Calculating the axial reasons in spherical trigonometry.

Calculating the axial reasons in spherical trigonometry.
Tokyo, 2009 L. Rabasco   

The crystallography uses as spherical trigonometry for the determination of the axial angles being worth of the stereographic representations and linear algebra. From the origins of the goniometry by the 1688 (measurement of the interface angles in crystalline solids), angular measurement one of the most practicable forms was demonstrated there as to help for determination  nature of a crystalline body and its minerallogical cataloguing.  The use from 1823 by Franz E. Neumann of the stereographic projections like means of representation of the angular relations of the externally appreciable surfaces of a crystal and its relation with the internal structure, forced the cristallógraphs to become familiar with the daily handling of the mathematics. Unlike circular trigonometry, where the angular sum is constant, in the resolution of spherical triangles it is not thus. In addition, as much the vertices as the sides are expressed for angular reasons. The use of “the crossed multiplication”, a variant of the determinant of linear algebra, allows to determine the indices of the faces in the intersection  zones. Thus the determinants became necessary to make agile the work of the determination of the different angular reasons.  Nowadays a new tool comes to help us: the programming, with which our “modern” computers can solve laborious calculations at a moment without the troublesome necessity of the calculation manual and the odious verifications. For that they want to use as this program, I have written an adaptation for the calculation of angular reasons in problems of spherical trigonometry.

Advertisements