# Algebra

## 1910 Submissions

 viXra:1910.0613 [pdf] submitted on 2019-10-29 00:18:26

### The Two Couriers Problem

Authors: William F. Gilreath
Comments: 6 Pages. Published in Transmathematica 2019

The Two Couriers Problem is an algebra problem, originally stated in 1746 by the French mathematician Clairaut. For over a century, the Two Couriers Problem has been re-used in various forms as a mathemat- ical problem, in textbooks and journals, by different mathematicians and authors. The Two Couriers Problem involves cases where division by zero arises in practice, where each has a real-world, actual result for the solution. Thus the Two Couriers Problem is a centuries old algebra problem with actual applied results that involve division by zero. It is an excellent mathematical problem to evaluate different methods for dividing by zero. Division by zero has many different mathematical approaches. Conventional mathematics handles division by zero as an indeterminate or undefined result. Transmathematics defines division by zero as either nul- lity or explicitly positive or negative infinity. Two other approaches are by Saitoh, who defines division by zero simply as zero, and Barukčić who defines division by zero as either unity or explicitly positive or implicitly negativity infinity. The question is, which approach is best to solve the mathematical problem of division by zero? The paramount goal of this paper is to use the Two Couriers Problem as an objective test to examine and evaluate mathematical approaches to division by zero – and find which one is best.
Category: Algebra

 viXra:1910.0345 [pdf] submitted on 2019-10-19 11:43:49

### Unimodular Rotation of E8 to H4 600-Cells

Authors: J Gregory Moxness

We introduce a unimodular Determinant=1 8x8 rotation matrix to produce four 4 dimensional copies of H4 600-cells from the 240 vertices of the Split Real Even E8 Lie group. Unimodularity in the rotation matrix provides for the preservation of the 8 dimensional volume after rotation, which is useful in the application of the matrix in various fields, from theoretical particle physics to 3D visualization algorithm optimization.
Category: Algebra

 viXra:1910.0293 [pdf] replaced on 2019-10-18 07:34:11

### Motivating Abstract with Elementary Algebra

Authors: Timothy W. Jones