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