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Topic: Unit cube


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  Unit cube - Wikipedia, the free encyclopedia
A unit cube is a cube all of whose sides are 1 unit long.
The volume of a 3-dimensional unit cube is 1 cubic unit, and its total surface area is 6 square units.
The term unit cube is also used to refer to "cubes" in n-dimensional spaces, for other values of n than 3.
en.wikipedia.org /wiki/Unit_cube   (96 words)

  
 NationMaster - Encyclopedia: Unit cube   (Site not responding. Last check: 2007-10-31)
A unit cube is a 3-dimensional geometric figure that consists of a cube in which all of its dimensions are 1 unit long.
Units of space per unit of time is the definition of speed, hence the electric current is a speed.
In order to ascertain the relation between this arbitrary system and the natural system of units it is necessary to measure some one physical quantity whose magnitude can be identified in the natural system, as was done in the previous determination of the relations between the natural and conventional units of space, time, and mass.
www.nationmaster.com /encyclopedia/Unit-cube   (248 words)

  
 Soma cube - Wikipedia, the free encyclopedia
The Soma cube is a solid dissection puzzle invented by Piet Hein during a lecture on quantum mechanics by Werner Heisenberg.
The pieces of the Soma cube consist of all possible combinations of four or fewer unit cubes, excluding all regular shapes (i.e., the 1x1x1, 1x1x2, 1x1x3, 1x1x4 and 1x2x2 cuboids).
The Soma cube is often regarded as the 3D equivalent of polyominos.
en.wikipedia.org /wiki/Soma_cube   (335 words)

  
 Cube (geometry) - Biocrawler   (Site not responding. Last check: 2007-10-31)
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_%28geometry%29   (442 words)

  
 Unit cube - the free encyclopedia   (Site not responding. Last check: 2007-10-31)
A unit cube is a cube all of whose sides are 1 unitlong.
The volume of a 3-dimensional unit cube is 1 cubic unit, andits total surface area is 6 square units.
The term unit cubeis also used to refer to "cubes" in n-dimensional spaces,for other values of n than 3.
www.free-web-encyclopedia.com /default.asp?t=Unit_cube   (59 words)

  
 Soma cube
The Soma cube is a mathematical puzzle by Piet Hein.
The soma cube is often regarded as the 3d equivalent of tangrams.
There are 240 distinct solutions of the soma cube puzzle, up to rotations and reflections: these are easily generated by a recursive search computer program similar to that used for the eight queens puzzle.
www.nebulasearch.com /encyclopedia/article/Soma_cube.html   (310 words)

  
 Reference.com/Encyclopedia/Cube
A cube (or regular hexahedron) is a three-dimensional Platonic solid composed of six square faces, facets or sides, with three meeting at each vertex.
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.
www.reference.com /browse/wiki/Cube_%28geometry%29   (615 words)

  
 Circumnavigating a cube and a tetrahedron
For the unit dodecahedron, the route shown is made up of a diagonal of each face (so is 12 times the golden ratio); while for the unit icosahedron, the route shown is made up of 12 altitudes of triangles.
In themselves, they not of great interest because their length is equal to the number of corners of a regular polyhedron (so the results would be 4 for a unit tetrahedron, 8 for a cube, 6 for an octahedron, 20 for a dodecahedron and 12 for an icosahedron).
Note that a unit Cube is larger than a unit Octahedron, and that a unit Dodecahedron is larger than a unit Icosahedron.
www.btinternet.com /~se16/js/circumnavcubetetra.htm   (3033 words)

  
 EBTX - The Relationship between e and pi   (Site not responding. Last check: 2007-10-31)
Now, clearly the hypothetical "unit cube" of the Euclidean manifold might shrink to the limit of 0 or it might expand without limit.
I propose then that the unit cube is "stretched" greater than 1 unit while others are correspondingly compressed (inverse fractions) and that therefore the probability of finding a new particle in a hypothetical unit cube (unstretched) is less than 1/2.
Or, put another way, the probability of finding a particle in the unit which is now 3 is still 1/2 and that in the 1/3 cube is still 1/2.
www.ebtx.com /ntx/ntx33a1.htm   (515 words)

  
 Volume Lessons by MATHguide
A unit cube can be 1" x 1" x 1" or 1 yd x 1 yd x 1 yd or 1 ft x 1 ft x 1 ft or a cube by some other unit.
Since the length is 3 units and the width is 6 units, the bottom layer of cubes measure rows and columns that are 3 units by 6 units.
To find the volume of a square based pyramid, we will start with a cube, which is a prism that has edges of equal length, which have been labelled with the traditional letter s.
www.mathguide.com /lessons/Volume.html   (2009 words)

