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Open AccessArticle

Quaternionic Product of Equilateral Hyperbolas and Some Extensions

1
Faculty of Mathematics, University “Al. I. Cuza”, 700506 Iasi, Romania
2
Department of Applied Mathematics, Faculty of Sciences, University of Craiova, 00585 Craiova, Romania
*
Author to whom correspondence should be addressed.
These authors contributed equally to this work.
Mathematics 2020, 8(10), 1686; https://doi.org/10.3390/math8101686
Received: 10 August 2020 / Revised: 21 September 2020 / Accepted: 29 September 2020 / Published: 1 October 2020
(This article belongs to the Special Issue Geometric Methods and their Applications)
This note concerns a product of equilateral hyperbolas induced by the quaternionic product considered in a projective manner. Several properties of this composition law are derived and, in this way, we arrive at some special numbers as roots or powers of unit. Using the algebra of octonions, we extend this product to oriented equilateral hyperbolas and to pairs of equilateral hyperbolas. Using an inversion we extend this product to Bernoulli lemniscates and q-lemniscates. Finally, we extend this product to a set of conics. Three applications of the given products are proposed. View Full-Text
Keywords: equilateral hyperbola; quaternion; product; projective geometry; octonion equilateral hyperbola; quaternion; product; projective geometry; octonion
MDPI and ACS Style

Crasmareanu, M.; Popescu, M. Quaternionic Product of Equilateral Hyperbolas and Some Extensions. Mathematics 2020, 8, 1686.

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