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# Topic: Cube geometry

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 Cube Engine Games The engine, though designed for simplicity and elegance as opposed to feature and eyecandy checklists, still competes nicely thanks to its novel "6-directional heighfield deformable cube octree" world structure that is the basis for its in-game editing. Cube is the original game that started it all. Cube is also smaller in every way, in download, in hardware requirements (runs well on older video cards!), and in source code (the absolutely tiny code base is a very easy start for those wishing to experiment). www.cubeengine.com   (319 words)

 Cube (geometry) - Biocrawler   (Site not responding. Last check: 2007-11-07) The cube is a special kind of square prism, of rectangular parallelepiped and of triangular trapezohedron, and is dual to the octahedron. A cube can be inscribed in a dodecahedron so that each vertex of the cube is a vertex of the dodecahedron and each edge is a diagonal of one of the dodecahedron's faces; taking all such cubes gives rise to the regular compound of five cubes. If each edge of a cube is replaced by a one ohm resistor, the resistance between opposite vertices is 5/6 ohms, and that between adjacent vertices 7/12 ohms. www.biocrawler.com /encyclopedia/Cube_(geometry)   (362 words)

 Cube - LoveToKnow 1911 Kb(30s, a cube), in geometry, a solid bounded by six equal squares, so placed that the angle between any pair of adjacent faces is a right angle. A famous problem concerning the cube, namely, to construct a cube of twice the volume of a given cube, was attacked with great vigour by the Pythagoreans, Sophists and Platonists. Similarly the "cube root" of a quantity is another quantity which when multiplied by itself twice gives the original quantity; thus is the cube root of a (see Arithmetic and Algebra). www.1911encyclopedia.org /Cube   (787 words)

 AllRefer.com - cube (Mathematics) - Encyclopedia The volume of a cube is equal to the product of its dimensions, and since its dimensions are equal, the volume is equal to the third power, or cube, of any one of its dimensions. Hence, in arithmetic and algebra, the cube of a number or letter is that number or letter raised to the third power. The problem of constructing a cube with a volume equal to twice that of a given cube using only a compass and a straightedge is known as the problem of the duplication of the cube and is one of the famous geometric problems of antiquity. reference.allrefer.com /encyclopedia/C/cube.html   (263 words)

 nature's word | musings on sacred geometry The cube is, as noted in Chapter One, an excellent representative of the inherent unity of all things. If we reconsider the prior example of how the square root of three is generated from the cube, we will remember that it is generated by joining the opposing corners (the two opposites representing duality) with a line, i.e., making the relation between the two. In the example of the cube, it is the two corners that represent our red and blue characteristics, and the line that stretches between them that would be our purple, "shared" portion. www.unitone.org /naturesword/sacred_geometry/square_three/in_geometry   (2223 words)

 geometry help: different way to make a 6 sided square - Help.com For a cube centered at the origin, with edges parallel to the axes and with an edge length of 2, the Cartesian coordinates of the vertices are Geometry was one of the two fields of pre-modern mathematics, the other being the study of numbers. Geometry now uses methods of calculus and abstract algebra, so that many modern branches of the field are not easily recognizable as the descendants of early geometry. help.com /post/20230-different-way-to-make-a-6-sided-squ   (574 words)

 Cube Information The cube is a special kind of square prism, of rectangular parallelepiped and of 3-sided trapezohedron, and is dual to the octahedron. A cube is the three-dimensional case of the more general concept of a measure polytope. A cube can be inscribed in a dodecahedron so that each vertex of the cube is a vertex of the dodecahedron and each edge is a diagonal of one of the dodecahedron's faces; taking all such cubes gives rise to the regular compound of five cubes. www.bookrags.com /wiki/Cube   (588 words)

 Welcome To Applied Scientific Research Simulation of flow over cubes is relevant to a large number of industrial applications such as: convective cooling of microprocessor chips or buildings, drag and noise reduction in cars and trucks, or control of wind-induced vibrations in highrises. The cube geometry is very simple, yet the flow around it manifests interesting 3-D structures that are prominent in more complex configurations. The wake behind the cube, while symmetric during the early stages of its formation, is highly unsteady and asymmetric due to the introduction of random, noise-level disturbances to the flow field. www.applied-scientific.com /MAIN/GALLERY/CUBE/Cube.html   (648 words)

 Full Repository This component is a visual representation of a Cube primitive and can be used to introduce a Cube into a Java3D scene. The effects of the transformation are immediately visible as they are applied to geometry in the main viewport when the user interpolates through the camera transformation. The cosine relationships based on relative patch rotation and the 1/r^2 relationship based on distance are plotted on a graph as the geometry is manipulated. www.cs.brown.edu /exploratories/freeSoftware/catalogs/repository.html   (2864 words)

 Geometry Clipart ETC Cube A regular body with six square faces; a rectangular parallelopiped, having all its edges equal. Cuboctahedron A solid with fourteen faces formed by cutting off the corners of a cube parallel to the coxial octahedron far enough to leave the original faces squares, while adding eight triangular faces at the truncations. Cube trunctuated by octahedron "When a corner or an edge of one form is replaced by a face of another form, the first is said to be trunctuated by the second." — Ford, 1912 etc.usf.edu /clipart/galleries/math/geometry.htm   (1231 words)

