unit cube sentence in Hindi
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- The box is translated so that its center is at the origin, then it is scaled to the unit cube which is defined by having a minimum corner at (-1,-1,-1 ) and a maximum corner at ( 1, 1, 1 ).
- Just check all six vertices against the plane for distance, and when you find the closest one, because it's a unit cube you already know its magnitude and it could be normalized with a single scalar multiplication .-Rainwarrior 19 : 47, 6 September 2006 ( UTC)
- As a background, R ( p, q ) is the Euclidean distance between points P and Q in a meshed unit cube ( in all there are N = n ^ 3 regularly spaced points ), and x ( p, q ) is just x-component of the distance.
- If a point in the Hilbert cube is specified by a sequence \ lbrace a _ n \ rbrace with 0 \ leq a _ n \ leq 1 / n, then a homeomorphism to the infinite dimensional unit cube is given by h ( a ) _ n = n \ cdot a _ n.
- Since the octant divides the unit cube on the origin up like a Voronoi diagram, each point in the octant closest to its nearest vertex, if you know the octant of that point, you know which vertex of the cube is closest .-Rainwarrior 20 : 12, 8 September 2006 ( UTC)
- In fact, the Banach Tarski paradox demonstrates that it is impossible to find a finitely-additive measure ( or a Banach measure ) defined on all subsets of a Euclidean space of three ( and greater ) dimensions that is invariant with respect to Euclidean motions and takes the value one on a unit cube.
- The main interest, of mine, was using this to constrain what groups the homotopy groups, in the normal sense, can be based on how they are constructed from the unit cubes ( the Torus being a product of two circles, which in turn are quotients of the interval, etc . ).
- "' Maria Adelaide Sneider "'( 6 December 1937 1 May 1989 ) was an Italian mathematician working on capacity of the unit cube, this work also led her to give a rigorous proof of Green's identities for large classes of hypersurfaces with singularities, and later to develop an accurate mathematical analysis of the points effect.
- The 3 & times; 3 & times; 3 version, which is the version usually meant by the term " Rubik's Cube, " has nine square faces on each side, for a total area of fifty-four faces, and occupies the volume of twenty-six unit cubes ( not counting the invisible cube in the center ).
- Note that the sides and edges of a " k "-cell need not be equal in ( Euclidean ) length; although the unit cube ( which has boundaries of equal Euclidean length ) is a 3-cell, the set of all 3-cells with equal-length edges is a strict subset of the set of all 3-cells.
- An equivalent statement is the following : any centrally symmetric convex body in \ mathbf { R } ^ n has a linear image which contains the unit cross-polytope ( the unit ball for the \ ell _ 1 ^ n norm ) and is contained in the unit cube ( the unit ball for the \ ell _ { \ infty } ^ n norm ).
- :My previous comment wasn't about the " number " of points ( indeed, in the continuous limit, \ left ] 0, 1 \ right [ ^ 3 has just as many points as \ mathbb { R } ^ 3 ), but about the restrictions placed on R _ { pq } and x _ { pq } by the requirement that both p and q must lie within the unit cube.
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