Geometry

1609 Submissions

[2] viXra:1609.0365 [pdf] submitted on 2016-09-25 18:17:04

An Additional Brief Solution of the CPP Limiting Case of the Problem of Apollonius Via Geometric Algebra (Ga)

Authors: James A. Smith
Comments: 5 Pages.

This document adds to the collection of GA solutions to plane-geometry problems, most of them dealing with tangency, that are presented in References 1-7. Reference 1 presented several ways of solving the CPP limiting case of the Problem of Apollonius. Here, we use ideas from Reference 6 to solve that case in yet another way.
Category: Geometry

[1] viXra:1609.0082 [pdf] submitted on 2016-09-06 19:08:36

The Geometry of the MRB Constant

Authors: Marvin Ray Burns
Comments: 8 Pages. This classic paper shows the utter simplicity of the geometric description of the MRB constant (oeis.org/A037077).

The MRB constant is the upper limit point of the sequence of partial sums defined by S(x)=sum((- 1)^n*n^(1/n),n=1..x). The goal of this paper is to show that the MRB constant is geometrically quantifiable. To “measure” the MRB constant, we will consider a set, sequence and alternating series of the nth roots of n. Then we will compare the length of the edges of a special set of hypercubes or ncubes which have a content of n. (The two words hypercubes and n-cubes will be used synonymously.) Finally, we will look at the value of the MRB constant as a representation of that comparison, of the length of the edges of a special set of hypercubes, in units of dimension 1/ (units of dimension 2 times units of dimension 3 times units of dimension 4 times etc.). For an arbitrary example we will use units of length/ (time*mass* density*…).
Category: Geometry