تقرير
Invariant and Preserving Transforms for Cross Ratio of 4-Points in a line on Desargues Affine Plane
| العنوان: | Invariant and Preserving Transforms for Cross Ratio of 4-Points in a line on Desargues Affine Plane |
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| المؤلفون: | Zaka, Orgest, Peters, James F. |
| سنة النشر: | 2022 |
| المجموعة: | Mathematics |
| مصطلحات موضوعية: | Mathematics - General Mathematics, 51-XX, 51Axx, 51A30, 51E15, 51N25, 30C20, 30F40 |
| الوصف: | This paper introduces advances in the geometry of the transforms for cross ratio of four points in a line in the Desargues affine plane. The results given here have a clean, based Desargues affine plan axiomatic's and definitions of addition and multiplication of points on a line in this plane, and for skew field properties. In this paper are studied, properties and results related to the some transforms for cross ratio for 4-points, in a line, which we divide into two categories, \emph{Invariant} and \emph{Preserving} transforms for cross ratio. The results in this paper are (1) the cross-ratio of four points is \emph{Invariant} under transforms: Inversion, Natural Translation, Natural Dilation, Mobi\"us Transform, in a line of Desargues affine plane. (2) the cross-ratio of four points is \emph{Preserved} under transforms: parallel projection, translations and dilation's in the Desargues affine plane. Comment: 16 pages, 8 figures, 24 References. arXiv admin note: substantial text overlap with arXiv:2209.02636, arXiv:2209.14241, arXiv:2208.12745 |
| نوع الوثيقة: | Working Paper |
| URL الوصول: | http://arxiv.org/abs/2211.16055 |
| رقم الأكسشن: | edsarx.2211.16055 |
| قاعدة البيانات: | arXiv |
| الوصف غير متاح. |