Definition:Homogeneous Cartesian Coordinates

Definition
Let $\CC$ denote the Cartesian plane.

Let $P = \tuple {x, y}$ be an arbitrary point in $\CC$.

Let $x$ and $y$ be expressed in the forms:

where $Z$ is an arbitrary real number.

$P$ is then determined by the ordered triple $\tuple {X, Y, Z}$, the terms of which are called its homogeneous Cartesian coordinates.

Also denoted as
This can also be presented as:
 * $P = \tuple {X : Y : Z}$