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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| Format: | Article |
| Language: | English |
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Kyrgyz Turkish Manas University
2024-12-01
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| Series: | MANAS: Journal of Engineering |
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| Online Access: | https://dergipark.org.tr/en/download/article-file/3893349 |
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| author | Şeyda Kılıçoglu Semra Yurttançıkmaz |
| author_facet | Şeyda Kılıçoglu Semra Yurttançıkmaz |
| author_sort | Şeyda Kılıçoglu |
| collection | DOAJ |
| description | 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. |
| format | Article |
| id | doaj-art-f25376ed12974ac5badeb94c16559673 |
| institution | Kabale University |
| issn | 1694-7398 |
| language | English |
| publishDate | 2024-12-01 |
| publisher | Kyrgyz Turkish Manas University |
| record_format | Article |
| series | MANAS: Journal of Engineering |
| spelling | doaj-art-f25376ed12974ac5badeb94c165596732025-01-08T09:28:23ZengKyrgyz Turkish Manas UniversityMANAS: Journal of Engineering1694-73982024-12-0112218519110.51354/mjen.14754831437A modelling of the natural logarithm and Mercator series as 5^th, 6^th, 7^th order Bézier curve in planeŞeyda Kılıçoglu0https://orcid.org/0000-0003-0252-1574Semra Yurttançıkmaz1https://orcid.org/0000-0001-6712-3687Başkent ÜniversitesiAtatürk ÜniversitesiIn 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.https://dergipark.org.tr/en/download/article-file/3893349natural logarithmmercator series5^thorder bézier curve6^thorder bézier curve7^thorder bézier curve. |
| spellingShingle | Şeyda Kılıçoglu Semra Yurttançıkmaz 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 natural logarithm mercator series 5^thorder bézier curve 6^thorder bézier curve 7^thorder bézier curve. |
| title | A modelling of the natural logarithm and Mercator series as 5^th, 6^th, 7^th order Bézier curve in plane |
| title_full | A modelling of the natural logarithm and Mercator series as 5^th, 6^th, 7^th order Bézier curve in plane |
| title_fullStr | A modelling of the natural logarithm and Mercator series as 5^th, 6^th, 7^th order Bézier curve in plane |
| title_full_unstemmed | A modelling of the natural logarithm and Mercator series as 5^th, 6^th, 7^th order Bézier curve in plane |
| title_short | A modelling of the natural logarithm and Mercator series as 5^th, 6^th, 7^th order Bézier curve in plane |
| title_sort | modelling of the natural logarithm and mercator series as 5 th 6 th 7 th order bezier curve in plane |
| topic | natural logarithm mercator series 5^thorder bézier curve 6^thorder bézier curve 7^thorder bézier curve. |
| url | https://dergipark.org.tr/en/download/article-file/3893349 |
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