# Definition:Analytic Geometry

## Definition

**Analytic geometry** is the study of geometry by algebraic manipulation of systems of ordered pairs of variables representing points in Cartesian space.

Traditionally, the subject is divided into two main branches:

### Plane Analytic Geometry

**Plane analytic geometry** is the branch of analytic geometry that makes an algebraic study of the real number plane $\R^2$.

### Solid Analytic Geometry

**Solid analytic geometry** is the branch of analytic geometry that makes an algebraic study of the real vector space $\R^3$.

## Also known as

**Analytic geometry** is also sometimes referred to as:

**Coordinate geometry****Cartesian geometry****Algebraic geometry****Analytical geometry**

## Historical Note

The discipline of **analytic geometry** is traditionally supposed to have originated with the work of René Descartes, hence its name of **Cartesian geometry**.

There exists a story that he first invented it while watching a fly crawling across the ceiling while he was lying in bed in the morning.

However, it appears that Descartes may in fact have obtained his key ideas from Nicole Oresme's *Tractatus de configurationibus qualitatum et motuum*.

It is also worth pointing out that Pierre de Fermat had the same idea at the same time as Descartes, independently of him, and, according to some sources, did considerably more with it.

Be that as it may, Descartes and Fermat corresponded with each other on the subject, so it may be accurate to suggest that there was considerable overlap between them.

## Also see

- Results about
**analytic geometry**can be found**here**.

## Sources

- 1947: William H. McCrea:
*Analytical Geometry of Three Dimensions*(2nd ed.) ... (previous) ... (next): Chapter $\text {I}$: Coordinate System: Directions: $\S 1$. Introductory - 1952: T. Ewan Faulkner:
*Projective Geometry*(2nd ed.) ... (previous) ... (next): Chapter $1$: Introduction: The Propositions of Incidence: $1.1$: Historical Note - 1989: Ephraim J. Borowski and Jonathan M. Borwein:
*Dictionary of Mathematics*... (previous) ... (next):**analytic geometry** - 1992: Frederick W. Byron, Jr. and Robert W. Fuller:
*Mathematics of Classical and Quantum Physics*... (previous) ... (next): Volume One: Chapter $1$ Vectors in Classical Physics: $1.1$ Geometric and Algebraic Definitions of a Vector - 1998: David Nelson:
*The Penguin Dictionary of Mathematics*(2nd ed.) ... (previous) ... (next):**analytic geometry** - 1998: David Nelson:
*The Penguin Dictionary of Mathematics*(2nd ed.) ... (previous) ... (next):**coordinate geometry (analytic geometry)** - 2008: David Nelson:
*The Penguin Dictionary of Mathematics*(4th ed.) ... (previous) ... (next):**analytic geometry** - 2008: David Nelson:
*The Penguin Dictionary of Mathematics*(4th ed.) ... (previous) ... (next):**coordinate geometry (analytic geometry)** - 2014: Christopher Clapham and James Nicholson:
*The Concise Oxford Dictionary of Mathematics*(5th ed.) ... (previous) ... (next):**analytic geometry**