General Mathematics

The Various Representative Values Representing Between the Two Figures, and How to Create These Representative Values

Authors: Sungmin Kang
Comments: 2 Pages. (Author name added to the article by viXra Admin as required; also, please cite and list scientific references)

There are countless means that are neither arithmetic nor geometric means, and to satisfy the mean, f(x,y) must be a one-to-one correspondence to a bivariate function f(x,x).
Category: General Mathematics

A New Binary Encoding Disk from Shen Nong's Diagrams in I-Ching and Its Application -- Also Uncovering the e, φ, Spiral Fractal, Fibonacci and TM Sequences in the Encoding Disk

Authors: Hua-Fang Wu
Comments: 24 Pages. In Chinese

The Shen Nong's Diagrams of I-Ching is a set of "the dichotomy approach" Diagrams of I-Ching discovered by the author in 1994, which has been published in Chinese core journals. The diagram contains the geometric sequence of 1, 2, 4, 8... Shen Nong's Diagrams of I-Ching actually represents a new binary coding scheme with a specific arrangement and combination of YIN and YANG symbols, in which, the circular diagram constitutes an encoding disk that can be used as a photoelectric code disk. In recent years, the author has discovered that the Fibonacci sequence, TM sequence, φ, e, Pascal's triangle (Yang Hui Triangle), the integer value of the fine structure constant 137, and the spiral fractal structure, which cross coexistence on the encoding disk. Even the spiral structure of the Milky Way is very similar to the spiral of the encoding disk. This provides us with a new perspective and entry point for studying these mathematical and scientific issues and even the internal connections among them, and it is expected to that the encoding disk will be basic tool, which, like Pascal's triangle, will be widely used in the field of mathematical and scientific research.
Category: General Mathematics

Analytical Exploration and Extension of the Function

Authors: Lynette E. M. Z. Winslow
Comments: 6 Pages.

This paper investigates the function ( f(x) = int_{-infty}^{+infty} e^{(-x)^{|u|}} , du ), focusing on its analytical expression and extension over the real number domain. We employ techniques analogous to the analytic continuation of the Gamma function to extend ( f(x) ) beyond its initial domain, addressing convergence issues and exploring its properties across the entire real line.
Category: General Mathematics

An Example of Tan(π/2) = 0 from Seiyo Sampo

Authors: Saburou Saitoh, Hiroshi Okumura
Comments: 2 Pages. (Note by viXra Admin: Further repetition may not be accepted)

We show a very simple and pleasant example tan(π/2) = 0 from Seiyo Sampo.
Category: General Mathematics

Tan(pi/2)=0 from Jacobi's Method in Diagonalization of Matrices

Authors: Saburou Saitoh
Comments: 3 Pages.

In this note, we would like to show the simple result $tan(pi/2)=0$ from Jacobi's formula in diagonalization of matrices.
Category: General Mathematics

Computationally Efficient Differenceless Derivatives with Equidistant Steps and It's Applications

Authors: Yuri Mahotin
Comments: 15 Pages.

Computationally efficient differenceless derivatives with equidistant steps have been developed, which makes it possible to calculate an unlimited number of derivatives. The new algorithm can be applied in various fields of science and technology. As an example, we provide step-by-step instructions on how to improve the accuracy of the predicted trajectory of a flying missile.
Category: General Mathematics

An Oscillatory Integral

Authors: Edgar Valdebenito
Comments: 4 Pages.

Some remarks on an oscillatory integral [are given].
Category: General Mathematics

Solution of Wallis’s Integral Using Complex Functions

Authors: Kazuaki Shimada
Comments: 2 Pages. (Note by viXra Admin: A separate abstract is requited)

This article shows the value of the Wallis integral when n is an even number, n≥2 using the integration of a complex function. Proof of the Wallis product is generally derived using partial integrals, but here derivation using complex integrals is introduced.
Category: General Mathematics

On the Equation: S=(1/2)gamma(1/2,s^2) , S>0

Authors: Edgar Valdebenito
Comments: 3 Pages.

