User:Boris Tsirelson/Sandbox1: Difference between revisions
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===Definitions=== | ===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 distances: | ||
Revision as of 23:52, 28 March 2010
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: