相关论文: Geometric solution of a quintic equation by two-fo…

After Abel Ruffini theorem and Galois Theory the search for a method or formula to solve quintic equation ends. This paper discuss about the radical solution of quintic equation using a method that could be proved in some simple steps. A…

The requirement for solving a polynomial is a means of breaking its symmetry, which in the case of the quintic, is that of the symmetric group S_5. Induced by its five-dimensional linear permutation representation is a three-dimensional…

In this paper we prove that a generic rational equation of degree $7$ is solvable by 2-fold origami. In particular we show how to septisect an arbitrary angle. This extends the work of Alperin & Lang and Nishimura on 2-fold origami.…

Everybody knows from school how to solve a quadratic equation of the form $x^2-px+q=0$ graphically. But this method can become tedious if several equations ought to be solved, as for each pair $(p,q)$ a new parabola has to be drawn.…

Different authors have done analysis regarding sums of powers References number 1,2 and 3, but systematic approach for solving Diophantine equations having sums of many biquadratics equal to a quartic has not been done before. In this paper…

Using the circle method, we obtain asymptotic formulae for the number of integer solutions to certain quadratic polynomials that are uniform in the coefficients of the polynomial.

According to the Abel-Ruffini theorem [1] and Galois theory [2], there is no solution in finite radicals to the general quintic equation. This article takes a different approach and proposes a new method to solve the quintic by iteration of…

Some physical applications of the Passare-Tsikh solution of a principal quintic equation are discussed. As an example, a quintic equation of state is solved in detail. This approach provides analytical approximations for several problems…

We develop recursion equations to describe the three-dimensional shape of a sheet upon which a series of concentric curved folds have been inscribed. In the case of no stretching outside the fold, the three-dimensional shape of a single…

We give a method to resolve 4-dimensional symplectic orbifolds making use of techniques from complex geometry and gluing of symplectic forms. We provide some examples to which the resolution method applies.

Details for known solutions of some geometric and algebraic problems with the help of origami are presented: two theorems of Haga, the general cubic equation, especially the heptagon equation, doubling the cube as well as the trisection of…

An efficient way to get implicit equations of conics on five points and quadrics on nine, using pencils of conics and quadrics, is revealed. Parallel axis right cones intersect on a conic. An example, to show how to place five coplanar…

Extends previous work on a quintic-solving algorithm to equations of the eighth-degree.

We study a general method of the field intersection problem of generic polynomials over an arbitrary field $k$ via formal Tschirnhausen transformation. In the case of solvable quintic, we give an explicit answer to the problem by using…

This paper presents new formulary solutions for quantic polynomial equations in general forms, where we present five solutions for any fifth degree polynomial equation with real coefficients, and thereby having the possibility to calculate…

A subset of traveling wave solutions of the quintic complex Ginzburg-Landau equation (QCGLE) is presented in compact form. The approach consists of the following parts. - Reduction of the QCGLE to a system of two ordinary differential…

We use ideas from our previous work to obtain some theorems that will allow us to obtain the integer solution of a quadratic polynomial in two variables that represents a natural number

In this article we solve a class of two parameter polynomial-quintic equation. The solution follows if we consider the Jacobian elliptic function $sn$ and relate it with the coefficients of the equation. The solution is the elliptic…

This paper presents a simplified method of expressing the solution to cubic equations in terms of function evaluation only. The method eliminates the need to manipulate the original coefficients of the cubic polynomial and makes the…

In this article we give solution of the general quintic equation by means of the Rogers-Ramanujan continued fraction. More precisely we express a root of the quintic as a known algebraic function of the Rogers-Ramanujan continued fraction.