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[6] viXra:2103.0160 [pdf] replaced on 2021-05-18 08:50:27
Authors: M.J. Kronenburg
Comments: 45 Pages.
The principal inverse tangent and cotangent functions for complex arguments can be defined as formulas involving principal
natural logarithms, but these are not odd on the imaginary axis,
which they must be according to their definitions as inverse functions.
These formulas are therefore modified in such a way that they become odd on the imaginary axis,
by choosing the other branch on the lower branch cut,
and the corresponding addition formulas for complex and real arguments are derived.
With these addition formulas their values on their branch cuts are determined,
confirming these modified formulas.
Some new formulas for the (hyperbolic) inverse tangent and cotangent functions for complex arguments
and some new addition formulas for these functions for real arguments are derived.
Some new formulas for the inverse sine and cosine functions and their connections with the
inverse tangent and cotangent functions for complex arguments are provided,
and from these some new addition formulas for the inverse sine and cosine functions for real arguments are derived.
Some duplication and bisection formulas for the inverse tangent, cotangent, sine and cosine
functions are derived.
Category: General Mathematics
[5] viXra:2103.0131 [pdf] submitted on 2021-03-19 20:57:32
Authors: Robert S. Miller
Comments: 220 Pages. [Corrections made by viXra Admin to conform with the requirements on the Submission Form]
An approach to resolution of instances of division by zero, infinities and the negative radical using a primary focus within the mathematical discipline of Algebra via direct substitutions with example problems. It demonstrates the necessity of space-time being a composed of a multiple directions; three space only directions, three time-like space directions, one space-like time direction, and one time-only direction.
Category: General Mathematics
[4] viXra:2103.0081 [pdf] submitted on 2021-03-13 12:40:05
Authors: Edgar Valdebenito
Comments: 5 Pages.
We recall some integrals for pi/sqrt(phi).
Category: General Mathematics
[3] viXra:2103.0034 [pdf] submitted on 2021-03-05 20:23:46
Authors: Robert Yusupov
Comments: 9 Pages. [Corrections made by viXra Admin to conform with scholarly norm]
This article presents formulas for the areas of triangles resulting from some partitions of the main triangle. In total, five options for dividing a triangle by line segments are considered. The derivation of the formulas does not cause much difficulty, therefore the explanations are not presented. This article is of interest to schoolchildren and everyone interested in elementary mathematics.
В настоящей статье представлены формулы о площадях треугольников, получающихся при некоторых разбиениях основного треугольника. Всего рассмотрено пять вариантов деления треугольника отрезками прямых. Вывод формул не вызывает особого труда, поэтому пояснения не представлены. Настоящая статья представляет интерес школьникам и всем интересующимся начальной математикой.
Category: General Mathematics
[2] viXra:2103.0028 [pdf] submitted on 2021-03-04 19:19:51
Authors: Egger Mielberg
Comments: 26 Pages.
Traditional mathematical logic is "what follows from what".
Sense logic - "what belongs to what".
Traditional mathematical logic is "a collection of abstract objects not related to the outside world." Sense logic is "a set of objects and events that describe the state of the real world." Below, we present a new paradigm of logic based on semantic connections between the considered objects of any nature. The Sense Logic is not a part of traditional mathematics. Its main task is to describe the phenomena of the real world from the standpoint of their semantic coherence.
Category: General Mathematics
[1] viXra:2103.0023 [pdf] submitted on 2021-03-04 19:44:36
Authors: Zhi Li, Hua Li
Comments: 9 Pages. Assisted by viXra Admin
A general formula with a parameter for the radical solution of a quintic is derived, based on the well-known Cardano-Tartaglia equation. According to the characteristics of the coefficients of the quintic in the standard Bring-Jerrard form, the range of a real root of the equation is determined, and the parameter can be quickly fixed
with the required accuracy in the selected range by a trisection iteration, and all the roots of the quintic can be found. The technique has the potential to be extended to higher degree equations.
Category: General Mathematics
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