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Geometric approaches to establish the fundamentals of Lorentz spaces $ℝ_{2}^{3}$ and $ℝ_{1}^{2}$

Sevilay Çoruh Şenocak; Salim Yüce — 2024

Mathematica Bohemica

The aim of this paper is to investigate the orthogonality of vectors to each other and the Gram-Schmidt method in the Minkowski space $ℝ_{2}^{3}$ . Hyperbolic cosine formulas are given for all triangle types in the Minkowski plane $ℝ_{1}^{2}$ . Moreover, the Pedoe inequality is explained for each type of triangle with the help of hyperbolic cosine formulas. Thus, the Pedoe inequality allowed us to establish a connection between two similar triangles in the Minkowski plane. In the continuation of the study, the rotation...

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Geometric approaches to establish the fundamentals of Lorentz spaces ℝ 2 3 and ℝ 1 2

Geometric approaches to establish the fundamentals of Lorentz spaces $ℝ_{2}^{3}$ and $ℝ_{1}^{2}$