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Advances in Mathematical Physics
Volume 2015 (2015), Article ID 808250, 6 pages
http://dx.doi.org/10.1155/2015/808250
Research Article

Orthogonal Projections Based on Hyperbolic and Spherical -Simplex

1Department of Mathematics, Faculty of Science, Gazi University, 06500 Ankara, Turkey
2Department of Mathematics, Art and Sciences Faculty, Nigde University, 51100 Nigde, Turkey

Received 4 December 2014; Accepted 23 February 2015

Academic Editor: Giorgio Kaniadakis

Copyright © 2015 Murat Savas et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

Orthogonal projection along a geodesic to the chosen k-plane is introduced using edge and Gram matrix of an n-simplex in hyperbolic or spherical n-space. The distance from a point to k-plane is obtained by the orthogonal projection. It is also given the perpendicular foot from a point to k-plane of hyperbolic and spherical n-space.