“Pyramid”的概念、定义、习题解题方法及翻译-数学辞典

单词

Pyramid

释义

Pyramid

A Polyhedron with one face a Polygon and all the other faces Triangles with a commonVertex. An -gonal regular pyramid (denoted ) has EquilateralTriangles, and is possible only for , 4, 5. These correspond to the Tetrahedron,Square Pyramid, and Pentagonal Pyramid, respectively. A pyramid therefore has a single cross-sectional shape inwhich the length scale of the Cross-Section scales linearly with height. The Area at a height is given by

(1)

where

is the base Area and

is the pyramid height. The Volume is therefore given by

(2)

These results also hold for the Cone, Tetrahedron (triangular pyramid), Square Pyramid, etc.

The Centroid is the same as for the Cone, given by

(3)

The Surface Area of a pyramid is

(4)

where

is the Slant Height and

is the base Perimeter. Joining two Pyramids together attheir bases gives a Bipyramid, also called a Dipyramid.

See also Bipyramid, Elongated Pyramid, Gyroelongated Pyramid, Pentagonal Pyramid, Pyramid, PyramidalFrustum, Square Pyramid, Tetrahedron, Truncated Square Pyramid

References

Beyer, W. H. (Ed.) CRC Standard Mathematical Tables, 28th ed. Boca Raton, FL: CRC Press, p. 128, 1987.

Hart, G. W. ``Pyramids, Dipyramids, and Trapezohedra.'' http://www.li.net/~george/virtual-polyhedra/pyramids-info.html.

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