sphere A geodesicdome is a spherical or partial spherical thin shell structure shell structure ... sphere . A dome is enclosed, unlike open geodesic structures such as playground climbers. Typically a geodesicdome design begins with an icosahedron inscribed in a hypothetical sphere, tiling ... geodesic paths over the surface of the dome. Geodesic designs can be used to form any curved, enclosed ... Silent Running . The first dome that could be called geodesic in every respect was designed after ... Some 20 years later, Buckminster Fuller R. Buckminster Fuller named the domegeodesic from field experiments ... in Tony Rothman s book Science la Mode , Princeton University Press, 1989. ref The geodesicdome appealed ..., and construction speed. Leveraging the geodesicdome s stability, the US Air Force experimented ... out of the weather. This method does not require expensive steel hubs. File Vitra geodesicdome tubing.jpg ... dome designed by Synergetics. Inc. non geodesic. Temporary greenhouse domes have been constructed by stapling ... Fuller hoped that the geodesicdome would help address the postwar housing crisis. This was consistent ... and consequent greater construction costs. Fuller himself lived in a geodesicdome in Carbondale ... sphere corresponds to the structural strut of the physical geodesicdome . A chord geometry chord is a straight ... , or octahedron . The desired frequency of the subsequent geodesic sphere or dome is the number ... can take part in the process at each deliberation stages. Largest geodesicdome structures ... sphere Concrete domeDome Domed city Fullerene s, molecules which resemble the geodesicdome ... Hugh Kenner , who wrote Geodesic Math and How to Use It Monolithic dome Pentakis dodecahedron ... geodesic domes. Sindome An online Cyberpunk RPG that takes place in a giant geodesicdome. Space ... GeodesicDome Notes GeodesicDome Notes 57 dome variants featured 1V to 10V of various ... GeodesicDome by T.E. Dorozinski http sketchup.google.com 3dwarehouse cldetails?mid 1f33552966b6f22224e5217d8a2e013a ... more details
Infobox NRHP name ASM Headquarters and GeodesicDome nrhp type image Russell Township ASM Headquarters & GeodesicDome OHPTC 5912348229 .jpg caption location 9639 Kinsman Rd., Materials Park, Ohio 44073 ... International Headquarters and GeodesicDome , in Russell Township, Geauga County, Ohio Russell Township .... The dome is the world s largest open air geodesicdome , and is rare among Synergetics, Inc. designed geodesic domes in that it was never intended to be a covered structure. ref name nrhpreg Design Originally serving as headquarters for the American Society for Metals in September 1959, the geodesicdome was built on a 100 acre parcel donated by William Hunt Eisenman 1886 1958 , a charter member ..., and nano technology. ref name Theobald The geodesicdome is actually two domes, one inside the other ... nrhpreg ref cite journal last Dunbar first WL title Ohio s 11 story GeodesicDome Seems to Float journal ... circular building, capped by a geodesicdome, symbolizes humanity s mastery of metals and materials ... Places Registration ASM Headquarters and GeodesicDome url http www.nps.gov history nr feature ... Fuller s role in the design of ASM s dome. While Fuller was a founding partner of Synergetics, Inc. and a patent holder for geodesicdome designs, he was divested of all interest in Synergetics, Inc. before this dome was conceived. The geodesicdome was designed by Thomas C. Howard of Synergetics, Inc. in Raleigh, North Carolina , the owner of Synergetics, Inc. and designer of many geodesic domes ... dome now demolished in Baton Rouge, LA, and Poliedro de Caracas in Venezuela . ref cite web title DOME HOUSES url http www.trianglemodernisthouses.com domes.htm publisher Triangle Modernist Archive ... during its construction, recalls that the dome engineering firm was the College of Engineering at the University ..., Theobald refers to the dome Engineers, speaking very little of any involvement by Fuller, which would ... Building and Dome url http www.asminternational.org portal site www renovation history publisher ASM ... more details
geometry of curves Exponential map GeodesicdomeGeodesic general relativity Geodesics as Hamiltonian ...File Spherical triangle.svg thumb right 150px A geodesic triangle on the sphere. The geodesics are great circle arcs. In mathematics , particularly differential geometry , a geodesic IPAc en icon d ... along it. The term geodesic comes from geodesy , the science of measuring the size and shape of Earth in the original sense, a geodesic was the shortest route between two points on the Earth s surface ... a geodesic between two vertex graph theory vertices nodes of a graph mathematics graph . Geodesics ... with constant velocity , meaning that the distance from f s to f t along the geodesic ... of the curve minimizing the energy leads to the same equations for a geodesic here constant velocity ... its energy. The resulting shape of the band is a geodesic. In Riemannian geometry