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Topic: Tetrahedral

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	PlanetMath: tetrahedral number
		This means that tetrahedral numbers can be looked up in Pascal's triangle.
		Tetrahedral numbers have practical applications in sphere packing.
		This is version 3 of tetrahedral number, born on 2006-06-02, modified 2006-06-11.
	planetmath.org /encyclopedia/TetrahedralNumber.html (241 words)

	Tetrahedral loose-fill packing - Patent 5213867
		Although tetrahedral containers, for liquids or other free-flowing products, especially food products, have been made of materials such as laminated paper, the advantages of the use of empty tetrahedral units, which can be formed of recycled material, as loose-fill packing, and which need not be sealed against the escape of contents, have not been recognized.
		Special tetrahedral forms can be produced which are capable of filling a volume completely with no spaces between the tetrahedral units, but the present invention relates to loose-fill, where such tight nesting is not desired.
		Tetrahedral loose-fill of the present invention can be made at the facilities of the loose-fill users, who need simply to store old magazines at their premises in their high density form until it is desired to convert the paper into packing material.
	freepatentsonline.com /5213867.html (4679 words)

	Tetrahedral numbers
		Tetrahedral numbers are pyramidal numbers and are the sum of consectuive triangular numbers.
		The first few are 1,4,10,20,35,56,84,120...The tetrahedral number is a figurate number : a number that can be represented by a regular geometric arrangement of equally spaced points.As the name suggests tetrahedral numbers can be visualised as a tetrahedron of points.
		The first tetrahedral number is 1, the second is 4, the third is 10, the forth is 20, and so on.
	milan.milanovic.org /math/english/tetrahedral/tetrahedral.html (429 words)

	Math Forum: Pascal's Triangle
		A tetrahedral number is a figurate number: a number that can be represented by a regular geometric arrangement of equally spaced points.
		Tetrahedral numbers correspond to placing discrete points in the configuration of a tetrahedron (triangular base pyramid).
		Tetrahedral numbers are the sum of consecutive triangular numbers.
	mathforum.org /workshops/usi/pascal/pascal_tetrahedral.html (95 words)

	CHEM2P32 Lecture 11. Square and Tetrahedral Complexes
		Tetrahedral coordination results when ligands are placed on alternate corners of a cube.
		The resulting d-orbital splitting diagram for tetrahedral coordination is the inverse of the diagram for octahedral coordination, as shown below.
		The tetrahedral crystal field stabilization energy is calculated the same way as the octahedral crystal field stabilization energy.
	chemiris.labs.brocku.ca /~chemweb/courses/chem232/CHEM2P32_Lecture_11.html (592 words)

	MATLAB Central - Steve on Image Processing » Blog Archive » Tetrahedral interpolation for colorspace ...
		In both tetrahedral and trilinear interpolation the grid points along each of the three axes serve to divide the volume into a set of rectangular hexahedra.
		In tetrahedral interpolation, the hexahedron is further subdivided into six tetrahedra.
		Tetrahedral interpolation can be used to convert colors more accurately and with lower computational cost.
	blogs.mathworks.com /steve/?p=96 (1298 words)

	Tetrahedral Kite Plan (General)
		I am created this plan for a tetrahedral kite (which can fold flat) simply due to the fact that I was unable to find a good description of how to build the joints of the kite anywhere on the net.
		The problem with tetrahedral kites is that the joints have to be able to connect six (6) or more spars coming together (or through) the joint at the same time!!!.
		A 16 cell sierpinsky tetrahedral built by joining 4, 4 cell tetras like this plan details, is probably the simplest and easist way of increasing the number of cells a tetrahedral kite has, and thus stabilising it.
	www.cit.gu.edu.au /~anthony/kites/tetra/plan (1120 words)

