# Definition:Euclidean Geometry

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## Definition

**Euclidean geometry** is the branch of geometry in which the parallel postulate applies.

An assumption which is currently under question is whether or not ordinary space is itself **Euclidean**.

**Euclidean geometry** adheres to Euclid's postulates.

## Also see

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

## Source of Name

This entry was named for Euclid.

## Historical Note

**Euclidean geometry** was initially developed in Greece between about $600$ and $300$ BCE.

It was codified at the end of this period and published as Euclid's *The Elements*.

As a system, it was regarded as logically sound for some $2000$ years, although there are in fact a number of unstated and concealed assumptions.

David Hilbert re-cast **Euclidean geometry** in $1899$, in his *Grundlagen der Geometrie*, which used:

- three undefined entities: point, line and plane
- $28$ assumptions, known as Hilbert's axioms.

## Sources

- 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):**Euclidean geometry** - 1993: Richard J. Trudeau:
*Introduction to Graph Theory*... (previous) ... (next): $1$. Pure Mathematics: Euclidean geometry as pure mathematics - 1998: David Nelson:
*The Penguin Dictionary of Mathematics*(2nd ed.) ... (previous) ... (next):**Euclidean geometry** - 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):**Euclidean 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):**Euclidean geometry**