Functions and Analysis

2303 Submissions

[3] viXra:2303.0158 [pdf] submitted on 2023-03-29 02:16:27

[A Note Mathematician] Brook Taylor

Authors: Edgar Valdebenito
Comments: 11 Pages.

Brook Taylor was an English mathematician, invented integration by parts, and discovered the celebrated formula known as Taylor's expansion.
Category: Functions and Analysis

[2] viXra:2303.0144 [pdf] submitted on 2023-03-23 05:19:28

Solving Triangles Algebraically

Authors: Joseph Bakhos
Comments: 10 Pages. Published April 19, 2023. Applied Mathematical Sciences, Vol. 17, 2023, no. 8, 379-390 doi: 10.12988/ams.2023.917399 pdf available at: http://www.m-hikari.com/ams/ams-2023/ams-5-8-2023/p/bakhosAMS5-8-2023.pdf

Quaterns are a new measure of rotation. Since they are defined in terms of rectangular coordinates, all of the analogue trigonometric functions become algebraic rather than transcendental. Rotations, angle sums and differences, vector sums, cross and dot products, etc., all become algebraic. Triangles can be solved algebraically. Computer algorithms use truncated infinite sums for the transcendental calculations of these quantities. If rotations were expressed in quaterns, these calculations would be simplified by a few orders of magnitude. This would have the potential to greatly reduce computing time. The archaic Greek letter koppa is used to represent rotations in quaterns, rather than the traditional Greek letter theta. Because calculations utilizing quaterns are algebraic, simple rotation in the first two quadrants can be done "by hand" using "pen and paper." Using the approximate methods outlined towards the end of the paper, triangles may be approximately solved with an error of less than 3% using algebra and a few simple formulas.
Category: Functions and Analysis

[1] viXra:2303.0120 [pdf] submitted on 2023-03-19 02:16:48

Graphical Representation of Quaternions and Their Concomitant Functions

Authors: Stephen C. Pearson
Comments: 33 Pages. (Note by viXra Admin: Future hand-written submission will not be accepted))

In this particular paper we will demonstrate that, by invoking the concept of a 'quaternionic quasi-complex component', it is possible to graphically represent all quaternions and their concomitant functions with the aid of specific quaternionic analogues of the Argand diagram from complex variable analysis, bearing in mind that the algebraic and analytic properties of the aforesaid numbers and functions have been comprehensively elucidated in the author's antecedent papersIn this particular paper we will demonstrate that, by invoking the concept of a ‘quaternionic quasi-complex component’, it is possible to graphically represent all quaternions and their concomitant functions with the aid of specific quationic analogues of the Argand diagram from complex variable analysis, bearing in mind that the algebraic and analytic properties of the aforesaid numbers and functions have been comprehensively elucidated in the author’s antecedent papers [2]; [3]; [4] & [5].
Category: Functions and Analysis