Related papers: On the babylonian method of extracting root square…
We investigate ``shell structure'' from Babylonian times: periodicities and beats in computer-simulated lunar data corresponding to those observed by Babylonian scribes some 2500 years ago. We discuss the mathematical similarity between the…
In this article, we use Robba's method to give an estimate of the Newton polygon for the L function on torus and we can draw the Newton polygon in some special cases.
This paper is devoted to the analysis of a false generalization of the rule of Sarrus and its properties that can be derived with the help of dihedral groups. Further, we discuss a Sarrus-like scheme that could be helpful for students to…
This paper presents new six solutions for sixth degree polynomial equation in general forms basing on new theorems, where the possibility to calculate the six roots of any sixth degree equation nearly simultaneously. The proposed roots for…
We consider so-called squaring the square-puzzles where a given square (or rectangle) should be dissected into smaller squares. For a specific instance of such problems we demonstrate that a mathematically rigorous solution can be quite…
In this paper I present a kind of proof for classical Euclidean geometric problems which relies on both synthetic and analytic geometry. Using the elementary tools of polynomial algebra and multivariate calculus we manage to reduce the…
We prove the Jordan curve theorem by generalizing the sweepline algorithm for trapezoidal decomposition of a polygon. Our proof uses Zorn's lemma (or, equivalently the axiom of choice). Though several proofs have been given for the Jordan…
In this paper some generalizations of the sum of powers of natural numbers is considered. In particular, the class of sums whose generating function is the power of the generating function for the classical sums of powers is studying. The…
In most introductory numerical analysis textbooks, the treatment of a single nonlinear equation often consists of a collection of all-purpose methods that frequently do not work or are inefficient. These textbooks neglect to teach the…
The roots of any polynomial of degree m with integer coefficients, can be computed by manipulation of sequences made from 2m distinct symbols and counting the different symbols in the sequences. This method requires only 'primitive'…
Math is widely considered as a powerful tool and its strong appeal depends on the high level of abstraction it allows in modelling a huge number of heterogeneous phenomena and problems, spanning from the static of buildings to the flight of…
A combinatorial methods are used to investigate some properties of certain generalized Stirling numbers, including explicit formula and recurrence relations. Furthermore, an expression of these numbers with symmetric function is deduced.
We present new estimates for sums of the divisor function, and other similar arithmetic functions, in short intervals over function fields. (When the intervals are long, one obtains a good estimate from the Riemann hypothesis.) We obtain an…
In this paper, we revisit the chaotic number of iterations needed by Newton's method to converge to a root. Here, we consider a simple modified Newton method depending on a parameter. It is demonstrated using polynomiography that even in…
We present improved algorithms for fast calculation of the inverse square root for single-precision floating-point numbers. The algorithms are much more accurate than the famous fast inverse square root algorithm and have the same or…
Iterative methods for the simultaneous determination of all roots of an equation are dis-cussed. The multiplicities of the roots are assumed to be known in advance. The methods are proved to have a cubical rate of convergence. Numerical…
In this note, we provide bijective proofs of some identities involving the Bell number, as previously requested. Our arguments may be extended to yield a generalization in terms of complete Bell polynomials. We also provide a further…
We give formulas for the number of polynomials over a finite field with given root multiplicities, in particular in cases when the formula is surprisingly simple (a power of q). Besides this concrete interpretation, we also prove an…
Linearized polynomials appear in many different contexts, such as rank metric codes, cryptography and linear sets, and the main issue regards the characterization of the number of roots from their coefficients. Results of this type have…
We prove several formulas for the distribution of positive roots.