geodesics ... on a sphere is a geodesic but not the shortest path between the points. The map t t sup 2 sup from the unit interval to itself gives the shortest path between 0 and 1, but is not a geodesic ... s. The article geodesic general relativity discusses the special case of general relativity in greater ... paths between them. Metric geometry In metric geometry , a geodesic is a curve which is everywhere ... of the reals to the metric space M is a geodesic if there is a mathematical constant constant v ... the notion of geodesic for Riemannian manifolds. However, in metric geometry the geodesic considered ... for all t sub 1 sub , t sub 2 sub I , the geodesic is called a minimizing geodesic or shortest ... this minimizing sequence need not converge to a geodesic. Riemannian geometry In a Riemannian .... This is the geodesic equation , discussed Affine geodesics below . Calculus of variations Techniques ... In an appropriate sense, zeros of the second variation along a geodesic arise along Jacobi field ... mechanics Hamiltonian . Affine geodesics A geodesic on a smooth manifold M with an affine connection ... more details
A geodesic airframe alternatively, geodetic is a type of construction for the airframe s of aircraft developed by United Kingdom British aeronautical engineer Barnes Wallis in the 1930s. It makes use of a space frame formed from a spirally crossing basket weave of load bearing members. ref name Buttler93 Buttler, p.93 ref The principle is that two geodesicdomegeodesic arcs can be drawn to intersect on a curving surface the fuselage in a manner that the Torsion mechanics torsional load on each cancels out that on the other. ref name Buttler94 Buttler, p.94 ref Early examples Image Constitutiondiagonalriders.gif thumb right 300px 18th century American warships Diagonal rider in their construction. The diagonal rider structural element was used by Joshua Humphreys in the Original six frigates of the United States Navy first US Navy sail frigates in 1794. Citation needed date March 2011 Diagonal riders are viewable in the interior hull structure of the preserved USS Constitution on display in Boston Harbor. Citation needed date March 2011 The structure was a pioneering example of non Orthogonality orthogonal structural components. Citation needed date March 2011 However they do not constitute a space frame. The diagonal riders were included in these naval vessels construction to reduce ... of geodesic design is a misnomer. In a geodetic structure, the strength and structural integrity, and indeed ... thumb Wellington Mk.X HE239 of No. 428 Squadron RCAF No.428 Sqn. RCAF, illustrating the geodesic construction .... Image Vickers Warwick geodesic fuselage.JPG thumb right A section of the rear fuselage from a Warwick showing the geodesic construction in duralumin. On exhibit at the Armstrong & Aviation Museum at Bamburgh ... to the airframe and distinguish it from geodesic which is the proper term for a line on a curved ... frames exposed see photo . The benefits of the geodesic construction were partly offset by the difficulty ... Geodesic Airframe Category Airship technology Category Structural system Category Aerospace ... more details
Unreferenced date October 2008 In differential geometry and dynamical systems , a closed geodesic on a Riemannian manifold M is the projection of a closed orbit of the geodesic flow on M . Examples On the unit sphere , every great circle is an example of a closed geodesic. On a compact hyperbolic surface , whose fundamental group has no torsion, closed geodesics are in one to one correspondence with non trivial conjugacy class es of elements in the Fuchsian group of the surface. A prime geodesic is an example of a closed geodesic. Definition Geodesic Flow mathematics flow is an math mathbb R math group action action on tangent bundle T M of a manifold M defined in the following way math G t V dot gamma V t math where math t in mathbb R math , math V in T M math and math gamma V math denotes the geodesic with initial data math dot gamma V 0 V math . It defines a Hamiltonian flow on co tangent bundle with the pseudo Riemannian metric as the Hamiltonian quantum mechanics Hamiltonian . In particular it preserves the pseudo Riemannian metric math g math , i.e. math g G t V ,G t V g V,V . , math That makes possible to define geodesic flow on unit tangent bundle math UT M math of the Riemannian manifold math M math when the geodesic math gamma V math is of unit speed. See also Selberg trace formula Zoll surface geodesic References Arthur Besse Besse, A. Manifolds all of whose geodesics are closed , Ergebisse Grenzgeb. Math. , no. 93, Springer, Berlin, 1978. Category Differential geometry Category Dynamical systems Category Geodesic mathematics ... more details
In mathematics &mdash specifically, in differential geometry &mdash a geodesic map or geodesic mapping or geodesic diffeomorphism is a Function mathematics function that preserves geodesic s . More precisely, given two pseudo Riemannian manifold pseudo Riemannian manifold s M , g and N , h , a function &phi M &rarr N is said to be a geodesic map if &phi is a diffeomorphism of M onto N and the image under &phi of any geodesic arc in M is a geodesic arc in N and the image under the inverse function &phi sup &minus 1 sup of any geodesic arc in N is a geodesic arc in M . Examples If M , g and N , h are both the n dimension al Euclidean space E sup n sup with its usual flat Riemannian metric metric , then any Euclidean isometry is a geodesic map of E sup n sup onto itself. Similarly, if M , g and N , h are both the n dimensional unit hypersphere sphere S sup n sup with its usual round metric, then any isometry of the sphere is a geodesic map of S sup n sup onto itself. If M , g is the unit sphere S sup n sup with its usual round metric and N , h is the sphere of radius 2 with its usual round metric, both thought of as subsets of the ambient coordinate space R sup n 1 sup , then the expansion map &phi R sup n 1 sup &rarr R sup n 1 sup given by &phi x 2 x induces a geodesic map of M onto N . There is no geodesic map from the Euclidean space E sup n sup onto the unit sphere S sup n sup , since they are not homeomorphism homeomorphic , let alone diffeomorphic. The gnomonic projection of the hemisphere to the plane is a geodesic map as it takes great circles to lines and its inverse takes ... is not a geodesic map, since g geodesics are always straight lines in R sup 2 sup , whereas h geodesics ... model Klein model , the identity i D &rarr D is a geodesic map, because ... urlname GeodesicMapping title Geodesic mapping Category Differential geometry ... more details
In Riemannian geometry , the geodesic curvature math k g math of a curve lying on a submanifold of the ambient space measures how far the curve is from being a geodesic . For instance it applies to Curvature Curves on surfaces curves on surfaces . The notion of geodesic curvature allows to distinguish the part of the curvature in ambient space that is due to the submanifold the normal curvature math k n math and the one that comes from the curve itself. The curvature math k math of the curve is related to these two by math k sqrt k g 2 k n 2 math . In particular geodesics have zero geodesic curvature they are straight , and that is their definition, so that math k k n math , which explains why they appear to be curved in ambient space whenever the submanifold is. Definition Consider a curve lying on a submanifold math M math in ambient manifold math bar M math , parametrized by arclength math s math , with unit tangent vector math T math . The geodesic curvature is the norm of the projection of the derivative math dT ds math on the tangent plane to the submanifold. Conversely the normal curvature is the norm of the projection of math dT ds math on the normal bundle to the submanifold at the point considered. Example Let math M math be the unit sphere math S 2 math in three dimensional Euclidean space. The normal curvature of math S 2 math is identically 1. Great circles have curvature math k 1 math , which implies zero geodesic curvature, thus they are geodesics. Smaller circles of radius math r math will have curvature math 1 r math and geodesic curvature math k g sqrt 1 r 2 r math . Some results involving geodesic curvature The geodesic curvature is no other than the usual ... Surfaces isbn 0 486 63433 7 . springer id G g044070 title Geodesic curvature first Yu.S. last Slobodyan year 2001 . External links Mathworld urlname GeodesicCurvature title Geodesic curvature curvature Category Curvature mathematics Category Differential geometry of surfaces Category Geodesic mathematics ... more details
Unreferenced date December 2009 In mathematics , a prime geodesic on a hyperbolic geometry hyperbolic surface is a primitive closed geodesic , i.e. a geodesic which is a curve closed curve that traces out its image exactly once. Such geodesics are called prime geodesics because, among other things, they obey an asymptotic analysis asymptotic distribution law similar to the prime number theorem . Technical background We briefly present some facts from hyperbolic geometry which are helpful in understanding prime geodesics. Hyperbolic isometries Consider the Poincar half plane model H of 2 dimensional hyperbolic geometry . Given a Fuchsian group , that is, a discrete subgroup of projective linear group PSL 2, R , group action acts on H via linear fractional transformation . Each element of PSL 2, R in fact defines an isometry of H , so is a group of isometries of H . There are then 3 types of transformation hyperbolic, elliptic, and parabolic. The loxodromic transformations are not present because we are working with real number s. Then an element of has 2 distinct real fixed ... a closed geodesic of H first, by connecting the geodesic semicircle joining the fixed points of h , we get a geodesic on H called the axis of h , and by projecting this geodesic to M , we get a geodesic on H . This geodesic is closed because 2 points which are in the same orbit under the action ... and possibly false, as it fails to distinguish between geodesic loops and closed geodesics. It can ... fields. Dynamical systems and ergodic theory In dynamical systems, the closed geodesic s represent the Periodic function periodic group action orbits of the GeodesicGeodesic flow geodesic flow . Number theory In number theory, various prime geodesic theorems have been proved which are very similar ... Fuchsian model Analytic number theory Zoll surface DEFAULTSORT Prime Geodesic Category Riemann surfaces Category Differential geometry Category Dynamical systems Category Number theory Category Geodesic ... more details
orphan date October 2009 In mathematics , a complex geodesic is a generalization of the notion of geodesic to complex number complex spaces. Definition Let X , be a complex Banach space and let B be the open set open unit ball in X . Let denote the open unit disc in the Complex plane Other meanings of complex plane complex plane C , thought of as the Poincar disc model for 2 dimensional real 1 dimensional complex hyperbolic geometry . Let the Poincar metric on be given by math rho a, b tanh 1 frac a b 1 bar a b math and denote the corresponding Carath odory metric on B by d . Then a holomorphic function f B is said to be a complex geodesic if math d f w , f z rho w, z , math for all points w and z in . Properties and examples of complex geodesics Given u X with u 1, the map f B given by f z zu is a complex geodesic. Geodesics can be reparametrized if f is a complex geodesic and g Aut is a bi holomorphic automorphism of the disc , then f small o small g is also a complex geodesic. In fact, any complex geodesic f sub 1 sub with the same image as f i.e., f sub 1 sub f arises as such a reparametrization of f . If math d f 0 , f z rho 0, z math for some z &ne 0, then f is a complex geodesic. If math alpha f 0 , f 0 1, math where &alpha denotes the Caratheodory length of a tangent vector, then f is a complex geodesic. References cite book author Earle, Clifford J. and Harris, Lawrence A. and Hubbard, John H. and Mitra, Sudeb chapter Schwarz s lemma and the Kobayashi and Carath odory pseudometrics on complex Banach manifolds title Kleinian groups and hyperbolic 3 manifolds Warwick, 2001 editor Komori, Y., Markovic, V. and Series, C. eds series London Math. Soc. Lecture Note Ser. 299 pages 363&ndash 384 publisher Cambridge Univ. Press location Cambridge year 2003 Category Hyperbolic geometry Category Metric geometry ... more details
Disputed date April 2009 In mathematics &mdash specifically, in Riemannian geometry &mdash geodesic convexity is a natural generalization of convex set convexity for sets and convex function functions to Riemannian manifold s. It is common to drop the prefix geodesic and refer simply to convexity of a set or function. Definitions Let M , g be a Riemannian manifold. A subset C of M is said to be a geodesically convex set if, given any two points in C , there is a minimizing geodesic contained within C that joins those two points. Let C be a geodesically convex subset of M . A function f C R is said to be a strictly geodesically convex function if the composition math f circ gamma 0, T to mathbb R math is a strictly convex function in the usual sense for every unit speed geodesic arc &gamma 0, T &rarr M contained within C . Properties A geodesically convex subset of a Riemannian manifold is also a convex metric space with respect to the geodesic distance. Examples A subset of n dimensional Euclidean space E sup n sup with its usual flat metric is geodesically convex if and only if it is convex in the usual sense, and similarly for functions. The northern hemisphere of the 2 dimensional sphere S sup 2 sup with its usual metric is geodesically convex. However, the subset A of S sup 2 sup consisting of those points with latitude further north than 45 south is not geodesically convex, since the geodesic great circle joining two points on the southern boundary of A may well leave A e.g. in the case of two points 180 apart in longitude , in which case the geodesic arc passes over the south pole . References cite book last Rapcs k first Tam s title Smooth nonlinear optimization in R sup n sup series Nonconvex Optimization and its Applications 19 publisher Kluwer Academic Publishers location Dordrecht year 1997 pages xiv 374 isbn 0 7923 4680 7 MathSciNet id 1480415 cite book last Udriste first Constantin title Convex functions ... more details
In mathematics , a complete manifold or geodesically complete manifold is a Pseudo Riemannian manifold pseudo Riemannian manifold for which every maximal inextendible geodesic is defined on math mathbb R math . Examples All compact space compact manifolds and all homogeneous space homogeneous manifolds are geodesically complete. Euclidean space math mathbb R n math , the sphere s math mathbb S n math and the torus tori math mathbb T n math with their usual Riemannian metric s are all complete manifolds. A simple example of a non complete manifold is given by the punctured plane math M mathbb R 2 setminus 0 math with its usual metric . Geodesics going to the origin cannot be defined on the entire real line. Path connectedness, completeness and geodesic completeness It can be shown that a finite dimensional Connected space Path connectedness path connected Riemannian manifold is a complete metric space if and only if it is geodesically complete. This is the Hopf Rinow theorem . This theorem does not hold for infinite dimensional manifolds. The example of a non complete manifold the punctured plane given above fails to be geodesically complete because, although it is path connected, it is not a complete metric space any sequence in the plane converging to the origin is a non converging Cauchy sequence in the punctured plane. References Citation last1 O Neill first1 Barrett title Semi Riemannian Geometry publisher Academic Press isbn 0 12 526740 1 year 1983 . See chapter 3, pp. 68 . DEFAULTSORT Complete Manifold Category Riemannian geometry Category Manifolds ... more details
Image Geodesic Grid ISEA3H illustrated.png Geodesic Discrete Global Grid PYXIS WorldView 400px right A geodesic grid is a technique used to model the surface of a sphere such as the Earth with a subdivided polyhedron , usually an icosahedron . Introduction A geodesic grid is a global Earth reference that uses cells or tiles to statistically represent data encoded to the area covered by the cell location. The focus of the discrete cells in a geodesic grid reference is different from that of a conventional lattice based Earth reference where the focus is on a continuity of points used for addressing location and navigation. In biodiversity science, geodesic grids are a global extension of local discrete grids that are staked out in field studies to ensure appropriate statistical sampling and larger multi use grids deployed at regional and national levels to develop an aggregated understanding of biodiversity. These grids translate environmental and ecological monitoring data from multiple spatial and temporal scales into assessments of current ecological condition and forecasts of risks to our natural resources. A geodesic grid allows local to global assimilation of ecologically significant ... into a grid in this case, over the geodesy shape of the Earth . Geodesic grids have been .... Another approach gaining favour uses geodesic sphere grids generated by the subdivision of a platonic ... the new cells onto a sphere . In this geodesic grid , each of the vertices in the resulting geodesic ... geodesic grid inherits many of the virtues of 2D hexagonal grids, and specifically avoids problems ... in video games. The quadrilateralized spherical cube is a kind of geodesic grid based on subdividing ... History The earliest use of the icosahedral geodesic grid in geophysical modeling dates back to 1968 ... equation on a spherical geodesic grid journal Tellus volume 20 pages 642 653 year 1968 doi 10.1111 ... http kiwi.atmos.colostate.edu BUGS geodesic BUGS climate model page on geodesic grids http www.sou.edu ... more details
The Dome commonly refers to Millennium Dome , a former Millennium exhibition venue in London, England, now redeveloped as The O2 entertainment venue Louisiana Superdome , home of the New Orleans Saints american football team Hubert H. Humphrey Metrodome , home of the Minnesota Vikings american football team The Dome may also refer to The Dome, Edinburgh , an 1847 built Graeco Roman style building in Edinburgh s New Town, Scotland The Dome Dubai , a planned 44 floor skyscraper in Jumeirah Lake Towers, Dubai, UAE The Dome periodical , a British arts periodical published from 1897 to 1900 The Dome Sydney , an indoor sports arena in the Sydney Olympic Park, Australia The Dome television program , a German television program and music event The Dome Center incorporating the Dome Arena, a fair and convention complex in Henrietta, New York The Dome Leisure Centre , an arena and leisure centre in Doncaster, England Dome of Discovery , a building of the 1951 Festival of Britain, demolished on closure Brighton Dome , an 1805 built arts venue housing three venues Brighton, England Carrier Dome , a stadium owned by Syracuse University, Syracuse, New York See also Dome disambiguation disambig ... more details