 Doubling the cube The origins of the problem of doubling the cube may be somewhat obscure as we have just seen, but there is no doubt that the Greeks had known for a long time how to solve the problem of doubling the square. Although these many different methods were invented to double the cube and remarkable mathematical discoveries were made in the attempts, the ancient Greeks were never going to find the solution that they really sought, namely one which could be made with a ruler and compass construction. Gauss had stated that the problems of doubling a cube and trisecting an angle could not be solved with ruler and compasses but he gave no proofs. www-groups.dcs.st-and.ac.uk /~history/HistTopics/Doubling_the_cube.html   (2955 words)

 Notes on Finite Geometry (Site Map) An invariance of symmetry The diamond theorem on a 4x4x4 cube, and a sketch of the proof. Portrait of O A table of the octahedral group O using the 24 patterns from the 2x2 case of the diamond theorem. Study of O A different way of looking at the octahedral group, using cubes that illustrate the 2x2x2 case of the diamond theorem. finitegeometry.org /sc/map.html   (794 words)

 Metatron - Crystalinks Metatron's cube is also considered a holy glyph, and was often drawn around an object or person to ward off demons and satanic powers. This idea is also present in alchemy, in which the cube was favored as a containment circle or creation circle. The simplest means of constructing Metatron's Cube is to begin with a cube flattened along a diagonal that passes through its center, such that it becomes a 2D figure, equivalent to a regular hexagon divided via its own diagonals into six equilateral triangles. www.crystalinks.com /metatron.html   (663 words)

 Geometry Solution Geometry Solutions is a sophisticated calculator that calculates the perimeter, lateral and surface areas, and volume of plane and solid geometric figures. The formulas used to calculate the perimeter and area of each kind of geometric figure is also given. Geometry Solutions and geometric formulas when used together will strengthen your knowledge and abilities in geometry. www.gomath.com /geometrycal.html   (159 words)

 Cubes The isometries for the cube are rotations and reflections. Note that the symmetry group of the 3-cube is not the same as the group of rotations of the cube about some line. These additional symmetries arise from the reflections of the cube that are isometries but which can not be carried out physically in 3-dimensional space. www.ams.org /featurecolumn/archive/cubes7.html   (501 words)

 Conformance Nist, Bindable Nodes, Viewpoint As a result, the viewer should see a cubic geometry, with the word FRONT displayed, Text at the bottom of the world should show the position to be 0 0 10, and indicating the cube geometry with the pointing device should result in a "jumpcut" to the REAR view. This is indicated by a cube geometry displaying the word FRONT on its face, Text at the bottom of the world indicating that the Viewpoint position is 0 0 10, and Text at the top of the world indicating the the FRONT viewpoint is bound to the top of the stack. The word RIGHT should appear on the cube, Text at the bottom of the world should show the new Viewpoint position to be 10 0 0, and Text at the top of the world should indicate that the RIGHT Viewpoint is now bound to the top of the Viewpoint stack. www.web3d.org /x3d/content/examples/Conformance/BindableNodes/Viewpoint/index.html   (1586 words)

 Cube Map OpenGL Tutorial Cube map texturing is a form of texture mapping that uses a 3D direction vector (a fancy phrase that means nothing more than a direction) to index into a texture that is six square 2D textures arranged like the faces of a cube. Because the texture images for cube maps are merely the six cube faces of a cube environment, the cube map textures are easier to acquire from photographs or render dynamically. Another advantage of using cube map textures to generate stable specular highlights is that the number of specular light sources (all encoded in a single cube map texture) is independent of the rendering performance. developer.nvidia.com /object/cube_map_ogl_tutorial.html   (4284 words)

 Space figures and basic solids A cube and a pyramid are both polyhedrons; a sphere, cylinder, and cone are not. The volume of a cube is the cube of the length of one of its sides. The surface area of a cube is six times the area of one of these sides. www.mathleague.com /help/geometry/3space.htm   (955 words)

 Finite Geometry of the Square and Cube - Home Page These traditional and supposedly well-known structures are, surprisingly, closely related to small finite geometries. Such designs are formed by assembling two-colored square tiles or two-colored cubical blocks into larger squares or cubes, when the number of tiles or blocks in the larger arrays is a power of two. Similar structural diagrams can be made for the 64 and 63 points of, respectively, finite affine and projective spaces of 6 and 5 dimensions over the 2-element field, and the graphic symmetries that result generalize the results in fewer dimensions. finitegeometry.org /sc   (297 words)

 Construction of Incidence and Coset Geometries The rank three geometry consisting of the vertices, edges and faces of the cube, with symmetric inclusion as incidence might be encoded in the following way. The first 8 vertices of the graph correspond to the vertices of the cube, the next 12 vertices correspond to the edges of the cube and the last 6 are the faces of the cube. Construct the coset geometry CG obtained from the group G and the set S of subgroups of G. If G is a permutation group and S is a set of subgroups of G, the corresponding coset geometry, obtained by using Tits' algorithm (see above) is constructed. www.umich.edu /~gpcc/scs/magma/text1238.htm   (732 words)

