Parabolic Numbers: A New Perspective
Thus far, many studies have been conducted on $p$-complex numbers. Depending on the sign of $p$, there are three cases: hyperbolic, dual, and elliptic. In the literature, dual numbers are called parabolic numbers, but they do not parameterize parabolas. Therefore, a number system that parameterizes...
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| Format: | Article |
| Language: | English |
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Naim Çağman
2024-12-01
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| Series: | Journal of New Theory |
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| Online Access: | https://dergipark.org.tr/en/download/article-file/4115950 |
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| author | Furkan Semih Dündar |
| author_facet | Furkan Semih Dündar |
| author_sort | Furkan Semih Dündar |
| collection | DOAJ |
| description | Thus far, many studies have been conducted on $p$-complex numbers. Depending on the sign of $p$, there are three cases: hyperbolic, dual, and elliptic. In the literature, dual numbers are called parabolic numbers, but they do not parameterize parabolas. Therefore, a number system that parameterizes parabolas is worth studying. This paper defines $p$ as a function of the coordinate $y$ and obtains a number system named parabolic numbers whose circles are parabolas. These parabolic numbers complete the set of number systems where circles are conic sections. Finally, this paper discusses the prospect of further research. |
| format | Article |
| id | doaj-art-413d5e4533fe498a8b06a56e50f1e106 |
| institution | DOAJ |
| issn | 2149-1402 |
| language | English |
| publishDate | 2024-12-01 |
| publisher | Naim Çağman |
| record_format | Article |
| series | Journal of New Theory |
| spelling | doaj-art-413d5e4533fe498a8b06a56e50f1e1062025-08-20T03:10:56ZengNaim ÇağmanJournal of New Theory2149-14022024-12-014971510.53570/jnt.15266992425Parabolic Numbers: A New PerspectiveFurkan Semih Dündar0https://orcid.org/0000-0001-5184-5749AMASYA UNIVERSITYThus far, many studies have been conducted on $p$-complex numbers. Depending on the sign of $p$, there are three cases: hyperbolic, dual, and elliptic. In the literature, dual numbers are called parabolic numbers, but they do not parameterize parabolas. Therefore, a number system that parameterizes parabolas is worth studying. This paper defines $p$ as a function of the coordinate $y$ and obtains a number system named parabolic numbers whose circles are parabolas. These parabolic numbers complete the set of number systems where circles are conic sections. Finally, this paper discusses the prospect of further research.https://dergipark.org.tr/en/download/article-file/4115950parabolic numbers$p$-complex numberscoordinate dependence |
| spellingShingle | Furkan Semih Dündar Parabolic Numbers: A New Perspective Journal of New Theory parabolic numbers $p$-complex numbers coordinate dependence |
| title | Parabolic Numbers: A New Perspective |
| title_full | Parabolic Numbers: A New Perspective |
| title_fullStr | Parabolic Numbers: A New Perspective |
| title_full_unstemmed | Parabolic Numbers: A New Perspective |
| title_short | Parabolic Numbers: A New Perspective |
| title_sort | parabolic numbers a new perspective |
| topic | parabolic numbers $p$-complex numbers coordinate dependence |
| url | https://dergipark.org.tr/en/download/article-file/4115950 |
| work_keys_str_mv | AT furkansemihdundar parabolicnumbersanewperspective |