We solve the equation: s=(1/2)Gamma(1/2,s^2), s>0, where Gamma(x,y) is the incomplete gamma function.
Category: General Mathematics

Triples "Ф, e, π" and "π, 4, 6" as Input Data for Modified Koide-Formulas and the Common Grounds of the Results

Authors: Andreas Ball
Comments: 8 Pages.

In this report the common grounds of the results of modified Koide-Formulas are presented, in which the Triples "Ф, e, π" and "π, 4, 6" are set as basis values of various exponents.The figures of the first Triple are the Quotient of the Golden Ratio Ф, the Euler Figure Figure e and the Circle Figure π. Besides the circle/sphere diameter the figures of the second Triple "π, 4, 6" determine the circle area and the sphere volume. The exact exponent value, which results by the Equalization of the two modified Koide-Formulas, is close to the figure 0.444, which is also used at an approximation for the mass ratio of the elementar particles Tauon and Electron. The results of the two Koide-Formulas are close to each other over a relatively wide exponent range.
Category: General Mathematics

An [Attempted] Proof of Fermat's Last Theorem

Authors: Miguel Ángel Rodríguez-Roselló
Comments: 5 Pages.

This article presents an extraordinarily simple proof of Fermat's Last Theorem (FLT), which may be the "marvelous proof" he claimed to have, but which did not fit in the margin of the book he was reading (the Arithmetica of Diophantus of Alexandria). As a consequence of the proof, an alternative formulation of the Pythagorean terns is arrived at.
Category: General Mathematics

Collatz’s Conjecture, Proposal, Solution and Analysis

Authors: Daniel Oliivares
Comments: 5 Pages.

The Collatz conjecture has baffled mathematicians for decades due to its apparent simplicity and the lack of a formal proof. In the next Paper we will address a possible solution to the conjecture by modifying it and the reasons for it and we will analyze determining factors for it. all conditions are met.
Category: General Mathematics

Some Missed Opportunities for Archimedes and Early pi-Computors

Authors: Warren D. Smith
Comments: 4 Pages.

We point out some simple improvements to Archimedes' "regular polygon methods" for computing and bounding π , which all the workers before 1650 could have used, but did not. All methods employed before the 1970s to compute the first D decimals of π required order D or more arithmetic operations (±, ×, ÷, x^1/2, x^-1/2). But we shall show that if Archimedes or his followers had been a bit smarter, they could have sped that up to O(D^2/3).
Category: General Mathematics

Revised Attempt to Prove the Collatz Conjecture

Authors: Krishna Paliwal
Comments: 4 Pages.

TThis paper tries to prove the Collatz Conjecture using a rigorous and logical approach trying to break down 80+ year old and proving that allsequences will eventually always reach to 1.
Category: General Mathematics

Proof of the Collatz Conjecture

Authors: Uğur Pervane
Comments: 4 Pages. (Note by viXra Admin: Please cite and list scientific references)

The Collatz conjecture has long been unresolved. This paper will provide a proof of the Collatz conjecture. The proof will begin by noting that if the conjecture is false, there must be infinitely many examples that violate the conjecture, and will emphasize the impossibility of this scenario. Using probability within the Collatz problem, we can demonstrate that a certain portion of numbers will reach one according to the Collatz algorithm. The total probability must sum to one for the conjecture to be true. If the total probability does not sum to one, it will be a number very close to one. However, if the probability total is even one in a million less than one, there must be an infinite number of numbers that do not satisfy the Collatz algorithm, because a finite number cannot make up for the probability shortfall. This means that there must either be sequences that increase exponentially to infinity or cycles that repeat themselves. However, the probability of selecting the elements of a single sequence that increases to infinity from an infinite set is zero, so there must be infinitely many sequences that increase to infinity and violate the algorithm. The self-repeating cycles must also be infinite in number, but the number of elements in the cycles cannot go to infinity, so there must be infinitely many cycles with the same number of elements. This is impossible, because cycles with the same number of elements are finitely arranged within themselves, and a single element that violates the algorithm will emerge from any of these arrangements. An infinite number of sequences increasing to infinity is also impossible because they would intersect each other. As a result, the Collatz conjecture is true.
Category: General Mathematics

