New Approach to Obtain the Perimeter of an Ellipse

Abstract

In different periods in history, mathematicians introduced formulas to calculate the perimeter of an ellipse. Using the existing formula, the accurate perimeter of an ellipse cannot be measured as they provide only an approximate value. In this research project, our main intense is to produce a new formula to measure perimeter of an ellipse. For this purpose and to achieve our target, earlier methods are studied. We understood that the arc length of the elliptical presently given by the incomplete elliptical integral of the second kind, however a closed form solution of the elliptical integral is unable to achieve our goal. At the next step of our study, we consider a first order homogeneous function with constant and it was not difficult to determine values of constant using equations in order to obtain required formula. After obtaining the formula the limitations and comparisons are discussed.