 GNUbik   (Site not responding. Last check: 2007-11-07) The geometry list consists of a version number, which will change if the definition of the cube object ever changes (scripts should check this to ensure compatibility or else things will surely break); the current version is 1 (one). If you were to look at a cube with face index 4 towards you (remember vector indeces are zero based), then the top face would have index 0 (zero), the bottom 1 (one), the left 2, the right 3, and the back 5. For any one move (a quarter turn of a slice of the cube), the first item in the specification is the face which lies parallel to the desired slice, and may be 0 (zero), 1 (one) or two corresponding to the back, right and bottom faces. www.gnu.org /software/gnubik/manual/html_node/Raw-interface.html   (752 words)

 Geometry Attempts to sew the s geometry to the current shape geometry if the a and b parameters are both nonzero. Attempts to sew the s geometry to the current shape geometry if the a and b parameters are both nonzero according to transformation matrix m. Deforms the current shape geometry in a similar manner to a quadric, but is just controlled by two parameters (p-center side "inflation", h-corner "inflation"). mrl.nyu.edu /~perlin/packing/render/doc/render/Geometry.html   (3151 words)

 Cube -- from Wolfram MathWorld A cube with unit edge lengths is called a unit cube. The Atomium is 334.6 feet high, and the nine spheres at the vertices and center have diameters of 59.0 feet. The distance between the spheres along the edge of the cube is 95.1 feet, and the diameter of the tubes connecting the spheres is 9.8 feet. mathworld.wolfram.com /Cube.html   (1006 words)

 Math Forum: Geometry Project of the Month   (Site not responding. Last check: 2007-11-07) A bunch of unit cubes are put together to form a larger cube. Then the large cube is taken apart and 24 of the small cubes have no paint on them at all. Instead of 24 cubes, what is the smallest number of unpainted cubes for which there is more than one possible answer to the question (about how many small cubes were in the large cube and how many of the faces were painted)? mathforum.org /pom2/index.html   (245 words)

 Solid geometry Summary In mathematics, solid geometry was the traditional name for the geometry of three-dimensional Euclidean space — for practical purposes the kind of space we live in. Eudoxus established their measurement, proving the pyramid and cone to have one-third the volume of a prism and cylinder on the same base and of the same height, and was probably the discoverer of a proof that the volume of a sphere is the cube of its radii. Analytic geometry and vector techniques have a major impact by allowing the systematic use of linear equations and matrix algebra; this becomes more important for higher dimensions. www.bookrags.com /Solid_geometry   (2205 words)

 The Geometry Junkyard: 3D Geometry An aperiodic set of Wang cubes, J. Culik and Kari describe how to increase the dimension of sets of aperiodic tilings, turning a 13-square set of tiles into a 21-cube set. Circumnavigating a cube and a tetrahedron, Henry Bottomley. Bo Atkinson studies the geometry of a solid of revolution of an Archimedean spiral. www.ics.uci.edu /~eppstein/junkyard/3d.html   (3708 words)

 Cube on Cube Pattern Another way to view a cube is to visualize two squares with four pillars connecting the two squares at the corners. The Cube on Cube Pattern will assist you to align your frequencies so that you may be aware of the various levels and eventually begin to move into mastery of the various planes. When each of the cubes has been activated and they are symbolically perfectly aligned, this will indicate a balance between your upper powers, or upper worlds (spirituality) with your lower powers or lower worlds (physicality) and that you have now reclaimed your powers in both realms. www.esotericacupuncture.com /cube_on_cube_pattern.htm   (2108 words)

 www.uni-verse.org - Completing the Cube Scene   (Site not responding. Last check: 2007-11-07) The cube geometry, as left from the Modelling tutorial, is not suitable for display in Quel Solaar just yet. Geometry created from Loq Airou is in the form of "unparented" geometry nodes; we need to create an object node and link it to the geometry in order to create a true object in the scene. To prepare for linking the newly created object node to the geometry node holding the cube from the previous tutorial, click once on the background (not on the new object node). www.uni-verse.org /Completing_the_Cube_Scene.63.0.html   (1403 words)

 The Diamond Body: Buckminster Fuller and the Qabala (Qabalah Kabbalah Qabbalah Cabala QBL) Einstein used non-Euclidean geometry to explain the relativity of time and space as the geometry that is produced by matter or matter by geometry. The geometry of Vector Equilibrium is inferred from that of closest-packed spheres of equal radius. This is the geometry of closest-packed spheres in the nucleus of the atom. members.tripod.com /Sourceress   (5178 words)

 Cube Engine Games Cube is an open source multiplayer and singleplayer first person shooter game built on an entirely new and very unconventional engine. Cube is a landscape-style engine that pretends to be an indoor FPS engine, which combines very high precision dynamic occlusion culling with a form of geometric mipmapping on the whole world for dynamic LOD for configurable fps & graphic detail on most machines. Allows in-engine editing of geometry in full 3D (you fly around the map, point / drag stuff to select it / modify it), which can even be done simultaneously with others in multiplayer (a first!). www.cubeengine.com /cube.php4   (341 words)

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