The Philosophical Nature of Zero, Negative, and Imaginary Numbers and the Use of Polar Coordinates in Complex Number Calculations

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

The so-Called Extrinsic Method

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

Proof of Collatz Conjecture

Authors: Abdelkrim ben Mohamed
Comments: 7 Pages.

In this paper we try prove the Collatz conjecture also known the 3x+1 problem.
Category: General Mathematics

Buffon’s Needle Without π

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

Unlocking New Perspectives in Science and Engineering: The Sphere-Base-One Mathematical System

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

From Derivation of Ancient Approximations of the Circle Figure π a Complete Solution of Leonardo da Vinci's Vitruvian Man

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

Improper Integrals of the Second Kind

Authors: Edgar Valdebenito
Comments: 3 Pages.

This document briefly discusses improper integrals of the second kind.
Category: General Mathematics

Truncated Taylor Solvers for Simple First-Order Ordinary Differential Equations

Authors: Steven Kenneth Kauffmann
Comments: 2 Pages.

Certain exact solutions of first-order ordinary differential equations naturally become corresponding solvers for simple first-order ordinary differential equations whose form is the equality of a twice continuously differentiable function of the dependent variable to the derivative with respect the independent variable of the dependent variable. When the twice continuously differentiable function of the dependent variable is replaced by its truncated Taylor expansions through second order about its initial value, the resulting first-order ordinary differential equations have exact solutions that naturally become corresponding solvers for those simple first-order ordinary differential equations.
Category: General Mathematics

Simple Results of 1/0=0/0= 0 by Elementary Figures

Authors: Saburou Saitoh
Comments: 3 Pages.

In this note, we would like to show the simple results $1/0= 0/0=0$ based on the elementary figures that are well-known and simple results on the complex plane. The logic and results are all reasonable and exceptionally pleasant lookings for undergraduate students.
Category: General Mathematics

Since Nothing Can’t Exist, Something Does

Authors: Thiago M. Nóbrega
Comments: 2 Pages.

The formalization presented provides a rigorous foundation for the philosophical argument that "nothing" cannot exist and therefore "something" must exist. By utilizing set theory and logical quantification, I establish a clear mathematical framework supporting this thesis. This foundational understanding has significant implications for various fields, including metaphysics, ontology, and cosmology.
Category: General Mathematics

The Unified Theory

Authors: Thiago M. Nóbrega
Comments: 3 Pages.

The Existence Principle is a novel theoretical framework that unifies ontological principles, the principle of least action, the bootstrap mechanism, Turing's universal machine, and von Neumann's architecture. By merging these concepts, I propose a comprehensive mathematical structure that demonstrates the self-consistent nature of reality, governed by physical laws and computational principles. This framework provides groundbreaking insights into the fundamental nature of existence, life, and the universe.
Category: General Mathematics

Optimization Problem

Authors: Edgar Valdebenito
Comments: 3 Pages.

[This paper consider] [w]hat the maximum value of f(x)=arctan(exp(-exp(x-2)))-arctan(exp(-exp(x+2)))[is].
Category: General Mathematics

Applicability Operator Approach to Mathematical Proofs

Authors: Jason Kodish
Comments: 2 Pages. (Note by viXra Admin: Please cite and list scientific references)

Teaching proofs of theorems and encouraging students to both comprehend written proofs and originate their own can at times be a difficult undertaking. This is due in part to the lack of a single unifying process by which one can approach mathematical proofs. In this paper a method using set theory as a foundation is presented.
Category: General Mathematics

Key to Leibnizian Mathematics

Authors: Adriaan van der Walt
Comments: 11 Pages.