	Tetrahedral kite structure (Site not responding. Last check: 2007-11-06)
		A tetrahedral kite having a sail formed by a pair of sheets of rhombus shape that lie facewise against one another and are joined together along their edges.
		The advantages of kites of tetrahedral shape, including those containing four or sixteen tetrahedral sails arranged to form large tetrahedral-shaped structures, were related by Alexander Graham Bell at the beginning of this century.
		The attachment of the edges of the sail to the struts of the frame is accomplished in a simple manner, and with the stresses in the sail evenly distributed along the length of the struts.
	www.sacnewsmonthly.com /invent/reinforcing_elements/tetrahedral_kite_structure.html (2600 words)

	More about Palindromic Tetrahedrals
		Tetrahedral numbers are defined and calculated by this extraordinary intricate and excruciatingly complex formula.
		Tetrahedral numbers which are sum of 2 tetrahedrals.
		Not the sum of 4 tetrahedrals (a finite sequence).
	www.worldofnumbers.com /tetra.htm (309 words)

	TETRAHEDRAL SPHERE
		The TETRAHEDRAL SPHERE is the central projection of the tetrahedron onto the surface of the unit sphere.
		The triangular sides of the tetrahedron become spherical triangles on the surface of the sphere.
		By this tranformation, the role of the topical quantum number is not changed.If spin and topical quantum number cause the fourfold degeneracy of the lowest state in the PSE, one might infer, that this degeneracy will extend to the higher states and cause the Occupation of States accordingly.
	www.neubert.net /TETRA.html (642 words)

	Tetrahedral Stellations of the Dodecahedron
		A tetrahedral 4-coloring of the dodecahedron can either have no adjacent faces of the same color (method 1) or groups of three of the same color (method 2).
		The notation here is tentative: A refers to a tetrahedrally arranged chiral group of twelve wedges in four edge-connected groups of three, C is the mirror image of A, and B is the remaining six reflexibly arranged wedges.
		Each of the following tetrahedral stellations of the dodecahedron is given by a subset of these six cells, but many possibilities are not included because either they close off a void in the center or their mirror image is already included.
	www.georgehart.com /virtual-polyhedra/stellations-dodecahedron-tetrahedral.html (690 words)

	Tetrahedral mesh generation with multiple elements through the thickness
		Garimella and M. Shephard, "Tetrahedral mesh generation with multiple elements through the thickness", in Proceedings of 4th Annual International Meshing Roundtable Conference, (Albuquerque, NM), pp.
		The problem of automatically generating unstructured tetrahedral meshes having a user specified number of elements in the thickness direction without over-refinement in the other directions is addressed in this paper.
		The procedures generate meshes with multiple elements through the thickness by anisotropically enriching an initial mesh, using local mesh modification procedures, wherever the mesh does not have a suffient number of elements through the thickness.
	math.lanl.gov /~rao/Publications/garimella-1995-tetrahedral.shtml (215 words)

	Tetrahedral Kites
		A tetrahedron, from which the word tetrahedral is derived, means a solid bounded by four surfaces.
		Doctor Alexander Graham Bell made serious attempts with huge kites made of tetrahedral units to solve the problem of airplane construction and much discussion of the principles was to be found in the magazines between the years 1903 and 1908.
		I have not found the single units to be as satisfactory as the bow kite, and the United States Weather Bureau has not found them to be as satisfactory for their work as the box kite perfected by Professor Martin.
	www.inquiry.net /outdoor/spring/kites/tetrahedral.htm (1047 words)

	Tetrahedral dimple pattern golf ball - Patent 5890974
		The present invention was developed to provide a new golf ball dimple pattern based on a tetrahedral design which provides improved flight characteristics to the ball.
		Accordingly, it is a primary object of the invention to provide a golf ball having two poles and an equator and a preselected number of dimples covering the surface of the ball and arranged in a geometrical lattice configuration based upon a subdivided tetrahedral lattice.
		When applying the true tetrahedral configuration to a golf ball surface, it turns out that the two triangles ST which straddle each pole P differ slightly from the remaining triangles T, all of which are identical.
	www.freepatentsonline.com /5890974.html (1591 words)

