Displaying similar documents to “Virtual points and separating sets in spherical circle planes.”

A new type of orthogonality for normed planes

Horst Martini, Margarita Spirova (2010)

Czechoslovak Mathematical Journal

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In this paper we introduce a new type of orthogonality for real normed planes which coincides with usual orthogonality in the Euclidean situation. With the help of this type of orthogonality we derive several characterizations of the Euclidean plane among all normed planes, all of them yielding also characteristic properties of inner product spaces among real normed linear spaces of dimensions d 3 .

An axiom system for full 3 -dimensional Euclidean geometry

Jarosław Kosiorek (1991)

Mathematica Bohemica

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We present an axiom system for class of full Euclidean spaces (i.e. of projective closures of Euclidean spaces) and prove the representation theorem for our system, using connections between Euclidean spaces and elliptic planes.