This document states the relevant basic assumptions of Mathematics that lead to some of the salient features of Abstract Mathematics. These features are then deduced from these assumptions in a fundamental way. Infinitesimals and Infinitesimal Numbers are introduced and then used in an example of a Riemann sum to create a contradiction that motivates the introduction of Leibnizian Mathematics as a model for Mathematics that is supplemental to Abstract Mathematics. Leibnizian Mathematics is then introduced by stating its basic assumptions. Lastly a list of the meanings of some words that are common to both models, but describe properties that differ between the models, is given. The reader is then referred to the document LEIBNIZIAN MATHEMATICS, posted on the link stated in the Comments below, where this model is developed.
Category: General Mathematics

Discussions on the Decomposition of Deformed Vector Products

Authors: Thierry L. A. Periat
Comments: 40 Pages. In French (Translation made by viXra Admin - Future non-compliant submission will not be accepted)

This paper is part of a series of explorations exposing methods for dividing distorted tensor products by number cubes. Here, the discussion focuses on three-dimensional spaces and anti-symmetric cubes on their low indices; i.e. actually on distorted vector products. The method only delivers the main parts of the divisions. They are divided into two classes. The other documents in the collection complete this investigation.

Ce document fait partie d'une série d'explorations exposant des méthodes permettant de diviser les produits tensoriels déformés par des cubes de nombres. Ici, la discussion se focalise sur les espaces de dimension trois et les cubes antisymétriques sur leurs indices bas ; c'est-à-dire en fait sur des produits vectoriels déformés. La méthode livre seulement les parties principales des divisions. Elles se répartissent en deux classes. Les autres documents de la collection complètent cette investigation.
Category: General Mathematics

On a Combinatorial Problem of Existing Matchings

Authors: Wladislaw Zlatjkovic Petrovescu
Comments: 2 Pages. (Abstract added by viXra Admin as required - Please conform)

In this paper we prove a classic combinatorial result on matchings.
Category: General Mathematics

Foundations of Differential Calculus: Does the Theory Satisfy the Criterion of Truth?

Authors: Temur Z. Kalanov
Comments: 16 Pages.

A detailed proof of the incorrectness of the foundations of the differential calculus is proposed. The correct methodological basis for the proof is the unity of formal logic and rational dialectics. The unity of formal logic and rational dialectics is the only correct criterion of truth. The proof leads to the following irrefutable statement: differential calculus represents an incorrect theory in mathematics and physics. The proof of this statement is based on the following irrefutable results: (1) the standard theory of infinitesimals and the theory of limits underlying the differential calculus are incorrect theories. The concepts of "infinitesimal quantity", "movement", "process of tendency", and "limit of tendency" are meaningless concepts in mathematics; (2) the concepts of "increment of argument" and "increment of function" as the starting point of the differential calculus are not defined correctly; (3) the definition of the derivative of a function is an incorrect because the following logical contradiction arises: the increment of the argument is both not equal to zero and equal to zero; (4) the differentials of the argument and the function - as infinitesimal quantities - do not take on numerical values. This means that the differentials of quantities have neither quantitative nor qualitative determinacy; (5) the definition of the total differential of a function of two (many) variables does not satisfy the formal-logical law of the lack (absence) of contradiction; (6) the theory of proportions completely refutes the theory of differential calculus. Thus, differential calculus does not satisfy the criterion of truth and is not correct scientific (mathematical) theory.
Category: General Mathematics

A Power Series Divergent at Half Pi Yields a Sequence Briskly Convergent to Pi

Authors: Steven Kenneth Kauffmann
Comments: 2 Pages.

