User:Boris Tsirelson/Sandbox1
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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: