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Topic: Hyperbolic paraboloids

Related Topics

Paraboloid

Ruled surface

Hyperboloid

Mean curvature

Minimal surface

Riemann surface

Hyperbola

Cartesian coordinate system

Calculus of variations

Curve

Klein bottle

Conic section

Hyperbole

List of curves

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	Structural building components incorporating integrated hyperbolic paraboloid elements - Patent 5020287
		The hyperbolic paraboloid configuration has been utilized successfully for a number of years in the building industry and has been applied in the shape of the potato chip presently marketed under the trademark Pringle.
		The principal object of the invention is to provide a family of structural building components formed from a plurality of integrated hyperbolic paraboloid elements which have a common midpoint and linear edges and allow for the prestressing of reinforcing elements along straight lines.
		The hyperbolic paraboloid elements B used in the tetralith A are designed so that from any given point on the surface of the element B two straight lines can, respectively, be projected between opposing linear edges through that point.
	www.freepatentsonline.com /5020287.html (2436 words)

	Paraboloid - Wikipedia, the free encyclopedia
		The hyperbolic paraboloid is shaped like a saddle and can have a critical point called a saddle point.
		With a = b an elliptic paraboloid is a paraboloid of revolution: a surface obtained by revolving a parabola around its axis.
		A daily life example of a hyperbolic paraboloid is the shape of a Pringles potato chip.
	en.wikipedia.org /wiki/Paraboloid (350 words)

	Quadric
		hyperbolic paraboloid of one sheet: $x^2/a^2 + y^2/b^2 - z^2/c^2 = 1$
		hyperbolic paraboloid of two sheets: $x^2/a^2 - y^2/b^2 - z^2/c^2 = 1$
		In real projective space, the ellipsoid, the elliptic hyperboloid, and the elliptic paraboloid are not different from each other; the two hyperbolic paraboloids are not different from each other (these are ruled surfaces[?]); the cone and the cylinder are not different from each other (these are "degenerate" quadrics, since their Gaussian curvature[?] is zero).
	www.ebroadcast.com.au /lookup/encyclopedia/qu/Quadric.html (270 words)

	Structural solar collector - Patent 4291679
		The upper surface of the building, e.g., roof or portion of the roof, is constructed in the form of a hyperbolic paraboloid having a concave surface directed in a specified, for example, southerly, direction.
		A hyperbolic paraboloid is a geometric shape of the class having double opposed curvature.
		12 is a representation of a hyperbolic paraboloid oriented with respect to the path of the sun such that the sun's rays are focused along an arc.
	www.freepatentsonline.com /4291679.html (4487 words)

	IGQS: Hyperbolic Paraboloid (Site not responding. Last check: 2007-10-10)
		Hyperbolic paraboloids are often referred to as "saddles," for fairly obvious reasons.
		All of these are important features of any hyperbolic paraboloid.
		Be very careful; if you hear somebody refer simply to a "paraboloid," they generally mean an elliptic paraboloid, or even a surface where A=0 or B=0.
	www.math.umn.edu /~rogness/quadrics/hypparab.shtml (289 words)

	The Church
		One of the innovative principles of the church is the introduction, for the first time in the history of architecture, of surfaces in the shape of a hyperbolic paraboloid, used both for the walls and the vaults that join the arches of the porch.
		Moreover, in the porch, the hyperbolic paraboloids enable the creation of vaults that are both concave and convex.
		All that was necessary, was to create a structure with wooden planks that corresponded to straight lines from which the curved surface of the hyperbolic paraboloid was generated.
	www.elbaixllobregat.net /coloniaguell/english/esglesia.asp (1373 words)

	Tetranometry
		Both the hyperbolic and the parabolic shapes were defined but apparently the combined shape of the hyperbolic paraboloid was not addressed in a manner that recognized that the surface of a warped plane generated from straight line elements can define the vertices or points of a tetrahedron.
		These particular hyperbolic paraboloids have vertices which are located equal distance apart and their edges are equal in length.
		Photo #2 pictures three separate hyperbolic paraboloids before they are merged and a tetralith which has been assembled by merging three hyperbolic paraboloids.
	www.tetranometry.com (1541 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)

	IGQS: Elliptic Paraboloid (Site not responding. Last check: 2007-10-10)
		This is probably the simplest of all the quadric surfaces, and it's often the first one shown in class.
		This surface is called an elliptic paraboloid because the vertical cross sections are all parabolas, while the horizontal cross sections are ellipses.
		Occasionally we get sloppy and just refer to it simply as a paraboloid; that wouldn't be a problem, except that it leads to confusion with the hyperbolic paraboloid.
	www.math.umn.edu /~rogness/quadrics/ellparab.shtml (262 words)

	Hyperbolic Paraboloids (Erik Demaine)
		A hyperbolic paraboloid is an infinite surface in three dimensions with hyperbolic and parabolic cross-sections.
		We use the term hypar to mean a hyperbolic paraboloid shape, or more formally a partial hyperbolic paraboloid, cut from the full infinite surface.
		This material is based on the paper ``Polyhedral Sculptures with Hyperbolic Paraboloids,'' which was presented at the 2nd Annual Conference of BRIDGES: Mathematical Connections in Art, Music, and Science, 1999.
	theory.lcs.mit.edu /~edemaine/hypar (566 words)