The tangent function's Taylor expansion about zero is a series of odd powers with positive coefficients; it converges when the absolute value of its argument is less than half pi, and diverges to positive infinity when its argument equals half pi, so with the aid of the ratio test it is seen that twice the square root of the ratio of its successive coefficients is a sequence which converges to pi. The odd derivatives of the tangent function are polynomials in powers of its square with positive integer coefficients, so a recursion of positive integers can be found from which the coefficients of the series described above may be successively obtained. Its related sequence which converges to pi does so monotonically from above, and appears to refine its approximation to pi by about one significant decimal figure per successive term.
Category: General Mathematics

Geometric Facts of a Circle Through Its Equation

Authors: Rajesh Sharma, Vijay Sharma
Comments: 4 Pages.

We derive equation of a circle passing through three distinct points in a different way and demonstrate that several basic geometric properties of a circle can be derived easily by means of this equation alone.
Category: General Mathematics

Squaring the Circle and Approximations to pi

Authors: Edgar Valdebenito
Comments: 4 Pages.

Since the 19th century when von Lindemann set out a proof of the transcendental properties of the mathematical constant Pi, mathematicians have taken the view that squaring the circle using a straight edge and compass is not possible.
Category: General Mathematics

A Sketch of Effective Learning Using Technology [Part 1]

Authors: Timothy Jones
Comments: 7 Pages.

A problem set from a calculus text is solved. The goal is to see whether or not modern calculators and a CAS are genuinely helpful.
Category: General Mathematics

The Peculiar Case of "p"

Authors: Simon A. Pritchett
Comments: 63 Pages.

Division by zero is a phenomenon described by confused mathematicians for hundreds of years. I would like to declare the value of one divided by zero to be equal to "p". I shall call p the pseudo-imaginary unit, as it shares several characteristics with i, the imaginary unit, as they both solve difficult equations that cannot be solved with basic algebraic and arithmetic mathematical operations, and they both extend real numbers into a new, larger set of numbers. In the case of i, the set is known as the complex numbers, whereas with p, it is known as the "pseudo-complex numbers".
Category: General Mathematics

Division by Zero 1/0 = 0/0 = 0 and Computers Real.div: New Information and Many Applications

Authors: Saburou Saitoh, Yoshinori Saitoh
Comments: 8 Pages.

In this note, we introduce the new information {bf real.div} on the division by zero results $1/0= 0/0=0$ that is recently informed and we would like to propose the related important problems on the division by zero calculus.
Category: General Mathematics

A Third Order Sequence

Authors: Edgar Valdebenito
Comments: 3 Pages.

We study the third order sequence:u(n)=3u(n-1)+6u(n-2)+3u(n-3) , u(0)=1,u(1)=3,u(2)=15,n=3,4,5,...
Category: General Mathematics

On the Generalization of Glaisher—Kinkelin‘s Constant and Its Applications

Authors: SonHyang Ri, Il Yun, Chol Ho Ji, Hong Rok Ri
Comments: 17 Pages.

In this paper, we have found the exquisite relation between Stirling’s formula andinteresting expression for Glaisher—Kinkelin’s constant,Bendersky—Adamchik’sconstant, andhave introduced new constants astheir generalization.As we calculate the singular integral or sum of series in form of closed expression by introducingconstant π, Euler constant, Glaisher-Kinkelin’s constant,Bendersky—Adamchik’sconstant, new constantswill play important role in calculating of the sum of multi-series which has the multi-power in general term. To demonstrate the superiority of our new constants in several calculations, we propose an exampleWe show that our new constants generalize Glaisher—Kinkelin’s constant and Bendersky—Adamchik’s constant
Category: General Mathematics

Differenceless Derivatives with Equidistant Steps

Authors: Yuri Mahotin
Comments: 3 Pages.

