User:Boris Tsirelson/Sandbox1: Difference between revisions

From Citizendium
Jump to navigation Jump to search
imported>Boris Tsirelson
No edit summary
imported>Boris Tsirelson
No edit summary
Line 12: Line 12:


[[Circle (mathematics)]]
[[Circle (mathematics)]]
=Plane=
==Non-axiomatic approach==
===Definitions===


Plane via distances:
Plane via distances:
Line 20: Line 26:


Plane via [[cartesian coordinates]]:
Plane via [[cartesian coordinates]]:
==Axiomatic approach==
==Modern approach==

Revision as of 23:50, 28 March 2010

Hilberts axioms

axiomatization

definition

chess

Euclidean space

Euclidean plane

Circle (mathematics)

Plane

Non-axiomatic approach

Definitions

Plane via distances:

Plane via right angles (orthogonality):

Plane via straight lines:

Plane via cartesian coordinates:

Axiomatic approach

Modern approach