Infobox mountain name Dome A photo elevation m 4091 elevation ref prominence m 1639 prominence ref listing ... inline type age first ascent easiest route Dome A or Dome Argus coord 80 22 S 77 21 E type mountain ... of a dome or eminence 4,093 meters elevation above sea level. It is located near the center of East ... the Australian Antarctic Territory Australian claim . Description Dome Argus is the summit of the massive ... , and therefore Dome Argus is considered to be the highest point in the East Antarctica Ranges. Dome A is a plain and the elevation visually is not noticeable. Below Dome A underneath at least 2400 meters thickness of ice sheet is the Gamburtsev Mountain Range . The name Dome Argus was given by the Scott ... samples for the research of climates in the past. ref name wo Temperatures at Dome A fall below ... CHINARE traversed 1228 km from Zhongshan Station to Dome A and located the highest point ... AWS was deployed at Dome A, and a second station was installed approximately half way between the summit ... at Dome A is powered by solar cell s and diesel fuel and requires yearly service and refuelling. ref ... Dome A coldest place on Earth publisher Wondermondo ref The coldest air temperature recorded at Dome ... Vostok , which is almost 600 m lower in elevation than Dome A. Analysis of satellite data and atmospheric models shows that the Ridge A which is located 144 km south east from Dome A is potentially ... called PLATO PLATeau Observatory on the dome in January 2008. ref cite web url http www.spaceref.com ... date 2009 12 22 title PLATO Dome A robotic observatory publisher UNSW accessdate 2009 12 22 ref Various ... a wireless network technology based observation system called DomeA WSN on the dome in January 2008. ref cite web url http www.chinanews.com.cn gn news 2008 01 24 1144158.shtml title Dome ... Station , China s third Station in Antarctica, was set up at the dome on January 27, 2009. ref cite ... Pole of Inaccessibility Ridge A Dome C also known as Dome Circe or Dome Charlie Dome F also known ... more details
Golden Dome may refer to Main Administration Building University of Notre Dame , is referred to as the Golden DomeDome of the Rock , a shrine of great religious significance in Jerusalem St. Michael s Golden Domed Monastery in Kiev, Ukraine Gold Dome , a geodesic shaped cultural center in Oklahoma City, Oklahoma Golden Dome Monaca , a multi purpose geodesic domed arena in Monaca, Pennsylvania Assassins Gate Green Zone , a landmark on the International Zone in Baghdad, Iraq, known as The Golden Dome The Golden Domes on the Fairfield, Iowa, campus of Maharishi University of Management Gold Dome Georgia State Capitol , is referred to as the Gold Dome because of the gold leaf applied to the structure. See also Dome disambiguation disambig Category Domes ... more details
rock strata Architecture Geodesicdome Monolithic dome Geography Antarctica Anderson Dome Arctowski DomeDome A Bonnabeau DomeDome C Dome F Law Dome Siege Dome Titan Dome Canada Dome Mine , Ontario People Malcolm Dome Ram Chandra Dome Other Dome band , a 1980s post punk band Dome coffeehouse , a chain of caf restaurants based in Perth, Western Australia Perth, Australia Dome constructor , a Japanese based racing car constructor Dome mathematics , a closed geometrical surface which can be obtained by sectioning off a portion of a sphere with an intersecting plane The Dome periodical The Dome ...wikt Dome File TUNISIE KAIROUAN 04.jpg thumb 240px Dome in architecture ribbed hemispherical dome resting on an octagonal drum in the Mosque of Uqba Great Mosque of Kairouan also called the Mosque of Uqba , city of Kairouan , Tunisia . A dome is a structural element of architecture that resembles the hollow upper half of a sphere. Dome may refer to Geology Dome geology , a deformational feature consisting of symmetrically dipping anticline s Granite dome , a dome of granite , formed by exfoliation Lava dome , a mound shaped growth resulting from the eruption of high silica lava from a volcano Lunar dome , a type of shield volcano found on the surface of the Earth s moon Resurgent dome , a volcanic dome that is swelling or rising due to movement in the magma chamber Salt dome , formed when a thick ... Le Dome Cafe Le D me Caf , historical Paris intellectual venue Dome car , a type of railway passenger car Dome GWCC Philips Arena CNN Center MARTA station , a passenger rail station in Atlanta, Georgia named after the Georgia Dome Teapot Dome scandal , Wyoming, United States Steam dome , a steam locomotive component Dome , a 1987 science fiction novel by Michael Reaves and Steve Perry author Steve Perry Dome, slang for fellatio Dome, slang for the upper half of the head or a bald head . A nickname for the Hubert H. Humphrey Metrodome . disambig de Dome fr D me it D me nl Dome pl Dome pt Domo ... more details
Multiple issues unreferenced November 2006 orphan February 2009 context October 2009 Tracking the interference amongst various layers, in a multi directional Solid Freeform Fabrication, is extremely important. The geodesic interference level is a common attribute of all the mutually interfering layers. The algorithm for multi directional deposition using geodesic interference level attribute was introduced by Rajeev Dwivedi and Radovan Kovacevic in 2005, at the Research Center for Advanced Manufacturing . DEFAULTSORT Intereference Geodesic Level Category Thin films ... more details
