In
geometry
Geometry (; ) is, with arithmetic, one of the oldest branches of mathematics. It is concerned with properties of space such as the distance, shape, size, and relative position of figures. A mathematician who works in the field of geometry is c ...
, a slab is a region between two parallel lines in the
Euclidean plane
In mathematics, the Euclidean plane is a Euclidean space of dimension two. That is, a geometric setting in which two real quantities are required to determine the position of each point ( element of the plane), which includes affine notions ...
,
or between two parallel planes or
hyperplane
In geometry, a hyperplane is a subspace whose dimension is one less than that of its '' ambient space''. For example, if a space is 3-dimensional then its hyperplanes are the 2-dimensional planes, while if the space is 2-dimensional, its hype ...
s in higher dimensions.
Set definition
A slab can also be defined as a set of points:
where
is the normal vector of the planes
and
.
Or, if the slab is centered around the origin:
where
is the thickness of the slab.
See also
*
Bounding slab
*
Convex polytope
*
Half-plane
*
Hyperplane
In geometry, a hyperplane is a subspace whose dimension is one less than that of its '' ambient space''. For example, if a space is 3-dimensional then its hyperplanes are the 2-dimensional planes, while if the space is 2-dimensional, its hype ...
*
Prismatoid
*
Slab decomposition
*
Spherical shell
References
Elementary geometry
Geometric shapes
Spherical geometry
{{geometry-stub