# Definition:Geometry

## Definition

**Geometry** is a branch of mathematics which studies such matters as form, position, dimension and various other properties of ordinary space.

It has been suggested that **geometry** can be divided into $3$ main branches:

**Metrical geometry**, that is to say, what is understood as**geometry**proper**Projective geometry****Analytic geometry**

## Also see

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

## Historical Note

The Greek historian Herodotus visited Egypt in about $450$ BCE and reported that the annual flooding of the Nile would wipe out all the boundaries between fields.

It is suggested that the discipline of **geometry** may have arisen there, from the need for the rulers to re-establish those boundaries subsequently.

**Geometry** was also used for surveying and building in Babylon.

By the time of the ancient Greeks the subject had become sufficiently abstract to allow for general geometric properties to be understood.

The discipline was consolidated by the publication of Euclid's *The Elements* in $\text {c. 300 BCE}$.

In $1637$ René Descartes published his dissertation on analytic geometry, which allowed mathematicians to attack problems of **geometry** using the techniques of algebra.

At the same time, analytic geometry was also discovered independently by Pierre de Fermat.

This led to the development of differential calculus, which led to the study of surfaces by Leonhard Paul Euler and Gaspard Monge.

In $1827$, the study of differential geometry was initiated by Carl Friedrich Gauss.

In $1639$, Girard Desargues pioneered the study of projective geometry, which was neglected at the time, but grew to considerable importance in the $19$th century.

Algebraic geometry was developed in the $19$th century by Arthur Cayley.

At around the same time non-Euclidean geometry was developed independently by Carl Friedrich Gauss, Nikolai Ivanovich Lobachevsky and János Bolyai.

Finally, Georg Friedrich Bernhard Riemann published his *Über die Hypothesen, welche der Geometrie zu Grunde liegen* in $1854$, in which he put forward the view of geometry as the study of any kind of space of any number of dimensions.

Hence the study of Riemannian geometry was born.

## Linguistic Note

The word **geometry** derives from the Greek words meaning **Earth** and **measure**, suggesting that the discipline arose from the need to measure land.

## Sources

- 1952: T. Ewan Faulkner:
*Projective Geometry*(2nd ed.) ... (previous) ... (next): Chapter $1$: Introduction: The Propositions of Incidence: $1.1$: Historical Note - 1965: A.M. Arthurs:
*Probability Theory*... (previous) ... (next): Chapter $2$: Probability and Discrete Sample Spaces: $2.1$ Introduction - 1998: David Nelson:
*The Penguin Dictionary of Mathematics*(2nd ed.) ... (previous) ... (next):**geometry** - 2008: David Nelson:
*The Penguin Dictionary of Mathematics*(4th ed.) ... (previous) ... (next):**geometry** - 2014: Christopher Clapham and James Nicholson:
*The Concise Oxford Dictionary of Mathematics*(5th ed.) ... (previous) ... (next):**geometry**