unreferenced date October 2008 The Solar Dome greenhouse is an offshoot of the 1960 s NATO developed early warning radar system. They asked the Buckminster Fuller organisation to design and develop giant golf ball radar domes. In Europe these were placed in RAF Fylingdales Fylingdales , North Yorkshire. These giant domes had to withstand extremes of wind and storm and yet remain unaffected. An ex German U boat engineer, Hans Lemke, living in Hunmanby North Yorkshire was fascinated by these domes and thought, If they can withstand these weather conditions then they would make an ideal domestic garden building, greenhouse or garden conservatory . He explored the Buckminster Fuller Geodesic domes and their principles and then designed and manufactured the first European domestic Geodesicdome , a 14 6 Solardome. The first Solardome was produced in 1969 and production continues to this day, although not in Hunmanby. http www.solardome.co.uk Category Greenhouses ... more details
Expert subject Physics date February 2009 Technical date August 2009 In general relativity , the geodesic deviation equation is an equation involving the Riemann curvature tensor , which measures the change in separation of neighbouring geodesic s or, equivalently, the tidal force experienced by a rigid body moving along a geodesic. In the language of mechanics it measures the rate of relative acceleration of two particles moving forward on neighbouring geodesics. In differential geometry , the geodesic deviation equation is more commonly known as the Jacobi field Jacobi equation . Let T sup a sup be the tangent vector to a given geodesic , and X sup a sup a vector field along connecting it to an infinitesimally near geodesic the deviation vector . The relative acceleration of the infinitesimally near geodesic is defined by math a a T b nabla b T c nabla c X a. math The geodesic deviation equation asserts that math a a R bcd aX bT cT d. math To more rigorously formulate the equation, let sub s sub t be a 1 parameter variation through geodesics i.e., for each fixed s , the curve swept out by sub s sub t as t varies is a geodesic with affine parameter. The tangent vector and deviation vector are respectively defined by math begin align T & frac d dt gamma 0 t X & left. frac d ds gamma s t right s 0 . end align math In order that sub s sub be a variation through geodesics, a necessary condition is that the geodesic equation holds math frac D 2 dt 2 X R X,T T. math The geodesic deviation equation can be derived from the second variation of the point particle Lagrangian along geodesics, or from the first variation of a combined Lagrangian. Clarify date September 2009 The Lagrangian ... physics quantization to be applied to the geodesic deviation system. Second it allows deviation to be formulated ... indexed momentum appears to have a corresponding generalization of geodesic deviation . Citation ... Geodesic Deviation Equation Category Geodesic mathematics Category Riemannian geometry Category Equations ... more details
Orphan date November 2010 This article is about a geologic feature. For the architectural design, see geodesic dome . Fuller Dome coord 86 38 S 156 18 W source GNIS is a dome shaped, ice covered mountain, convert 2,850 m high, at the northwest end of the Rawson Mountains Antarctica Rawson Mountains in the Queen Maud Mountains of Antarctica. It was mapped by the United States Geological Survey from surveys and U.S. Navy air photos, 1960 64, and was named by the Advisory Committee on Antarctic Names for C.E. Fuller , a storekeeper with U.S. Navy Squadron VX 6 on Operation Deep Freeze 1966 and 1967. ref name gnis References Reflist refs ref name gnis cite gnis type antarid id 5381 name Fuller Dome accessdate 2012 04 12 ref usgs gazetteer id 5381 Category Mountains of the Ross Dependency Category Amundsen Coast RossDependency geo stub ... more details
In geometric data analysis and statistical shape analysis , principal geodesic analysis is a generalization of principal component analysis to a Euclidean geometry non Euclidean , non linear setting of manifolds suitable for use with shape descriptors such as medial representation s. References http midag.cs.unc.edu pubs papers TMI04 Fletcher PGA.pdf Principal Geodesic Analysis for the Study of Nonlinear Statistics of Shape statistics stub geometry stub Category Image processing Category Digital geometry Category Differential geometry Category Topology Category Data analysis ... more details
Infobox Stadium stadium name Nagoya Dome image Image Nagoya Dome 01.JPG 300px Fukuoka Dome location Nagoya , Japan opened March 15, 1997 owner Nagoya Dome Co. operator surface construction cost architect tenants Chunichi Dragons Central League 1997 Present time current seating capacity 40,500 dimensions Left Field 100 m 328.1 ft br Center Field 122 m 400.3 ft br Right Field 100 m 328.1 ft br Height of Outfield Fence 4.8 m 15.7 ft Nagoya Dome , constructed in 1997, is a baseball field, located in the city of Nagoya , Japan . The dome has the capacity to seat up to 38,414 people official 40,500 people . It is an example of a geodesicdome . It has served as HQ for the Chunichi Dragons baseball team, since its opening. It has also served baseball teams Orix Blue Wave and Kintetsu Buffaloes , sometimes during the year. Official theme song for The Nagoya