	Wikinfo \| Quadric
		elliptic paraboloid: x2/a2 + y2/b2 - z = 0
		hyperbolic paraboloid of one sheet: x2/a2 + y2/b2 - z2/c2 = 1
		hyperbolic paraboloid of two sheets: x2/a2 - y2/b2 - z2/c2 = 1
	www.wikinfo.org /wiki.php?title=Quadric (346 words)

	Abstract, Nexus 2000, Alessandra Capanna: Conoids and Hyperbolic Paraboloids in Le Corbusier's Philips Pavilion (Site not responding. Last check: 2007-10-10)
		Conoids and Hyperbolic Paraboloids in Le Corbusier's Philips Pavilion
		Padiglione Philips, Bruxelles (Universale di Architettura 67, January 2000), on the correspondence between the geometry of hyperbolic paraboloids and technical and acoustic needs, and its final and aesthetics consequences.
		Alessandra Capanna, "Conoids and Hyperbolic Paraboloids in Le Corbusier's Philips Pavilion", pp.
	www.nexusjournal.com /conferences/N2000-Capanna.html (520 words)

	Architectural Fabric Structures
		The guiding principle behind these structures is the minimal surface principle, such as that displayed by hyperbolic paraboloids (so called "monkey saddle") observed in materials such as soap bubbles and other minimal surface materials.
		The first set of structures were anisotropic hyperbolic paraboloids, or "monkey saddles." These are also designated as "two up, two down" or 2/2 configurations, referring to the number of tension points which act away from gravity and towards gravity.
		The second structure employed 4 up and 4 down points, which results in a concatenation and intersection of hyperbolic paraboloids, creating a "compound monkey saddle." These structures were assembled and can be seen in Figures 7 and 8.
	fibers.philau.edu /ntc/f00p01/phase1.html (1626 words)

	paraboloids.html
		It isn't clear right away whether it is elliptic or hyperbolic, but the graph makes it clear.
		It's hard to see unless you rotate this graph, but this surface only opens up, never down, but there is one direction in which the height of the surface stays constant.
		This paraboloid is balanced perfectly between the elliptic and hyperbolic cases.
	www-math.bgsu.edu /~zirbel/calc3/paraboloids.html (153 words)

	Local Properties
		For instance, the family of paraboloids described by Eq.4 is depicted as the straight dashed line.
		All of the points such that c^2< ab correspond to elliptic paraboloids whereas all of the points such that c^2 >ab corresponds to hyperbolic paraboloids.
		The sequence starts with a paraboloid attached to a small value of r (elliptic region) and ends with a paraboloid belonging to the parabolic region.
	www.vision.caltech.edu /savarese/more_details2.html (1689 words)

	structure 1
		Considering virtical upward orientation with multi-story condition, the system, I thought, should be divided into many smaller parts to gain geometrical stiffness with pretension by air pressure as low as possible.
		cooling tower - a huge chimney, which had taken the form of reinforced concrete hyperbolic paraboloids.
		Cable-net cooling tower at Schmehausen(central mast and hyperbolic paraboids of cable-net with a cladding material: height 180 m, diameter 141 m - 91 m)
	www.iit.edu /~tamahir/track01/str.html (260 words)

	Gaudi and Barcelona Club (Site not responding. Last check: 2007-10-10)
		The outline of the crypt is about 36.5 x 27 meters, and is reminiscent of a tortoise shell with star-like edges.
		This star shape is due to the inclination of the outer walls, which form regular surfaces, in this case hyperbolic paraboloids.
		The windows, which allow natural illumination of the crypt, have a perceptible hyperbolic shape, for Gaudí considered the hyperbole the shape which best received and distributed sunlight.
	www.gaudiclub.com /ingles/i_vida/colonia2.asp (516 words)

	The GNU 3DLDF Paraboloids Page (Site not responding. Last check: 2007-10-10)
		It corresponds to the type class Paraboloid in the C++ code.
		Objects of both of these types are referenced in the 3DLDF language by objects of type paraboloid.
		I've started working on paraboloids, but as of this date, they are not yet fully functional.
	www.gnu.org /software/3dldf/parablds.html (160 words)

	The Geometry Junkyard: All Topics
		Ok, renaming a hyperbolic paraboloid a "helical right triangle" and saying that it's "a revolutionary foundation for new knowledge" seems a little cranky but there are some interesting pictures of shapes formed by compounds of these saddles.
		Hyperbolic planar tessellations, image gallery of many regular and semiregular tilings by Don Hatch.
		Packing circles in the hyperbolic plane, Java animation by Kevin Pilgrim illustrating the effects of changing radii in the hyperbolic plane.
	www.ics.uci.edu /~eppstein/junkyard/all.html (9770 words)

