A modelling of the natural logarithm and Mercator series as 5^th, 6^th, 7^th order Bézier curve in plane
Özet
In this study first, natural logarithm function 𝑓𝑓(𝑥𝑥) = ln𝑥𝑥 with base 𝑒𝑒 has been
examined as polynomial function of 5𝑡𝑡ℎ, 6𝑡𝑡ℎ, 7𝑡𝑡ℎ order Bézier curve. By modelling
matrix representation of 5𝑡𝑡ℎ, 6𝑡𝑡ℎ, 7𝑡𝑡ℎ order Bézier curve we have found the control
points in plane. Further, Mercator series for the curves ln(1 + 𝑥𝑥) and ln(1 − 𝑥𝑥) have
been written too as the polynomial functions as 5𝑡𝑡ℎ, 6𝑡𝑡ℎ, 7𝑡𝑡ℎ order Bézier curve in
plane based on the control points with matrix form in 𝐄𝐄 2. Finally, the curve ln(1 −
𝑥𝑥 2) has been expressed as 5𝑡𝑡ℎ, 6𝑡𝑡ℎ, 7𝑡𝑡ℎ order Bézier curve, examined the control points
and given matrix forms.
Atıf için künye
Yurttançıkmaz, S., & Kılıçoğlu, Ş. (2024). A modelling of the natural logarithm and Mercator series as 5^th, 6^th, 7^th order Bézier curve in plane. Manas Journal of Engineering, 12(2), 185–191. https://doi.org/10.51354/mjen.1475483
BibTeX
@article{yurttancikmaz2024-57347,
author = {Yurttançıkmaz, Semra and Kılıçoğlu, Şeyda},
title = {A modelling of the natural logarithm and Mercator series as 5^th, 6^th, 7^th order Bézier curve in plane},
journal = {Manas Journal of Engineering},
year = {2024},
volume = {12},
number = {2},
pages = {185--191},
issn = {1694-7398},
doi = {10.51354/mjen.1475483},
url = {https://akademik.atauni.edu.tr/yayinlar/57347-a-modelling-of-the-natural-logarithm-and-mercator-series-as-5th-6th-7th-order}
}