A modelling of the natural logarithm and Mercator series as 5^th, 6^th, 7^th order Bézier curve in plane

Year 2024, Volume: 12 Issue: 2, 185 - 191, 27.12.2024

Şeyda Kılıçoglu , Semra Yurttançıkmaz

https://doi.org/10.51354/mjen.1475483

Abstract

In this study first, natural logarithm function f(x)=lnx with base e has been examined as polynomial function of 5^th, 6^th,7^th order Bézier curve. By modelling matrix representation of 5^th, 6^th,7^th order Bézier curve we have found the control points in plane. Further, Mercator series for the curves ln(1+x) and ln(1-x) have been written too as the polynomial functions as 5^th, 6^th,7^th order Bézier curve in plane based on the control points with matrix form in E^2. Finally, the curve ln(1-x^2) has been expressed as 5^th, 6^th,7^th order Bézier curve, examined the control points and given matrix forms.

Keywords

Natural logarithm, Mercator series, 5^thorder Bézier curve, 6^thorder Bézier curve, 7^thorder Bézier curve.

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