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Affine planes: An example of research on geometric structures

Published online by Cambridge University Press:  03 November 2016

Günter Pickert
Günter Pickert*
Affiliation:
Mathematisches Institut, Justus Liebig-Universität, 6300 Giessen, Federal Republic of Germany
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Extract

At the end of the nineteenth century David Hilbert made the decisive step in the foundations of geometry (for the historical development see [1]): a road was opened to a theory of geometric structures. In spite of the fact that one spoke (and speaks still today!) strangely enough of ‘implicitly’ defining the geometrical concepts through the axioms, it became clear in the sequel that the axiom system of Hilbert constitutes an ‘explicit’ definition: not of course for ‘point’, ‘line’, etc. but of the concept ‘euclidean geometry’ (or ‘euclidean space’).

Type
Research Article
Information
The Mathematical Gazette , Volume 57 , Issue 402 , December 1973 , pp. 278 - 291
Copyright
Copyright © Mathematical Association 1973

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