Definition:Homogeneous Cartesian Coordinates

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This page is about Homogeneous Cartesian Coordinates. For other uses, see Homogeneous.


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:

\(\ds x\) \(=\) \(\ds \dfrac X Z\)
\(\ds y\) \(=\) \(\ds \dfrac Y Z\)

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:

$P = \tuple {X : Y : Z}$

Also see

  • Results about homogeneous Cartesian coordinates can be found here.