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What is geometry? (English) Zbl 0717.51002

The author does not give a definition of geometry, but he discusses the major development of geometry. Geometry started with the Axioms of Euclid, the Coordinatization of Descartes leads to the space and to the group concept of Klein. Localization of geometry by Gauss/Riemann is the base of globalization and topology. Klein’s homogeneous spaces and Riemann’s local geometry are generalized to connections in a fiber bundle introduced by Cartan. Geometric development leads to applications in physics and biology for instance. Shortly said: A property is geometric, if it does not deal directly with numbers or if it happens on a manifold, where the coordinates themselves have no meaning.
Reviewer: J.Hoschek

MSC:

51-03 History of geometry
01A15 History of mathematics of the indigenous cultures of Europe (pre-Greek, etc.)
53-03 History of differential geometry
01-02 Research exposition (monographs, survey articles) pertaining to history and biography
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