Equidistant Set of Two Congruent Spheres and Its Orthogonal Projection on Rk
M. Cristian M. Carvajal *
Laboratorio de Investigación Lab[e]saM, Universidad de Playa Ancha, Valparaíso, Chile.
P. Ronald A. Manríquez
Laboratorio de Investigación Lab[e]saM, Universidad de Playa Ancha, Valparaíso, Chile.
S. Héctor R. Lorca
Laboratorio de Investigación Lab[e]saM, Universidad de Playa Ancha, Valparaíso, Chile.
C. José A. González
Laboratorio de Investigación Lab[e]saM, Universidad de Playa Ancha, Valparaíso, Chile.
*Author to whom correspondence should be addressed.
Abstract
In this paper some properties of equidistant sets are presented,a relatively new concept. The equidistant concept is characterized and among two congruent spheres of ℝn. Afterwards the behavior of the orthogonal projection onto ℝk is studied, concluding that the projection of equidistant set of two congruent spheres, is a translation of the equidistant set of the spheres projections.
Keywords: Midset, orthogonal projection, spheres, metric