Definition:Euclidean Geometry

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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.