General Mathematics

2607 Submissions

[2] viXra:2607.0113 [pdf] submitted on 2026-07-27 21:23:43

Arithmetic Dimensionality of Real Numbers

Authors: Robert S. Miller
Comments: 33 Pages. (Note by viXra Admin: Please cite and list scientific references)

This paper will explore the concept of Arithmetic Dimensionality, D_A, for real numbers, whose analog is the fractal dimensionality of geometric constructs, D_G. Beginning with a short review of how the dimension of a geometric object is calculated, it will be shown how this same concept can be applied to real numbers, and that the current understanding of numbers having a geometric dimension of 0 is not accurate. Instead it is show,, that although the point on a number line, like the x-axis is 0 dimensional, the numbers themselves may possess a fractal dimension. It is beyond to scope of this paper to prove the exact Geometric Fractal Dimension of transcendental numbers (like π and e) or irrational numbers (like √2). The goal however is to show (1) there exists a D_A and D_G for real numbers, (2) that D_A→D_G as the number of decimal digits considered n→∞ and (3) where D is a generic stand in for both D_A and D_G, it exists in Information Space or Sub-Hilbert Space of Geometric Dimension such that 0≤D<1.
Category: General Mathematics

[1] viXra:2607.0008 [pdf] submitted on 2026-07-03 11:42:09

Analyzing a Variant Version of a Fibonacci Polynomial

Authors: Marciano L. Legarde
Comments: 12 Pages.

In this paper, we introduce a new finite polynomial called the "Variant Fibonacci Polynomial". This polynomial is defined by using the standard Fibonacci sequence as both the coefficients and the exponents of each term. Although the definition is simple, it leads to several interesting mathematical properties.We begin by defining the polynomial and giving several examples. We then evaluate it at different values of x, identify its guaranteed real root, discuss its complex roots, and derive formulas for both its derivative and antiderivative. We also examine the infinite series version of the polynomial and observe when it converges and when it diverges.Finally, we discuss whether this polynomial could be used to construct a new type of series expansion for functions and whether such an expansion might eventually be useful for solving differential equations. While it is still too early to draw definite conclusions, the results of this paper suggest that the Variant Fibonacci Polynomial is an interesting mathematical object that deserves further study.
Category: General Mathematics