arXiv subjects

Gennady Arshad Notowidigdo

Publications and source records attributed to Gennady Arshad Notowidigdo.

2 recordsLinked to original sources

arXiv2021

Standardised co-ordinate geometry applied to affine rational trigonometry of a tetrahedron

The idea of standardised co-ordinates in three-dimensional affine space is defined, by way of the Standard tetrahedron. By performing an affine map on a general tetrahedron, we may replace the study of a general tetrahedron over a specific metrical structure with the study of a specific tetrahedron over a general metrical structure. Using the framework of Wildberger's rational trigonometry as well as the definitions of generalised scalar and vector products in the author's previous work, we will compute the various trigonometric invariants associated to the Standard tetrahedron, with the purpose of proving some more complicated results which are difficult to prove without this mechanism.

math.MG↗

arXiv2021

A rational trigonometric relationship between the dihedral angles of a tetrahedron and its circumradius

This paper will extend a known relationship between the circumradius and dihedral angles of a tetrahedron in three-dimensional Euclidean space to three-dimensional affine space over a general field not of characteristic two, using only the framework of rational trigonometry devised by Wildberger. In this framework, a linear algebraic view of trigonometry is presented, which allows the associated three-dimensional vector space of such a three-dimensional affine space to be equipped with a non-degenerate symmetric bilinear form; this will also generalise the results presented to arbitrary geometries parameterised by such a non-degenerate symmetric bilinear form.

math.MG↗