Solution of quintic equation by geometric method and based upon it: A mathematical model

Abstract

Purpose of writing this paper is to provide a new dynamic geometric method and also a mechanical model based upon it, to solve quintic equations. A triangle ABC with base BC, perpendicular AB of length equal to unity, hypotenuse AC, right angle at point B, is constructed. Perpendiculars BD, EF, GH upon AC, perpendiculars DE, FG upon BC, are drawn. Value of angle C is adjusted so that difference in lengths of BD and GH equals constant term of quintic equation transformed to Bring-Jerrard normal form, then one real root of given quintic equation equals length of perpendicular BD. Presently, there are two geometric methods available to solve quintic equations, first by paper folding art, called Origami and second given by Australian engineer, Edward Lill. This paper presents third simple and unique geometric method. Notwithstanding this dynamic geometric method, a mathematical model, explaining its fabrication, operation, has also been devised to present a real life picture of solution to the equations.