| viXra.org > General Mathematics > 2406 |
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| viXra.org > General Mathematics > 2406 |
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[7] viXra:2406.0164 [pdf] submitted on 2024-06-28 21:14:00
Authors: Bryce Petofi Towne
Comments: 12 Pages. (Note by viXra Admin: AI generated contents/results are in general not acceptable)
Mathematics serves as an abstract tool to study the natural world and its laws, aiding in our understanding and description of natural phenomena. In mathematics, real numbers, imaginary numbers, zero, and negative numbers are fundamental concepts, each with its unique importance and application. However, the philosophical nature of these concepts warrants further exploration. This paper aims to discuss the philosophical essence of imaginary numbers, zero, and negative numbers, argue that imaginary numbers have real-world counterparts, and explore the rationale and advantages of representing imaginary and complex numbers using polar coordinates. Furthermore, we extend our findings to more advanced mathematical problems in complex analysis, differential equations, and number theory, demonstrating the broader impact of our work.
Category: General Mathematics
[6] viXra:2406.0127 [pdf] submitted on 2024-06-23 02:54:53
Authors: Thierry L. A. Periat
Comments: 12 Pages.
The theory of the (E) question is concerned with the decomposition (synonym: division) of deformed tensor (resp. Lie) products. A first mathematical method (the intrinsic one) has been developed for the decomposition of deformed cross products. It only works in three-dimensional spaces and brings incomplete results. This document proposes a second approach bringing complete results, i.e.: the main and the residual parts of each decomposition, whatever the dimension D (D in N - {0, 1}) of the mathematical space is. But the method is plagued with a logical uncertainty. Fortunately, in any three-dimensional space, both methods can be calibrated through diverse scenarios. One of them may catch the attention of physicists since it re-introduces E. Cartan’s metrics induced by the evolution of surfaces.
Category: General Mathematics
[5] viXra:2406.0104 [pdf] replaced on 2024-07-09 10:34:33
Authors: Abdelkrim ben Mohamed
Comments: 7 Pages.
In this working paper we try to prove the Collatz conjecture also known the 3x+1 problem.
Category: General Mathematics
[4] viXra:2406.0090 [pdf] submitted on 2024-06-18 14:02:02
Authors: Mieczysław Szyszkowicz
Comments: 4 Pages.
Buffon's needle problem, posed by Georges-Louis Leclerc, Comte de Buffon in the 18th century, stands as a cornerstone in the realm of geometric probability. The problem encapsulates a scenario where a needle of a given length is dropped randomly onto a floor composed of parallel strips of equal width. The inquiry revolves around determining the likelihood that the needle will intersect a line between two strips. Here a new solution of this classical problem is proposed.
Category: General Mathematics
[3] viXra:2406.0080 [pdf] submitted on 2024-06-17 19:45:24
Authors: Athon Zeno
Comments: 5 Pages. (Note by viXra Admin: Please cite and list scientific references)
The Sphere-Base-One mathematical system is a novel framework that takes the sphere as the fundamental unit of volume and redefines the relationships between spheres, cubes, and other geometric objects. This innovative approach offers a fresh perspective on the nature of space and volume, challenging conventional notions of geometry and opening up new avenues for interdisciplinary research and discovery. By focusing on the sphere as the primary building block and exploring the negative space around it, the Sphere-Base-One system has the potential to unlock new insights and solutions in a wide range of scientific and engineering disciplines, including quantum physics, cosmology, surface chemistry, fluid dynamics, and electrical engineering. The simplification and reformulation of key equations in the Sphere-Base-One system may lead to easier calculations and, more importantly, to the identification of patterns and relationships that were previously obscured by the limitations of the traditional Cube-Base-One system. While not intended to replace the existing mathematical framework, the Sphere-Base-One system serves as a complementary tool that can be applied in parallel to drive progress and innovation across multiple fields. This article introduces the core concepts of the Sphere-Base-One system, explores its potential applications, and discusses the implications of this new mathematical paradigm for the future of scientific research and technological advancement.
Category: General Mathematics
[2] viXra:2406.0059 [pdf] submitted on 2024-06-13 20:50:09
Authors: Andreas Ball
Comments: 22 Pages. (Correction made by viXra Admin to conform with the requirements of viXra.org)
In this report the author tries to handle with four themes. Referring the first topic [Part 2] derivations of ancient approximations for the Circle Figure π are presented using the figures of the two- and three-dimensioninal case for the straight and the round. [Part 3] deals with possible connections between the Circle Figure π and the Golden Section Ф using modified terms as presented at the first topic.[In Part 4] a complete solution of the puzzle around the drawing Vitruvian Man of Leonardo da Vinci is presented, which is mostly based on the informations given by two german authors. [In Part 5] a system is described, which is based on the geometrical system of the drawing Vitruvian Man of Leonardo da Vinci and by which the attempt of a connection between the Circle Figure π and the Golden Section Ф is done.
Category: General Mathematics
[1] viXra:2406.0014 [pdf] submitted on 2024-06-04 19:17:36
Authors: Edgar Valdebenito
Comments: 3 Pages.
This document briefly discusses improper integrals of the second kind.
Category: General Mathematics
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