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arXiv · 0806.4052

Herleitung von Skalarprodukten aus Symmetrieprinzipien

Wolfgang Soergel
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Abstract

This is an attempt to model ambient space as a three-dimensional real affine space with a distinguished group of automorphisms containing the translations and acting freely and transitively on pairs consisting of a half-plane together with a half-line on its boundary. From there the existence of an invariant scalar product is deduced, which then also implies Pythagoras theorem in a quite precise form. This is in contrast to the usual procedure to model ambient space by asking for a distinguished scalar product and using Pythagoras theorem as known from high school to connect with reality.

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Wolfgang Soergel. 2008-06-25. Herleitung von Skalarprodukten aus Symmetrieprinzipien. https://doi.org/10.1007/s00591-008-0041-7

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