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[4] viXra:1907.0581 [pdf] replaced on 2019-08-26 11:18:55
Authors: Hiroshi Okumura
Comments: 5 Pages.
We consider a problem in Wasan geometry involving
a golden arbelos and give a characterization of the golden arbelos involving an Archimedean circle. We also construct a self-similar circle configuration using the figure of the problem.
Category: Geometry
[3] viXra:1907.0547 [pdf] submitted on 2019-07-27 15:33:13
Authors: Valery Timin
Comments: language: Russian, number of pages: 6, mailto:timinva@yandex.ru, Creative Commons Attribution 3.0 License
This paper deals with the orthonormal transformation of vectors of the 4-dimensional Galilean space. Such transformations are transformations of rotation and transition to a moving coordinate system. Formulas and matrices of these transformations are given.
The transition from one coordinate system to another, moving relative to the first, did long before the theory of relativity. The natural space for "transitions from one coordinate system to another" is the Galilean space. It is the space of classical mechanics. This paper focuses on the 4-dimensional interpretation of such transformations.
В данной работе рассмотрены вопросы ортонормированного преобразования векторов 4-мерного галилеева пространства. Такими преобразованиями являются преобразования поворота и перехода в движущуюся систему координат. Даны формулы и матрицы этих преобразований
Category: Geometry
[2] viXra:1907.0496 [pdf] replaced on 2019-07-25 15:42:08
Authors: Yuji Masuda
Comments: 1 Page.
This shows a geometry conposed of i,1,-1,∞.
Category: Geometry
[1] viXra:1907.0441 [pdf] submitted on 2019-07-23 14:46:52
Authors: Valery Timin
Comments: language: Russian, number of pages: 11, mailto:timinva@yandex.ru, Creative Commons Attribution 3.0 License
This paper deals with the orthonormal transformation of the coordinates of 3+1 - and 4-dimensional Galilean space. Such transformations are transformations of displacement, rotation, and transition to a moving coordinate system. Formulas and matrices of these transformations are given.
The reasons for writing this work and the next few are two reasons.
1. The space in which classical mechanics is defined is the Galilean space, more precisely, its 3+1-dimensional interpretation.
2. Unlike the Galilean space, which has all the properties of the space in which tensors are defined, in classical mechanics not all parameters are tensors. In this regard, it is impossible to define classical mechanics in 4-dimensional form in 4-dimensional space in a simple way.
В данной работе рассмотрены вопросы ортонормированного преобразования координат 3+1- и 4-мерного галилеева пространства. Такими преобразованиями являются преобразования смещения, поворота и перехода в движущуюся систему координат. Даны формулы и матрицы этих преобразований.
Category: Geometry
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