	Seiberling House - Coralville Iowa (Site not responding. Last check: 2007-10-10)
		This house was designed for Dr. Frank and Nancy Seiberling and overlooks the Coralville Reservoir.
		As a request to express the building technologies of the day, 7 concrete thin shell hyperbolic paraboloids were constructed and carried on 4 extra heavy steel pipe columns.
		This allowed great interior freedom to arrange furnishings and Frank and Nancy's art collection which was extensive and included many large pieces.
	www.raydcritesfaia.com /house2.htm (95 words)

	Conoids and Hyperbolic Paraboloids in Le Corbusier's Philips Pavilion by Alessandra Capanna for the Nexus Network ... (Site not responding. Last check: 2007-10-10)
		Conoids and Hyperbolic Paraboloids in Le Corbusier's Philips Pavilion by Alessandra Capanna for the Nexus Network Journal vol.2 no.3 July 2000
		Combinazioni compositive senza limiti", taken from a lecture given at the Dipartimento di Progettazione Architettonica e Urbana at the University of Rome.
		Alessandra Capanna, "Conoids and Hyperbolic Paraboloids in Le Corbusier's Philips Pavilion", abstract, Nexus Network Journal, vol.
	www.nexusjournal.com /N2000-Capanna.html (523 words)

	Milo Ketchum Memoirs - Hyperbolic Paraboloids and Domes (Site not responding. Last check: 2007-10-10)
		Milo Ketchum Memoirs - Hyperbolic Paraboloids and Domes
		I had seen the many inverted umbrella hyperbolic paraboloids (hypars) built by Candela in Mexico City, but there never was a chance to design one.
		The first hypar we designed was the First Methodist Church building in Boulder, Fig.
	www.ketchum.org /milo/Memoir6.html (769 words)

	Philips Pavilion PoËme Electronique
		Philips Industries commissioned Le Corbusier to build their pavilion for the 1958 World's Fair to be a showcase of their technology.
		It was an extremely complex installation with 350 speakers, all sorts of lights, slide and film projectors, sculpture and more.
		Xenakis' music and architecture was heavily based on mathematics, especially hyperbolic paraboloid shapes.
	stage.itp.nyu.edu /history/timeline/philipspavilion.html (191 words)

	Systems
		The hyperbolic paraboloid has a saddle shaped shell that is supported by cantilevers and concrete abutment.
		Constructing domes and hyperbolic paraboloids have a relatively high cost of construction because they are very complicated to construction.
		The appeal of this structural system is the large area it is able to span and it also can be very aesthetically pleasing.
	www.pages.drexel.edu /~ncy23/AE390/A4/systems.htm (701 words)

	Milo Ketchum Memoirs - Analysis of Hyperbolic Paraboloids
		Milo Ketchum Memoirs - Analysis of Hyperbolic Paraboloids
		After moving to Connecticut in 1962, my interest in analysis of hypars continued.
		I still hope to be able to do work in this field.
	www.ketchum.org /milo/Memoir7a.html (896 words)

	Academic Exchange Extra - December 2005
		An elliptic (or hyperbolic) paraboloid not an elliptic (or hyperbolic) paraboloid (Paraboloid, 2005)?
		Some know about this technique through their studies of Husserl, the mathematician and phenomenologist (see, e.g., van Manen, 1990).
		Mathematicians describe the essential features of circles, ellipses, hyperbolas, lines, elliptic and hyperbolic paraboloids, and other geometric figures in their one, two, or three dimensional domains.
	asstudents.unco.edu /students/AE-Extra/2005/11/indxmain.html (521 words)

	The GNU 3DLDF Website (Site not responding. Last check: 2007-10-10)
		Added pages for Elliptical Paraboloids, Hyperbolic Paraboloids, One-Sheet Hyperboloids, and Two-Sheet Hyperboloids.
		Added a Paraboloids page and a Hyperboloids page.
		Added code for finding the intersection of a polyhedron and a plane.
	gnu.fyxm.net /software/3dldf/?M=D (2822 words)

	_301_MapleResources.html (Site not responding. Last check: 2007-10-10)
		For HTML files exported by using Maple 8.01, this tool is
		Updated 1/24/2003 How to define and graph functions of several variables using plot3d, smartplot3d, the plots Library (implicitplot3d, pointplot3d, spacecurve, display3d), the plottools Library (point, line), examples of plots of Quadratic Surfaces (cylinders, ellipsoids, paraboloids, cones, hyperboloids (one and two sheets), hyperbolic paraboloids),
		How to define and graph functions of several variables using plot3d, smartplot3d, the plots Library (implicitplot3d, pointplot3d, spacecurve, display3d), the plottools Library (point, line), examples of plots of Quadratic Surfaces (cylinders, ellipsoids, paraboloids, cones, hyperboloids (one and two sheets), hyperbolic paraboloids)
	www.math.louisville.edu /~grbarn01/301/maple/_301_MapleResources1.html (938 words)

	Unique Creations & Inventions
		Six tetrahedral hyperbolic paraboloids in cuboctahedron as design for ferrocement playground structure.
		Roof of hyperbolic paraboloids ideally suited for thin-shell ferrocement construction
		Unique ergonomic and highly accurate adz will carve huge quantities of wood in a short time!
	www.whidbey.com /stilt/html/unique_creations___inventions.html (477 words)

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