User:Boris Tsirelson/Sandbox1

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Hilberts axioms

axiomatization

definition

chess

Euclidean space

Euclidean plane

Circle (mathematics)

Plane

Non-axiomatic approach

Definitions

It is tempting to define a plane as a surface with zero curvature (or something like that). However, this is not a good idea, since the notions of surface and curvature are much more complicated than the notion of plane.

Plane via distances:

Plane via right angles (orthogonality):

Plane via straight lines:

Plane via cartesian coordinates:

Axiomatic approach

Modern approach