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Topic: Hyperboloid

Related Topics

Hyperboloid of two sheets

Ruled surface

Quadric

Mean curvature

Cone (solid)

Minimal surface

Surface of revolution

Curvature

Soap film

Riemann surface

Hyperbola

Hyperbolic geometry

Trilateration

Parabola

Conic section

	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 (321 words)

	Connector Specifier - Medical connectors require reliability and long life
		The hyperboloid design is constructed from a series of beryllium copper wires that stretch to accommodate the pin upon insertion.
		Hyperboloid contacts are capable of withstanding extreme levels of shock and vibration while guaranteeing signal integrity, one of the main reasons that they are popular in industrial and aerospace applications.
		Due to the hyperboloid socket design, specifically the 360º wrap provided by the spring wires, immunity to high levels of shock and vibration is guaranteed even when measured over periods as small as 5 ns.
	cs.pennnet.com /Articles/Article_Display.cfm?Article_ID=204845&pc=gls (1508 words)

	Hyperboloid - Wikipedia, the free encyclopedia
		In mathematics, a hyperboloid is a quadric, a type of surface in three dimensions, described by the equation
		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 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 (247 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 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.
		Antoni Gaudi used structures in the form of hyperbolic paraboloid (hypar) and hyperboloid of revolution in the Sagrada Familia in 1910 [1].
		The vault of one of the stables at the Church of Colònia Güell appears to be a hyperboloid.
	en.wikipedia.org /wiki/Hyperboloid_structure (993 words)

	The Hyperboloid
		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.
		A hyperboloid of one sheet is parameterized by:
	www.math.hmc.edu /~gu/curves_and_surfaces/surfaces/hyperboloid.html (129 words)

	HexDome - Bridges
		The hyperboloid is a simple tensile structure, which I believe has - or should have - substantial significance for bridge builders.
		The hyperboloid is one of the two "doubly ruled" structures.
		As far as I know the best-known segmented hyperboloid structure is a tower in Russia: the [Shukhov tower].
	hexdome.com /bridges (385 words)

	Hyperboloid Wire Basket Connector Technology Provides High-Performance Interconnect Solutions (Site not responding. Last check: 2007-10-28)
		Hyperboloid wire basket connector technology has for a long time been used by the rail industry due to its ability to carry high currents and maintain signal integrity even under extreme levels of shock and vibration.
		Since the angle of the socket wires in the hyperboloid cage is inherently set by the design of the contact, tightcontrol of pin insertion and extraction forces is possible.
		Hyperboloid contacts have about half the resistance of conventional contact design, resulting in lower power consumption and reduced heat generation, which are important in power-sensitive applications or where heat generation causes problems in confined spaces.
	www.nasatech.com /Briefs/Oct04/HYPERTRONICS.html (880 words)

	Four Lines (Site not responding. Last check: 2007-10-28)
		In case (d) the interlacing of four lines consists of four generatrices of the hyperboloid, and is obviously isotopic to the left or the center interlacing in Figure 23.
		If the fourth line does not intersect the hyperboloid, then it can be brought in toward the hyperboloid until it is tangent to the hyperboloid, i.e., the first case can easily be reduced to case (b).
		Now if the fourth line intersects the hyperboloid in two pints, then everything depends on whether these points are in the same part of the hyperboloid into which the first three lines divide it, or are in different parts (the hyperboloid is divided into three sections).
	www.math.uu.se /~oleg/skewlines/Four_Lines.html (742 words)

	Hyperboloidal Mirrors
		Rees, 1970] appears to have been first to use a hyperboloidal mirror with a perspective lens to achieve a large field of view camera system with a single viewpoint.
		Yamazawa et al., 1995] also recognized that the hyperboloid is indeed a practical solution and implemented a sensor designed for autonomous navigation.
		The hyperboloidal mirror satisfies the fixed viewpoint constraint when the pinhole and the viewpoint are located at the two foci of the hyperboloid.
	homepages.inf.ed.ac.uk /rbf/CVonline/LOCAL_COPIES/BAKER/node10.html (160 words)

