| Abstrakt: |
In this paper some new geometric characterizations are given of the following algebraic properties of the underlying field K of an Euclidean plane E : - 1 is a square in K, the group of squares is of index 2 in K ∗ , K is Pythagorean, and K is Euclidean. In the first part ordinary incidence conditions of lines and circles in E are used for this purpose, while in the second these properties are characterized by comparing four betweenness relations introduced in E in a natural way. [ABSTRACT FROM AUTHOR] |
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