“Parallelepiped”的概念、定义、习题解题方法及翻译-数学辞典

单词

Parallelepiped

释义

Parallelepiped

In 3-D, a parallelepiped is a Prism whose faces are all Parallelograms. The volume of a 3-Dparallelepiped is given by the Scalar Triple Product

In -D, a parallelepiped is the Polytope spanned by Vectors , ..., in a Vector Space over the reals,

where

for

, ...,

. In the usual interpretation, the Vector Space is taken asEuclidean Space, and the Content of this parallelepiped is given by

where the sign of the determinant is taken to be the ``orientation'' of the ``oriented volume'' of the parallelepiped.

See also Prismatoid, Rectangular Parallelepiped, Zonohedron

References

Phillips, A. W. and Fisher, I. Elements of Geometry. New York: Amer. Book Co., 1896.

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