	Citations: Tetrahedral mesh generation in polyhedral regions based on convex polyhedron decompositions - Joe ...
		Tetrahedral mesh generation in polyhedral regions based on convex polyhedron decompositions.
		In Section 3, the input format and data structures are briefly described for the method of [JoS86] which generates convex polygon decompositions and triangular meshes in 2 D polygonal regions.
		Joe (1993), Tetrahedral mesh generation in polyhedral regions based on convex polyhedron decompositions, revised version, to appear in Intern.
	citeseer.ist.psu.edu /context/295702/0 (1052 words)

	Tetrahedral Sites (Site not responding. Last check: 2007-11-06)
		In a tetrahedral site the interstitial is in the center of a tetrahedra forms by four lattice atoms.
		The configuration on top is the tetrahedral position in the fcc lattice.
		The fl circles denote lattice points, the red circle marks one of the 8 the tetrahedral position.
	www.tf.uni-kiel.de /matwis/amat/def_en/kap_1/illustr/t1_3_4.html (104 words)

	The Tetrahedral Scheme
		It is different, however, because grid points can easily be indexed with reference to a regular cubic lattice; the hexagonal scheme operates on a rectangular grid in stretched or transformed coordinates.
		In fact, a tetrahedral scheme can be obtained directly from an octahedral scheme simply by removing half of the grid points it employs; as such, any given grid point in the tetrahedral scheme has four nearest neighbors.
		The bound is the same as the bound for passivity of a tetrahedral mesh.
	ccrma.stanford.edu /~jos/vonn/Tetrahedral_Scheme.html (426 words)

	[No title]
		In addition to stable tetrahedral molecules like methane and carbon tetrachloride, the building block of a diamond's unit cell is a tetrahedron because each carbon can covalently bond with 4 other surrounding carbons.
		Ligands in complex ions, and anions in crystals, assume a tetrahedral configuration around a central cation whenever the coordination number, or crystal coordination number, respectively is 4.
		The k-component of O is the perpendicular height of the centroid above the tetrahedron's equilateral triangular face in the xy-plane.
	www-personal.umich.edu /~hoaglund/tetrahed.html (1221 words)

	Tetrahedral Geometry
		An example of tetrahedral electron pair geometry (E. and molecular geometry is CH The carbon has 4 valence electrons and thus needs 4 more electrons from four hydrogen atoms to complete its octet.
		This molecule provides the basis for the tetrahedral geometries at each carbon in a hydrocarbon chain.
		This shows tetrahedral geometry for both the electron pair geometry and the molecular geometry.
	www.elmhurst.edu /~chm/vchembook/204tetrahedral.html (258 words)

	purevolume™ \| The Tetrahedral Experience
		The Tetrahedral Experience may be over but new things await on the horizon.
		The Tetrahedral Experience is a band from Vernon CT. They love playing music and love people to listen.
		The Tetrahedral Experience is out there to create music that is more illustrative than that of which produced thus far.
	www.purevolume.com /thetetrahedralexperience (234 words)

	Tetrahedral and Octahedral Sites in Closest Packing
		Tetrahedral and octahedral sites in closest packing can be occupied by other atoms or ions in crystal structures of salts and alloys.
		Use the diagram shown here as a starting point, and construct a tetrahedral arrangement by placing four spheres of radius R at alternate corners of a cube.
		Cations fitting into the tetrahedral sites cannot be smaller than 0.225 R. Usually, most ions are slightly larger than 0.225 R, but smaller than 0.414 R. In such cases, the cation coordination is tetrahedral, and a typical structure is ZnS, although covalent bonding is also involved in ZnS.
	www.science.uwaterloo.ca /~cchieh/cact/c123/tetrahed.html (878 words)

	SAW filter using tetrahedral amorphous carbon and method for manufacturing the same - Patent 6806795
		Here, the acoustic wave transmission medium of the tetrahedral amorphous carbon formed on the substrate is deposited by arc discharging with respect to fl lead.
		The acoustic wave transmission medium of the tetrahedral amorphous carbon formed on the substrate is deposited by laser ablation using fl lead.
		While the invention has been shown and described with reference to certain preferred embodiments thereof, it will be understood by those skilled in the art that various changes in form and details may be made therein without departing from the spirit and scope of the invention as defined by the appended claims.
	www.freepatentsonline.com /6806795.html (4024 words)

