Parallélotope

The parallélotope makes it possible to generalize the concepts of Parallélogramme and Parallélépipède to a vector space E of finished size unspecified N . It is a Polytope in center of symmetry, therefore the opposite hyperfaces are parallel.

One can define it as the image of a Hypercube by a application refines.

With N vectors x₁,…, x_n of E will be thus associated the Parallélotope determined by these vectors which is definite part of E like the whole of the combinations of the x_i to coefficients ranging between 0 and 1

$P=\; \backslash \; left\; \backslash \; \{x=\; \backslash \; sum\_\; \{i=1\}\; ^n\; t\_i\; x\_i,\; \backslash ,\; \backslash \; forall\; I,\; 0\; \backslash \; Leq\; t\_i\; \backslash \; Leq\; 1\; \backslash \; right\; \backslash \}$

The parallélotope right or paved is the figure obtained when the vectors x_i are orthogonal two to two. It is advisable to see in the general parallélotope an oblique kind of paved .

The determinant makes it possible to extend the concept of Volume to the parallélotopes, and to add a concept of orientation.

Random links:

Franz Unger | Communes of the province of Ancône | Real Lemieux | Dario Knežević | Herne Bay (Kent) | Confessionalization

© 2007-2008 speedlook.com; article text available under the terms of GFDL, from fr.wikipedia.org