In this paper, using the Lambert series and other known results, the authors consider the computation of a class of series involving the powers of generalized Fibonacci and Lucas numbers, and obtain their approximate values.

This note provides a self-contained introduction to conics as loci of points equidistant from circles, lines and points, including a study of the loci of points equidistant from two circles, separated, intersecting or touching. (Contains 1 table and 8 figures.)

Direct sum decomposition of Abelian groups appears in almost all textbooks on algebra for undergraduate students. This concept plays an important role in group theory. One simple example of this decomposition is obtained by using the kernel and range of a projection map on an Abelian group. The aim in this pedagogical note is to establish a direct…

A point "E" inside a triangle "ABC" can be coordinatized by the areas of the triangles "EBC," "ECA," and "EAB." These are called the barycentric coordinates of "E." It can also be coordinatized using the six segments into which the cevians through "E" divide the sides of "ABC," or the six angles into which the cevians through "E" divide the angles…