheets, elliptic paraboloid, hyperbolic paraboloid, conic surface, elliptic cylinder, hyperbolic cylinder, parabolic cylinder, 2 intersecting planes, 2 parallel planes, 1 plane, 1 point and empty place.
		The first 9 types are called non-degenerate, and they represent genuine curvilinear surfaces; the last 5 types are made up of straight-line objects.
	www.botik.ru /~duzhin/maple/lesson091.html (923 words)

	Quadric Surfaces
		The general form for the equation of the ellipsoid is
		The general form for the equation of the hyperboloid of one sheet is
		The general form for the equation of the hyperboloid of two sheets is
	www2.norwich.edu /frey/LiveGraphics3D/QuadricSurfaces.htm (228 words)

	origami.com \| Origami Listserv Search (Site not responding. Last check: 2007-10-23)
		>Joseph, your description IS clear, but it sounds more like a hyperboloid of
		I'll have to fold one and see what happens.
		Joseph Wu Witty quote is now back to the
	dev.origami.com /email/viewmessage.asp?id=156893 (116 words)

	The Geometry Junkyard: All Topics
		John Conway answers a question of Doug Zare on the polyhedra that can form periodic tilings of 3-dimensional hyperbolic space.
		A hyperboloid in Kobe, Japan, in the 1940s.
		Rick Nordal challenges folders to make a sequence of geometric shapes with a single sheet of origami paper as quickly as possible.
	www.ics.uci.edu /~eppstein/junkyard/all.html (9734 words)

	The GNU 3DLDF One-Sheet Hyperboloids Page (Site not responding. Last check: 2007-10-23)
		A copy of this license is included in the file COPYING.TXT
		Intersection of an One-Sheet Hyperboloid and a Line
		Intersection of an One-Sheet Hyperboloid and a Plane
	www.gnu.org /software/3dldf/hypdone.html (113 words)

	electrical connectors -- electrical connectors (Site not responding. Last check: 2007-10-23)
		Electrical connectors, interconnect solutions and hyperboloid contacts from...
		Flexible Electrical Connectors Flexible Electrical Connectors, Flexible Bus, Ground Straps and Flex Busbar are just some of the products produced by Storm Copper Components Co. to improve the...
		Electrical connectors solutions and hyperboloid contacts - Hypertac
	www.fddconnector.com /electricalconnectors (3402 words)

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