A modelling of the natural logarithm and Mercator series as 5^th, 6^th, 7^th order Bézier curve in plane
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 cu...
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| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
Kyrgyz Turkish Manas University
2024-12-01
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| Series: | MANAS: Journal of Engineering |
| Subjects: | |
| Online Access: | https://dergipark.org.tr/en/download/article-file/3893349 |
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| Summary: | 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. |
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| ISSN: | 1694-7398 |