  
 [No title]
1) the odd cube case the smallest cube one could construct in this case is the unit cube (ie a cube where each edge is of unit lenght, 1 centimer for example).
The volume of the obtained cube (of edge L+2), constructed by adding a shell of unit cubes, is given by the volume of the cube we started from (ie the cube of edge L) plus the number of unit cubes in the shell: (L+2)^3 = L^3 + (6L^2 + 12L + 8).
Consider constructing a hyper-cube (a cube in d dimensions) starting from a hyper-cube of edge L. This must be a hyper-cube of edge L+2.
www-pnp.physics.ox.ac.uk /~abdessel/cube.txt   (1820 words)

  
 Unit 22 Section 2 : Volume of a Cube
The volume of the cube is 8 m³ (8 cubic metres).
The volume of the cube is 8 000 000 cm³ (eight million cubic centimetres).
The area of one face of a cube is 81 cm².
www.cimt.plymouth.ac.uk /projects/mepres/book7/bk7i22/bk7_22i2.htm   (519 words)

  
 USAMTS Problem 1/1/14
Taking the red 3 x 3 x 3 cube, all of the red unit-faces must be showing, and none of the “inner faces” (the faces not showing) may be red.
Also, there are exactly 8 “corner” unit cubes with 3 red faces, 12 “edge” unit cubes with 2 red faces, 6 “central” unit cubes with one red face, and 1 “inner” unit cube with no red faces.
Thus, we have exactly three unit cubes that contain only two different colors among their faces; the rest have all 3 different colors among their faces.
www.mit.edu /people/agustya/Math/2-15.html   (1132 words)

  
 Math Forum - Ask Dr. Math   (Site not responding. Last check: 2007-10-31)
One day Katie used the unit cubes to build a larger floating cube that was three units long on each edge.
I know that each unit cube does not have the same number of faces painted red because some are on the corners and they should only have 3 faces painted (the top and the two sides) and there are 6 faces on the cube.
Note that for a unit cube to have all 6 of its faces painted, it would have to have all 6 of those faces exposed while part of the larger cube.
www.mathforum.com /library/drmath/view/61866.html   (549 words)

  
 Cube Info - Bored Net - Boredom   (Site not responding. Last check: 2007-10-31)
The cube is a special kind of square prism and of triangular trapezohedron, and is dual to the octahedron.
For instance, sugar is usually cut into cubes, and the familiar six-sided die is cube shaped.
In the four-dimensional geometry, the analogue of a cube has a special name - a tesseract.
www.borednet.com /e/n/encyclopedia/c/cu/cube.html   (306 words)

  
 Math Forum - POW Solutions, October 9-13, 1995   (Site not responding. Last check: 2007-10-31)
I eliminated the 3 unit cube because I had to find 23 unpainted cubes because there is one one unit cuve inside and if I paint one side of the large cube I would cover nine one unit cubes leaving a total of 18 one unit cubes.
The unpainted cubes are in the core and on the unpainted side of the large cube with dimensions of 2*3*4.
Therefore the 16 cubes of one surface of the large cube are left unpainted.
mathforum.org /pow/solu38.html   (4800 words)

  
 The Boltzmann Machine: Necker Cube Example   (Site not responding. Last check: 2007-10-31)
If there are alot of units active with positive connections to this unit and few active that have negative connections the sum will be large.
The activation of the unit is then set to 1 with probability p where p equals the sigmoid function of the summed weighted activation.
The network should gradually activate all of the units of one of the interpretations and deactivate the units of the other interpretation.
www.cs.cf.ac.uk /Dave/JAVA/boltzman/Necker.html   (545 words)

  
 Cube Coloring Problem
CEC is a consortium of teacher from 14 western states dedicated to improving the quality of education in the rural, western, United States, and particularly the quality of math and science Education.
Investigate what happens when different sized cubes are constructed from unit cubes, the surface areas are painted, and the large cubes are taken apart.
The cubes with one face painted occur as squares on the six faces of the original cube.
www.teachersdesk.com /lessons/math/Cube%20Coloring%20Problem.htm   (442 words)

  
 PinkMonkey.com Geometry Study Guide - 8.3 The cuboid and the cube
A cube is a square right prism with the lateral edges of the same length as that of a side of the base.
A unit cube is a cube with length equal to one unit.
ON form three sides of a unit cube as shown in Figure 8.6a Let another unit cube be placed on the right side of this unit cube such that one of its edges lies along seg.
www.pinkmonkey.com /studyguides/subjects/geometry/chap8/g0808301.asp   (574 words)

