Книга: TENSOR TRIGONOMETRY

In Geometry, division Planimetry includes metric part and trigonometry. In geometries of metric spaces from the end of XIX age their tensor forms are widely used. However the trigonometry is remained only in its scalar forms in a plane. The tensor trigonometry is development of the flat scalar trigonometry from Leonard Euler classic forms into general multi-dimensional tensor forms with vector and scalar orthoprojections and with step by step increasing complexity and opportunities. Described in the book are fundamentals of this new mathematical subject with many initial examples of its applications. In theoretic plan, the tensor trigonometry complements naturally Analytic Geometry and Linear Algebra. In practical plan, it has the clear instrument for solutions of various geometric and physical problems in homogeneous isotropic spaces, such as Euclidean, quasi- Euclidean and pseudo-Euclidean ones. In these spaces, the tensor trigonometry gives very simply general laws of motions in complete forms and with polar decompositions into principal and secondary motions, their descriptive trigonometric vector models, which are applicable also to n-dimensional non-Euclidean geometries in subspaces of constant radius embedded in enveloping metric spaces, and in the theory of relativity. In STR, these applications were considered till a tensor-trigonometric 4D pseudoanalog in the Minkowski space-time of the classic 3D theory by Frenet–Serret of Euclidean curves with absolute and relative local differentially-geometric parameters of a world line, kinematic and dynamic characteristics of a material object in world points. The book is intended for researchers in the fields of multi-dimensional spaces, analytic geometry, linear and common algebra with theory of matrices, non-Euclidean geometries, theory of relativity and to all those who is interested in new knowledges and applications, given by exact sciences. It may be useful for education purposes on this new subject in university departments of algebra, geometry and physics