On quaternionic product on some sets of hyperbolas
The aim of this paper is to introduce some products, induced by the quaternionic product, on the set of equilateral hyperbolas. The study is a mix of elements from Euclidean and projective geometry. Some properties of these products are highlighted and are connected with some special numbers as root...
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Published in | ITM Web of Conferences Vol. 34; p. 3004 |
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Main Authors | , |
Format | Journal Article Conference Proceeding |
Language | English |
Published |
Les Ulis
EDP Sciences
2020
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Abstract | The aim of this paper is to introduce some products, induced by the quaternionic product, on the set of equilateral hyperbolas. The study is a mix of elements from Euclidean and projective geometry. Some properties of these products are highlighted and are connected with some special numbers as roots or powers of the unit. Then we extend these products in a natural manner to oriented equilateral hyperbolas and to pairs of equilateral hyperbolas, using the algebra of octonions. Further, using an inversion, we extend these products to Bernoulli lemniscates and to Bernoulli q-lemniscates. Finally, using some isomorphisms, we extend these products to conics, and using an inversion, we extend these products to other curves. In order to highlight the importance of these studied products, the paper ends with some applications. |
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AbstractList | The aim of this paper is to introduce some products, induced by the quaternionic product, on the set of equilateral hyperbolas. The study is a mix of elements from Euclidean and projective geometry. Some properties of these products are highlighted and are connected with some special numbers as roots or powers of the unit. Then we extend these products in a natural manner to oriented equilateral hyperbolas and to pairs of equilateral hyperbolas, using the algebra of octonions. Further, using an inversion, we extend these products to Bernoulli lemniscates and to Bernoulli q-lemniscates. Finally, using some isomorphisms, we extend these products to conics, and using an inversion, we extend these products to other curves. In order to highlight the importance of these studied products, the paper ends with some applications. |
Author | Popescu, Marcela Crasmareanu, Mircea |
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Cites_doi | 10.1080/0025570X.2004.11953223 10.1007/s00283-014-9445-5 10.1090/spec/054/07 |
ContentType | Journal Article Conference Proceeding |
Copyright | 2020. This work is licensed under https://creativecommons.org/licenses/by/4.0/ (the “License”). Notwithstanding the ProQuest Terms and conditions, you may use this content in accordance with the terms of the License. |
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DOI | 10.1051/itmconf/20203403004 |
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References | R3 Akopyan (R1) 2014; 36 Hre¸tcanu (R6) 2013; 54 R5 Barnett (R2) 2004; 77 Özdemyr (R7) 2011; 35 Crasmareanu (R4) 2020; 66 |
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SubjectTerms | Conics equilateral hyperbola Euclidean geometry Hyperbolas Isomorphism octonion product Projective geometry quaternion |
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