	The Shukhov Tower Foundation (Site not responding. Last check: 2007-10-28)
		The shape of the Vortex is a hyperboloid of revolution: a slightly tapering column twisted to create the "waist" in the centre of the tower.
		The first hyperboloid tower by Shukhov was presented at the All-Russia exhibition in Nizhniy Novgorod in 1896.
		The most known hyperboloid tower from Shukhov is located on Shabolovka in Moscow and has the height of 160 meters.
	www.shukhov.ru /eng/news.html?n=8&id=1 (477 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)

	HYPERBOLOID Results Page
		HYPERBOLOID is a plasma spectrometer aimed at the investigation of the low energy ions dynamics in the polar ionosphere and magnetosphere on the INTERBALL Auroral Probe.
		Ion escape processes are frequently observed by HYPERBOLOID in the auroral and polar regions.
		Here, H+ ion escape is most clearly visible on the time/energy spectrogram (second spectrogram from bottom) between 22:28 and 22:40, and 22:52 and 23:00 UT. The spin-averaged moments displayed in the upper panel exhibit H+ escape velocities (Vx component, anti-parallel to the local geomagnetic field, blue curve) up to 30 km/s.
	www.iki.rssi.ru /auroral/hyper.htm (633 words)

	and Hyperboloids (Site not responding. Last check: 2007-10-28)
		The surface can be obtained by the revolution of a hyperbola around an axis of symmetry, and so is called a two-sheeted hyperboloid The intersections of planes with this hyperboloid can also be classified as ellipses, hyperbolas and parabolas, with the exception of some degenerate cases.
		We shall denote the upper sheet of the hyperboloid
		on the hyperboloid is the intersection of the hyperboloid and the plane determined by the origin and
	www.math.okstate.edu /~wrightd/INDRA/conics/node3.html (271 words)

	Quadratic surfaces of revolution (via CobWeb/3.1 planetlab2.tamu.edu) (Site not responding. Last check: 2007-10-28)
		Axis of revolution is the hyperboloid axis, hyperboloid is inside the asympthotic conical surface.
		Elliptic intersection of the hyperboloid of revolution can be constructed in the same way as the elliptic intersection of the ellipsoid of revolution.
		intersects hyperboloid of revolution in the major vertices A, B of the intersection hyperbola.
	www.km.sjf.stuba.sk.cob-web.org:8888 /Geometria/PREDNASKY/lecture8.htm (1499 words)

	Xah: Special Plane Curves: Hyperbola
		A hyperbola revolving around its transverse axis forms a surface called hyperboloid.
		Ruled surfaces are surfaces that for every point on the surface, there is a line on the surface passing it.
		There are only 3 doubly ruled surfaces: The hyperboloid, hyperbolic paraboloid, and plane.
	xahlee.org /SpecialPlaneCurves_dir/Hyperbola_dir/hyperbola.html (702 words)

	Vladimir Shukhov and the Invention of Hyperboloid Structures (Site not responding. Last check: 2007-10-28)
		Besides the innovations he brought to the oil industry and the construction of numerous bridges and buildings, he was the inventor of a new family of doubly-curved structural forms.
		Shukhov developed not only many varieties of light-weight hyperboloid towers and roof systems, but also the mathematics for their analysis.
		Unfortunately Shukhov’s work is poorly known today, particularly in the West; however, his direct influence may be seen in the work of two of the most important artist-architects of his time, as well as, more recently, two Western engineers.
	www.pubs.asce.org /WWWdisplay.cgi?0510374 (139 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.
		Having said all that, this is a shape familiar to any fan of the Simpsons, or even anybody who has only seen the beginning of the show.
	www.math.umn.edu /~rogness/quadrics/hyper1.shtml (489 words)

	[No title]
		The other spacetime, coming from a hyperboloid in the flat 5d spacetime with metric of signature (+ + - - -), is also maximally symmetric, and its isometry group is the 10-dimensional group SO(2,3).
		With the hyperboloid definition of dS, its topology is RxS^3.
		As it turns out, everyone's right, according to his or her own definition of "de Sitter space" and "spatially finite." When cosmologists talk about de Sitter space, we slice it up into constant-time hypersurfaces that are spatially flat and infinite.
	www.math.niu.edu /~rusin/known-math/00_incoming/universe (1835 words)

