General Mathematics

2301 Submissions

[5] viXra:2301.0122 [pdf] replaced on 2023-04-24 11:29:06

Relations Between e, π and Golden Ratios

Authors: Asutosh Kumar
Comments: 6 Pages.

We write out relations between the base of natural logarithms (e), the ratio of the circumference of a circle to its diameter (π), and the golden ratios of the additive p-sequences. An additive p-sequence is a natural extension of the Fibonacci sequence in which every term is the sum of p previous terms given p>=1 initial values called seeds.
Category: General Mathematics

[4] viXra:2301.0117 [pdf] replaced on 2023-04-19 09:36:36

Proof of Collatz Conjecture: the Sequence (2x+1)*2^y and the Sequence 6k+4

Authors: Bae Joonyoung
Comments: 7 Pages.

The Collatz conjecture is a conjecture that states that for any natural number n, the following operation will always result in 1:If n is even, divide it by 2.If n is odd, multiply it by 3 and add 1.However, it is still an open question whether this conjecture is always true or not.
Category: General Mathematics

[3] viXra:2301.0098 [pdf] replaced on 2025-02-10 16:34:09

On the Twin Prime Conjecture

Authors: Berndt Gensel
Comments: 16 Pages.

Every prime number $p geq 5$ has the form $6x-1$ or $6x+1$. We call $x$ the textbf{generator} of $p$. Twin primes are distinguished by a textbf{common generator} for each pair. Therefore it makes sense to search for the Twin Primes on the level of their generators. This paper presents a new approach to prove the textbf{Twin Prime Conjecture} by a method to extract all Twin Primes on the level of the Twin Prime Generators.We define the om{p_n}--numbers $x$ as numbers for that holds that $6x-1$ and $6x+1$ are coprime to the primes $5,7,ldots,p_n$. By dint of the average size $bd(p_n)$ of the om{p_n}--gaps we can prove the textbf{Twin Prime Conjecture}.
Category: General Mathematics

[2] viXra:2301.0060 [pdf] replaced on 2023-03-14 04:23:43

A Solution Of the Collatz Conjecture Problem

Authors: Baoyuan Duan
Comments: 19 Pages. correct errors in section VI

Build a special identical equation, use its calculation characters to prove and search for solution of any odd converging to 1 equation through (*3+1)/2^k operation, and get a solution for this equation, which is exactly same with that got from calculating directly. Then give a specific example to verify. Thus prove the Collatz Conjecture is true. Furthermore, analysis the even and odd sequences produced by iteration calculation during the procedure of searching for solution, build a weight function model, prove it decrease progressively to 0, build another complement weight function model, prove it increase to its convergence state. Indicate that this kind of iteration calculation has determined direction, and gradually regularly converges.
Category: General Mathematics

[1] viXra:2301.0035 [pdf] submitted on 2023-01-05 02:46:35

Kinematics of Point Motion Along Curves of the Second Order

Authors: Viktor Strohm
Comments: 29 Pages. (Correction made by viXra Admin - Please conform!)

The motion of a material point along curves of the second order is represented by a kinematic equation. Formulas for the dependence of acceleration and radius, speed and radius are derived. The direction of the velocity and acceleration vectors is determined. The conditions for the conservation of Kepler's laws when a material point moves along second-order curves are shown.
Category: General Mathematics