Differenceless derivatives with equidistant steps have been developed, whichmakes it possible to calculate an unlimited number of derivatives. One application ofthis algorithm is the extrapolation and prediction of functions over a wide range ofarguments, which can be used in various fields of science and technology.
Category: General Mathematics

A Theoretical Approach to the Navier-Stokes Millennium Problem using Dream Numbers

Authors: Oussama Basta
Comments: 13 Pages. (Name added to Article by viXra Admin as required)

This paper presents a theoretical exploration of the Navier-Stokes equations within the innovative framework of Dream Partial Differential Equations (DPDEs). Beginning with the concept of dream numbers and their application in defining new forms of derivatives, we extend these ideas to reformulate the Navier-Stokes equations. Our aim is to investigate whether this novel approach could potentially shed light on the Millennium Problem concerning the existence and smoothness of solutions to these equations in three dimensions.
Category: General Mathematics

Cool Formula for pi

Authors: Edgar Valdebenito
Comments: 3 Pages.

In this note we consider the sum: 1-1/9+1/45-1/189+...
Category: General Mathematics

Mark Burgin's Contribution to the Foundation of Mathematics

Authors: Felix M. Lev
Comments: 16 Pages. Published in Special Issue in Memory of Professor Mark Burgin, Philosophies 2024, 9(1), 8; https://doi.org/10.3390/philosophies9010008

In this paper I attempt to describe those Mark Burgin's results in non-Diophantine mathematics which are important for foundation of mathematics and its applications in quantum field theory. In particular, the elimination of divergences in Quantum Electrodynamics is described.
Category: General Mathematics

Uchida's Identities and Simple Results of 1/0=0/0= Tan(π/2)= Cot(π/2)=0

Authors: Saburou Saitoh
Comments: 4 Pages.

In this note, we would like to show the simple results 1/0=0/0= tan(π/2)= cot(π/2)=0 based on the simple identities that are discovered by Keitaroh Uchida. The logic and results are all reasonable and exceptionally pleasant lookings for high school students.
Category: General Mathematics

Convergence Condition for the Newton-Raphson Method: Application in Real Polynomial Functions

Authors: Juan Jorge Isaac Lopez
Comments: 5 Pages.

The Newton-Raphson method applies to the numerical calculation of the roots of Real functions, through successive approximations towards the Root of the function. The Newton-Raphson method has the drawback that it does not always converge. This work establishes the convergence condition of the Newton-Raphson method for Real functions in general; once the convergence condition is met, the method will always converge towards the Root of the function. In this work, the development of the application of the convergence condition is established to specifically solve Real polynomial functions.
Category: General Mathematics

Abraham Sharp's Formula

Authors: Edgar Valdebenito
Comments: 9 Pages.

In 1699,Abraham Sharp calculates pi to 72 decimal places by taking x=1/sqrt(3) in Gregory's series.
Category: General Mathematics

Weighted Riemann Zeta Limits on the Real Axis

Authors: Han Geurdes
Comments: 7 Pages.

It is investigated whether for real argument s the (s−1)n+1 weighted Riemann zeta ζ(n)(s) limits s ↓ 1 do exist. Here, we will look into n = 0,1. The answer to the question could very well be that assuming existence to be true gives a confusing outcome. That may support the possibility of incompleteness in concrete mathematics.
Category: General Mathematics

Proof of Collatz Conjecture

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

Proof of Collatz Conjecture

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

Differenceless Derivatives with Equidistant Steps

Authors: Yuri Mahotin
Comments: 3 Pages.

Differenceless derivatives with equidistant steps have been developed, which makes it possible to calculate an unlimited number of derivatives. One application of this algorithm is the extrapolation and prediction of functions over a wide range of arguments, which can be used in various fields of science and technology.
Category: General Mathematics

π − e , π + e , πe and π/e All Are Irrational Numbers

Authors: Amine Oufaska
Comments: 6 Pages.

It is proved that π − e , π + e , πe and π/e all are irrational numbers . The proof is essentially elementary , it is an argument by contradiction.
Category: General Mathematics