◀ ▲ ▶Branches / Geometry / Elements-euclid / Book--1-plane-geometry / Definition: 1.02: Line, Curve

Definition: 1.02: Line, Curve

And a line is a length without breadth.

Modern Definition

A curve (or a curved line) \(g\) is a connected subset of a Euclidean metric space \(A\in\mathbb R^n\) such that taking away a point \(A\in g\) disconnects \(g\).

Example of two curves in a plane:

Table of Contents

Explanations: 1

Mentioned in:

Definitions: 1 2 3 4 5 6 7
Explanations: 8

Thank you to the contributors under CC BY-SA 4.0!

Github:

non-Github:

@Calahan

@Casey

@Fitzpatrick

References

Adapted from CC BY-SA 3.0 Sources:

1. Callahan, Daniel: "Euclid’s 'Elements' Redux" 2014

Adapted from (Public Domain)

1. Casey, John: "The First Six Books of the Elements of Euclid"

Adapted from (subject to copyright, with kind permission)

1. Fitzpatrick, Richard: Euclid's "Elements of Geometry"