Slab (geometry)

In geometry, a slab is a region between two parallel lines in the Euclidean plane,^[1] or between two parallel planes in three-dimensional Euclidean space or between two hyperplanes in higher dimensions.^[2]

A slab can also be defined as a set of points:^[3] $${\displaystyle \{x\in \mathbb {R} ^{n}\mid \alpha \leq n\cdot x\leq \beta \},}$$ where ${\displaystyle n}$ is the normal vector of the planes ${\displaystyle n\cdot x=\alpha }$ and ${\displaystyle n\cdot x=\beta }$.

Or, if the slab is centered around the origin:^[4] $${\displaystyle \{x\in \mathbb {R} ^{n}\mid |n\cdot x|\leq \theta /2\},}$$ where ${\displaystyle \theta =|\alpha -\beta |}$ is the thickness of the slab.

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