	Surface -- Hyperboloid of Two Sheets (Site not responding. Last check: 2007-10-28)
		The axis of rotation of a hyperboloid of two sheets is coincident with the x' -axis.
		Note: If a single-sheet hyperboloid, rather than the default double-sheet hyperboloid, is desired, you must use the {x'
		Example of a two-sheet hyperboloid HYP2 with a-, b-, and c-parameters of.5,.35, and.35 respectively.
	www-phys.llnl.gov /N_Div/COG/Manual/Surface/HyperboloidOfTwoSheets.html (149 words)

	IngentaConnect Comparison of hyperbolic and hyperboloid conductor electrostatics (Site not responding. Last check: 2007-10-28)
		The potentials and fields of hyperbolic and hyperboloidal conductors are available analytically.
		The electric field near a hyperboloidal needle is stronger (ceteris paribus) than near a hyperbolic blade, and dies off faster.
		At the hyperboloid conductor the field varies as the 1/4 power of the local Gaussian curvature (which is the product of the two principal curvatures).
	www.ingentaconnect.com /content/iop/ejp/2006/00000027/00000001/art00009 (152 words)

	Surface -- Hyperboloid of One Sheet (Site not responding. Last check: 2007-10-28)
		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)

	Hyperboloids - definition from Biology-Online.org
		Hyperboloid of revolution, an hyperboloid described by an hyperbola revolving about one of its axes.
		The surface has two separate sheets when the axis of revolution is the transverse axis, but only one when the axis of revolution is the conjugate axis of the hyperbola.
		Having some property that belongs to an hyperboloid or hyperbola.
	www.biology-online.org /dictionary/Hyperboloids (161 words)

	Gateway To Russia - Article - The Siberian Hyperboloid (Site not responding. Last check: 2007-10-28)
		In a science fiction novel by Alexei Tolstoi, the hyperboloid invented by engineer Garin cut literally everything — the author imagined no limits to its power.
		Of course, the hyperboloid has yet to be invented so far, and enhancing lasers’ power remains one of the main problems for scientists.
		For the first time in history, scientists have built an 8 KW “Siberian hyperboloid.” It can cut through a 30-mm titanium sheet beautifully, while regular Western specimens cut sheets of no more than 7 mm thick.
	www.gateway2russia.com /st/art_165951.php (1366 words)

	Polymorf - Knowhere - Hyperboloid cylinders (Site not responding. Last check: 2007-10-28)
		Likewise, variations of the Tri-1 spaceframe whose unit cells were shown in Fig.
		d) previously, can be destabilized in a similar fashion to create hyperboloids.
		The hyperboloid cylinder design is commonly used for cooling towers.
	www.polymorf.net /engineer76.htm (162 words)

	Electrical connectors solutions and hyperboloid contacts - Hypertac
		Hypertac is part of the Smiths group and it has offices in Italy, France, Germany, UK, the USA, Japan and China and a global network of agents and distributors.
		Product range from PCB to modular, rectangular and circular connectors, and they are built upon the superior Hyperboloid contact technology, ideal for harsh environment where high reliability and safety are crucial.
		Hypertac experience in signal and power connectors results in customer-driven, reliable solutions with an easy use and unlimited application possibilities.
	www.hypertac.com (347 words)

	Mathematical Physics Final Honours and Diploma General Relativity Some Two Dimensional Surfaces
		It is perhaps not quite so clear, but will assumed here anyway, that the hyperboloid is also isotropic about every point.
		is a 3-dimensional space, analogous to the hyperboloid.
		Just as the 2-dimensioanl sphere has a finite area and the flat plane and the hyperboloid have infinite area, so the 3-dimensional sphere has a finite volume and flat 3-dimensional space and the 3-dimensional hyperboloid have infinite volume.
	www.thphys.may.ie /staff/bdolan/gr-2d/gr-2d-html.html (738 words)

	JCMT Optical Constants
		The form of the hyperboloidal secondary in the same coordinate system is
		The dimensions of the telescope were fixed (as described in ASR/MT/T/634/REH(84)) by choosing values for D
		Other parameter values follow from these and from standard equations for paraboloids, hyperboloids and lenses; they and other dimensions of the JCMT are given in the tables below.
	www.jach.hawaii.edu /JCMT/telescope/pointing/optics.html (607 words)

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