# Cartesian product (InstanceTopic, 3)

### From Higher Dimensions Database

The **Cartesian product** of two shapes *x* and *y*, with *n* and *m* dimensions respectively, is the shape defined by the set of all points whose first *n* co-ordinates are the co-ordinates of a point in shape *x* and last *m* co-ordinates are the co-ordinates of a point in shape *y*. The resulting shape has dimension *n*+*m*.

For example, the Cartesian product of a line and a square is a cube and the Cartesian product of two circles is a duocylinder.

The Cartesian product can also be referred to as the *square product*. It is one of the three bracketopic products and has the function MAX. It is also the square brick product.