Hyperrectangle

Definition

A hyper- rectangle in the -dimensional space is the Cartesian product of real intervals, ie

Examples

For one obtains an interval for a rectangle and a square.

For the special case that all intervals are equal to the unit interval, we obtain the unit hypercube

Properties

Limiting elements

Every - dimensional hyper rectangle

• Corners,
• Edges that abut each other at right angles and

In general, one-dimensional hyper- rectangle of

Limited hyper rectangles of dimension, where is.

Volume and surface area

The volume is a hyper- rectangle

This is the starting point for determining the volumes much more general quantities, as in the construction of the n-dimensional Lebesgue measure in measure theory is clear. Is the surface area