Circular surfaces and singularities in Euclidean 3-space E<sup>3</sup>
The approach of the paper is on circular surfaces. A circular surface is a one-parameter family of standard circles with fixed radius regarding a curve, which acts as the spine curve. In the study, we have parametrized circular surfaces and have provided its geometric properties like singularities a...
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| Format: | Article |
| Language: | English |
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AIMS Press
2022-04-01
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| Series: | AIMS Mathematics |
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| Online Access: | https://www.aimspress.com/article/doi/10.3934/math.2022701?viewType=HTML |
| _version_ | 1811335659022974976 |
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| author | Nadia Alluhaibi |
| author_facet | Nadia Alluhaibi |
| author_sort | Nadia Alluhaibi |
| collection | DOAJ |
| description | The approach of the paper is on circular surfaces. A circular surface is a one-parameter family of standard circles with fixed radius regarding a curve, which acts as the spine curve. In the study, we have parametrized circular surfaces and have provided its geometric properties like singularities and striction curves comparing with those of ruled surfaces. Furthermore, we have addressed the conditions of minimality of roller coaster surfaces. Meanwhile, we support the results of the approach by some examples. |
| first_indexed | 2024-04-13T17:28:26Z |
| format | Article |
| id | doaj.art-13cbeee53e0d446f806d0f3fd5c77b25 |
| institution | Directory Open Access Journal |
| issn | 2473-6988 |
| language | English |
| last_indexed | 2024-04-13T17:28:26Z |
| publishDate | 2022-04-01 |
| publisher | AIMS Press |
| record_format | Article |
| series | AIMS Mathematics |
| spelling | doaj.art-13cbeee53e0d446f806d0f3fd5c77b252022-12-22T02:37:41ZengAIMS PressAIMS Mathematics2473-69882022-04-0177126711268810.3934/math.2022701Circular surfaces and singularities in Euclidean 3-space E<sup>3</sup>Nadia Alluhaibi0Department of mathematics, College of Science and Arts, King Abdulaziz University, Rabigh, Saudi ArabiaThe approach of the paper is on circular surfaces. A circular surface is a one-parameter family of standard circles with fixed radius regarding a curve, which acts as the spine curve. In the study, we have parametrized circular surfaces and have provided its geometric properties like singularities and striction curves comparing with those of ruled surfaces. Furthermore, we have addressed the conditions of minimality of roller coaster surfaces. Meanwhile, we support the results of the approach by some examples.https://www.aimspress.com/article/doi/10.3934/math.2022701?viewType=HTMLlines of curvature and singularityroller coaster surface |
| spellingShingle | Nadia Alluhaibi Circular surfaces and singularities in Euclidean 3-space E<sup>3</sup> AIMS Mathematics lines of curvature and singularity roller coaster surface |
| title | Circular surfaces and singularities in Euclidean 3-space E<sup>3</sup> |
| title_full | Circular surfaces and singularities in Euclidean 3-space E<sup>3</sup> |
| title_fullStr | Circular surfaces and singularities in Euclidean 3-space E<sup>3</sup> |
| title_full_unstemmed | Circular surfaces and singularities in Euclidean 3-space E<sup>3</sup> |
| title_short | Circular surfaces and singularities in Euclidean 3-space E<sup>3</sup> |
| title_sort | circular surfaces and singularities in euclidean 3 space e sup 3 sup |
| topic | lines of curvature and singularity roller coaster surface |
| url | https://www.aimspress.com/article/doi/10.3934/math.2022701?viewType=HTML |
| work_keys_str_mv | AT nadiaalluhaibi circularsurfacesandsingularitiesineuclidean3spaceesup3sup |