Wedge
The term "wedge" has a number of different meanings in mathematics.
It is sometimes used as another name for the caret symbol.
The term also refers to the notation ( ^ ) used to indicate logical AND.
In solid geometry, ungulae like the conical wedge, cylindrical wedge, and spherical wedge are commonly known as wedges.
However, when the term is used by itself in solid geometry, "wedge" refers a right triangular prism turned so that it rests on one of its lateral rectangular faces (left figure). Harris and Stocker (1998) define a more general type of oblique wedge in which the top edge is symmetrically shortened, causing the end triangles to slant obliquely (right figure). The removal of six identical and oppositely-oriented oblique wedges from a cube gives the endododecahedron.
For an oblique wedge of base lengths a and b, top edge length c, and height h (right figure), the volume of the wedge is
![画像:int_0^h[a-(a-c)z/h]b(h-z)/hdz](/index.cgi/contrast/https://mathworld.wolfram.com/images/equations/Wedge/Inline8.svg){kind=link}
In the case of a right wedge c=a, this simplifies to
| V=1/2abh. |
(3)
|
The geometric centroid is located at a height
![画像: z^_=(<z>)/V=(int_0^h[a-(a-c)z/h]b(h-z)/hzdz)/V=((a+c)h)/(2(2a+c))](/index.cgi/contrast/https://mathworld.wolfram.com/images/equations/Wedge/NumberedEquation2.svg){kind=link}
above the base, which simplifies to z^_=h/3 for a right wedge c=a.
See also
AND, Caret, Endododecahedron, Pentagonal Wedge, Prism, Prismatoid, Tetragonal Antiwedge, UngulaExplore with Wolfram|Alpha
More things to try:
References
Bringhurst, R. The Elements of Typographic Style, 2nd ed. Point Roberts, WA: Hartley and Marks, p. 286, 1997.Harris, J. W. and Stocker, H. "Wedge." §4.5.2 in Handbook of Mathematics and Computational Science. New York: Springer-Verlag, p. 101, 1998.Referenced on Wolfram|Alpha
WedgeCite this as:
Weisstein, Eric W. "Wedge." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/Wedge.html