An orthant around a point denotes a subset of the - dimensional space in geometry , which lies on exactly one side of the axis-parallel hyperplanes running through . To be more precise, an orthant is the intersection of half-spaces of the that are parallel to an axis and run through . Formal:
-
is an orthant around if and only if there are numbers ( ) with .
It follows from this that there is an exactly orthant around a point .
Examples
- The eight orthants around the origin are called octants .