  
 Encyclopedia :: encyclopedia : Soma cube   (Site not responding. Last check: 2007-10-31)
The Soma cube is a solid dissection puzzle created by Piet Hein during a lecture on quantum mechanics by Werner Heisenberg.
The pieces of the Soma cube consist of all possible non-regular (i.e.
There are 240 distinct solutions of the soma cube puzzle, up to rotations and reflections: these are easily generated by a simple recursive backtracking search computer program similar to that used for the eight queens puzzle.
www.hallencyclopedia.com /topic/Soma_cube.html   (337 words)

  
 AppleInsider - Sources Reveal Rumored Apple Macintosh Cube
The unit, which is said to sport a logic-board containing a single 4X AGP graphics expansion slot and a processor slot capable of accepting an Apple G3 or G4 CPU card, is housed inside a cube-like Apple enclosure that measures a little over a foot in length on each side.
Two handles run horizontally along the base of the unit from front to rear, acting as legs.
On a side note, this rumored Apple cube is not expected to be the new enclosure for Apple's multiprocessor machines.
www.appleinsider.com /articles/0007/trinity.shtml   (763 words)

  
 Kadon Enterprises, Inc. Naming system, Hexacube (page 2 of 5)   (Site not responding. Last check: 2007-10-31)
To turn a pentomino (flat pentacube) into a 3-D hexacube, we simply add one unit cube to the top and bottom of any of the 5 unit square faces of the pentomino.
The X pentomino has only two distinct cube placements, and the I pentomino is not in this group at all, because no matter where we attach the cubelet, all six cubes still make a single cross-section.
The drawing shows the numbering key of the cube faces and the attached cube as a smaller square in its respective position.
www.gamepuzzles.com /hxnames2.htm   (251 words)

  
 Unit 22 Section 1 : Volume using the Unit Cube
This section introduces the idea of volume by counting up how many 1 cm cubes there are in a solid.
The volume of this cube is 1 cm³ (1 cubic centimetre)
The diagram below shows the cubes that are used to make the first layer of a cuboid.
www.cimt.plymouth.ac.uk /projects/mepres/book7/bk7i22/bk7_22i1.htm   (454 words)

  
 Cube Storage Unit
This is the "Cube" storage unit, a universal storage solution that is both beautiful and functional.
Each basic cube is sized to accommodate items as large as 11" X 10 3/4".
Two other sizes are available, a "half cube" that is the same width but only half the height and a "quarter cube", only 1/4 the size.
www.stanpikedesigns.com /cube.htm   (378 words)

  
 Transformation from unit cube to view frustum - iDevGames - Community Forum
Now, to do this, I've decided the most efficient way would be to represent my particles inside of a unit cube, and to use a transformation to move that cube from untransformed eye-space to the world space.
I need a matrix transform which will transform a unit cube at the origin to the view frustum (translated to wherever the camera is, and along the camera's direction).
The cube in question is the radius-1 cube, so if you want a unit cube you'd have to do an extra scale operation, but it's quite straightforward.
www.idevgames.com /forum/showthread.php?t=9610   (1201 words)

  
 [No title]
Using stackable unit cubes to connect between the algebraic and geometric contents.
The cube is then dipped (hypothetically) into a bucket of paint.
Describe the cube in terms of painted sides; number of cubes with 3 sides painted, = 8 number of cubes with 2 sides painted, = 12 number of cubes with 1 side painted, = 6 number of cubes with 0 sides painted.
www.cwu.edu /~math_science/Activities/happybirthdaytoacube.doc   (651 words)

  
 Soma cube   (Site not responding. Last check: 2007-10-31)
Seven pieces made out of unit cubes must beassembled into a 3x3x3 cube.
There are 240 distinct solutions of the somacube puzzle, up to rotations and reflections: these are easily generated by a recursivesearch computer program similar to that used for the eight queenspuzzle.
Right screw: unit cube placed on top of clockwise side.Chiral in 3D.
www.therfcc.org /soma-cube-102819.html   (272 words)

  
 Cube/Rectangular Prism Activity
Students manipulate cubes and rectangular prisms, drawing geometric shapes using grid paper and also manipulating geometric shapes using the ESCOT Runner software to observe geometric relations.
Pass out one sheet of isometric dot paper to each student and instruct them to draw a unit cube.
Discuss with the students the formulas to calculate the area and volume of a cube and rectangular prism given the length of the side or the length, height and width of the prism.
mathforum.org /alejandre/escot/cube.prism.html   (830 words)

  
 TOTE AND TRAY STORAGE UNITS
A 20 cube storage unit is hinged to a basic two shelf storage unit to provide ample storage space for the classroom.
These are two popular units in one very usable hinged configuration.
One side is open storage and the other is the 25 cube tote storage unit.
woodetccorp.com /gsaSTORAGEUNITSforTOTES.htm   (323 words)

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