Dome, Here For You , was written by local FM radio disk jockey, James Havens, and also released on CD by Victor Entertainment. See also Thin shell structure List of thin shell structures References http www.takenaka.co.jp takenaka e engi e c01 c01 1 2.html Takenaka Corporation web page on the construction of the Nagoya Dome External links http www.nagoya dome.co.jp Nagoya Dome website Commonscat inline coord 35 11 9.53 N 136 56 50.33 E region JP type landmark scale 2000 NPB Ballparks Chunichi Dragons Indoor baseball parks Category Buildings and structures completed in 1997 Category Sports venues in Nagoya Category Covered stadiums Category Baseball venues in Japan Category Domes Category Geodesic domes Category High tech architecture Category Event venues established in 1997 japan stadium stub de Nagoya Dome fr Nagoya Dome ko ja pl Nagoya Dome fi Nagoya Dome zh ... more details
Expert subject Mathematics date November 2008 How to date October 2009 Solving the geodesic equations is a procedure used in mathematics , particularly Riemannian geometry , and in physics , particularly in general relativity , that results in obtaining geodesic s. Physically, these represent the paths of usually ideal particles with no four acceleration proper acceleration , their motion satisfying the geodesic equations. Because the particles are subject to no four acceleration, the geodesics generally represent the straightest path between two points in a curved spacetime . The geodesic equation Main Geodesic On an n dimensional Riemannian manifold math M math , the geodesic equation written in a coordinate chart with coordinates math x a math is math frac d 2x a ds 2 Gamma a bc frac dx b ds frac dx c ds 0 math where the coordinates x sup a sup s are regarded as the coordinates of a curve s in math M math and math Gamma a bc math are the Christoffel symbol s. The Christoffel symbols are functions of the Metric mathematics metric and are given by math Gamma a bc frac 1 2 g ad left ... , the geodesic equations are a system of math n math ordinary differential equation s for the math ... to choose one that simplifies the geodesic equations. Mathematically, this means, a coordinate chart is chosen in which the geodesic equations have a particularly tractable form. Effective potentials When the geodesic equations can be separated into terms containing only an undifferentiated ... diagram s apply, in particular the location of turning points. Solution techniques Solving the geodesic ... Definitions general solution , of the geodesic equations. Most attacks secretly employ the point symmetry group of the system of geodesic equations. This often yields a result giving a family of solutions ..., and thus obtain a set of equations equivalent to the geodesic equations. This method has the advantage ... The Geodesic Equations Category General relativity Category Mathematical methods in general relativity ... more details
Refimprove date October 2008 Infobox Stadium stadium name Superior Dome image File 2009 0618 Marquette SuperiorDome.jpg center thumb 300px Opposite sides of the Superior Dome. location Northern Michigan ... USD architect tenants Image Nmu.JPG Thumb Center 300px alt Inside of Superior Dome with turf laid ... NCAA seating capacity 8,000 The Superior Dome , which opened as the world s largest wooden dome on September 14, 1991, ref name hunts cite web title Superior Dome url http hunts upguide.com marquette .... A nickname is the Yooper Dome . ref cite web title Superior Dome at NMU Marquette Michigan Attractions url http www.marquettemichiganhotels.net attractions superior dome publisher Marquette Michigan Hotels accessdate 13 November 2011 ref The dome is 14 stories tall, has a diameter of 536 ft 163.4 m , and covers an area of 5.1 acres 21,000 m . It is a geodesicdome constructed with 781 Douglas Fir beams and 108.5 miles 175 km of fir decking. The dome is designed to support snow ... of world records Book of World Records 2010 listed it as the fifth largest dome and largest wooden dome in the world. ref name nmu cite web title Superior Dome url http webb.nmu.edu SportsRecSports ... November 2011 ref Construction Construction of the Dome was completed in two phases. Phase I was finished ... and 1.3 million in loans. Total cost for the Superior Dome stands at 23.9 million. Use The Wildcat football team was the first to christen the Dome, hosting the first ever event in the facility on September ... of 7,942. Later that season, a Superior Dome attendance record was set at 8,432, when Northern ... in a televised game. citation needed date November 2011 The Dome features a retractable artificial ... takes 30 minutes, with full setup taking approximately two hours. ref name nmu The Superior Dome is also ... 400px alt Superior Dome view from Lake Superior Superior Dome view from Lake Superior . References ... view of the Superior Dome Michigan college football venues coord 46 33 36 N 87 23 37 W type landmark ... more details
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