# Definition:Cartesian Coordinate System

## Definition

A **Cartesian coordinate system** is a coordinate system in which the position of a point is determined by its relation to a set of perpendicular straight lines.

These straight lines are referred to as coordinate axes.

## Also defined as

In the definition of a **Cartesian coordinate system**, some older sources do not specify that the coordinate axes have to be perpendicular.

That is, such sources include **oblique coordinate systems** in the category of **Cartesian coordinate systems**

Such sources then refer to a Cartesian coordinate system in which the axes are specifically perpendicular as a **rectangular coordinate system**.

However, this is non-standard, and the contemporary view is that **Cartesian coordinate systems** are **rectangular** by default.

## Also known as

**Cartesian coordinates** are also known as **rectangular coordinates** or **orthogonal coordinates**.

## Also see

- Definition:Rectangular Coordinate System
- Definition:Oblique Coordinate System
- Definition:Orthogonal Coordinate System
- Definition:Rectilinear Coordinate System

- Results about
**cartesian coordinate systems**can be found**here**.

## Source of Name

This entry was named for René Descartes.

## Sources

- 1933: D.M.Y. Sommerville:
*Analytical Conics*(3rd ed.) ... (previous) ... (next): Chapter $\text I$. Coordinates: $2$. Coordinates - 1936: Richard Courant:
*Differential and Integral Calculus: Volume $\text { II }$*... (previous) ... (next): Chapter $\text I$: Preliminary Remarks on Analytical Geometry and Vector Analysis: $1$. Rectangular Co-ordinates and Vectors: $1$. Coordinate Axes - 1998: David Nelson:
*The Penguin Dictionary of Mathematics*(2nd ed.) ... (previous) ... (next):**Cartesian coordinate system** - 2008: David Nelson:
*The Penguin Dictionary of Mathematics*(4th ed.) ... (previous) ... (next):**Cartesian coordinate system** - 2010: Raymond M. Smullyan and Melvin Fitting:
*Set Theory and the Continuum Problem*(revised ed.) ... (previous) ... (next): Chapter $2$: Some Basics of Class-Set Theory: $\S 7$ Cartesian products: Remark