	Re: What about tetrahedral kites
		Tetrahedrals are not the easiest kites to set up and trim, while a flowform is up in no time.
		I used to fly a Pelibox in strong winds, but even that one took me about fifteen minutes before I got the tension right, and when walking around with it, it is a huge, hard to handle construction.
		This might be the only reason why you don't see any tetrahedral kites as camera lifters.
	arch.ced.berkeley.edu /kap/discuss/_kapdiscuss/00000169.htm (90 words)

	Tetrahedral
		Methane is tetrahedral in that its four hydrogen atoms define the vertices (points) of a tetrahedron.
		The bonds between carbons in diamond are also tetrahedral and these tetrahedra form an extended 3-D network that is diamond.
		A tetrahedron, in mathematics, is a polyhedron of four faces, and tetrahedral is the quality of beeing a tetrahedron.
	www.newton.dep.anl.gov /askasci/chem00/chem00377.htm (471 words)

	Tetrahedral Number Sequence
		The Tetrahedral Number Sequence can be easily understood if you think of a stack of marbles in the shape of a Tetrahedron.
		Each layer in the tetrahedron of marbles is actually part of the Triangular Number Sequence (1, 3, 6, etc).
		And both the triangular numbers and the tetrahedral numbers are on Pascal's Triangle.
	www.mathsisfun.com /tetrahedral-number.html (126 words)

	Citations: the Maximum Angle Condition for Linear Tetrahedral Elements - Krizek (ResearchIndex)
		Krizek, "On the maximum angle condition for linear tetrahedral elements", SIAM J. on Numerical Analtsis, Vol.
		The intention here is not to deal with the issue of how to construct an optimal mesh but instead to consider the related issue of how an existing mesh should be assessed given a solution.
		Krizek, "On the maximum angle condition for linear tetrahedral elements", SIAM Journal on Numerical Analysis 29 (1992), 513--520.
	citeseer.ist.psu.edu /context/426073/0 (712 words)

	Math Forum - Ask Dr. Math
		Math: I'm looking for a simple formula (and derivation) of the height of a tetrahedral pyramid with an equilateral triangle as a base.
		The "sides" making up the pyramid are isosceles triangles with 45-degree angles - essentially the pyramid is a portion of a standard cube.
		Date: 09/13/2001 at 12:22:44 From: Doctor Jubal Subject: Re: Height of tetrahedral pyramid Hi Bob, The height of a pyramid depends on its shape, so unlike the volume formula V=bh/3 that works for all pyramids, there's no succinct formula that will give the height of any pyramid.
	mathforum.org /library/drmath/view/51820.html (876 words)

	The Math Less Traveled » Blog Archive » Computing tetrahedral numbers
		I left off the discussion of tetrahedral numbers in my last post by posing the question of what the 144th tetrahedral number is, and promising to explain a quick way to figure it out without having to actually add up the first 144 triangular numbers.
		We’re almost there… the nth tetrahedral number, of course, is just the sum of the first n triangular numbers.
		Even this method has its limits, though — using J to compute the nth tetrahedral number actually causes your computer to store a list of the first n whole numbers in its memory, which is fine for values of n like 12 or 144.
	www.mathlesstraveled.com /?p=48 (1116 words)

	Amazon.com: Tetrahedral (Site not responding. Last check: 2007-11-06)
		Tetrahedral Structures in Amorphous Carbons (Reprint from Acta crystallographica, Vol.
		A tetrahedral model of accounting education: A framework for research [An article from: Journal of Accounting Education by I.T. Nelson
		On the synthesis of a tetrahedral cage chelate ligand (Massachusetts Institute of Technology.
	www.amazon.com /s?ie=UTF8&keywords=Tetrahedral&tag=acronymfinder-20&index=blended&link_code=qs&page=1 (340 words)

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