◀ ▲ ▶Branches / Geometry / Elements-euclid / Book--1-plane-geometry / Definition: 1.05: Surface

Definition: 1.05: Surface

And a surface is that which has length and breadth only.

Modern Definition

A surface (or a curved surface) \(s\) is a connected subset of a Euclidean metric space \(A\in\mathbb R^n\), \(n\ge 2\) such that taking away a line \(g\subset s\), and given any point \(A\in g\) on the line \(g\) will disconnect a sufficiently small neighborhood of \(A\) in \(s\).

Mentioned in:

Definitions: 1 2 3

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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"