Abstract
The aim of this work was to show that many theorems of the MINKOWSKI-plane can be proved by "counting", by "calculating", by working with "equations" for cycles and transformations — actually by primitive methods.
What remains to be done? We sketch only two themes.
It certainly would be very nice to study the known theorems of classical school geometry (Theorems of PYTHAGORAS, THALES, CEVA, PTOLEMÄUS, ...; six point circle of FEUERBACH; line of EULER; ...) and then to examine their validity in the MINKOWSKI-plane by using the methods developed in this paper.
Our work — especially the two theorems 11 and 13 — shows another, very important, but also very complicated problem. Is it possible to characterize the known MÖBIUS-MINKOWSKI- and LAGUERRE-planes — in short the BENZ-planes — in a theory of reflections like the "Spiegelungsgeometrie" by BACHMANN? What are the axioms of such a reflection geometry?
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References
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© 1980 Springer-Verlag
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Zeitler, H. (1980). On reflections in Minkowski-planes. In: Artzy, R., Vaisman, I. (eds) Geometry and Differential Geometry. Lecture Notes in Mathematics, vol 792. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0088677
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DOI: https://doi.org/10.1007/BFb0088677
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