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On Parabolic Trigonometry in a Degenerate Minkowski Plane
Author(s) -
Ingarden R. S.,
Tamássy L.
Publication year - 1990
Publication title -
mathematische nachrichten
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.913
H-Index - 50
eISSN - 1522-2616
pISSN - 0025-584X
DOI - 10.1002/mana.19901450107
Subject(s) - minkowski space , mathematics , parabola , lorentz transformation , trigonometry , degenerate energy levels , plane (geometry) , vertex (graph theory) , spherical trigonometry , geometry , transformation (genetics) , mathematical analysis , classical mechanics , physics , combinatorics , graph , biochemistry , chemistry , quantum mechanics , gene
A Minkowski plane is considered having a parabola as indicatrix curve and taking for its center the vertex of the parabola causing by this a degeneration of the Minkowski geometry. After a short discussion of the concept of the length and angle, the trigonometrical functions of this geometry has been calculated and their basic properties explained. A two‐parameter pseudogroup of generalized rotations has been found as an analogon of the Lorentz transformation group in special relativity. The theory has applications to thermodynamics.