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Quaternionic Product of Equilateral Hyperbolas and Some Extensions

Author

Listed:
  • Mircea Crasmareanu

    (Faculty of Mathematics, University “Al. I. Cuza”, 700506 Iasi, Romania
    These authors contributed equally to this work.)

  • Marcela Popescu

    (Department of Applied Mathematics, Faculty of Sciences, University of Craiova, 00585 Craiova, Romania)

Abstract

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.

Suggested Citation

  • Mircea Crasmareanu & Marcela Popescu, 2020. "Quaternionic Product of Equilateral Hyperbolas and Some Extensions," Mathematics, MDPI, vol. 8(10), pages 1-16, October.
    • Handle: RePEc:gam:jmathe:v:8:y:2020:i:10:p:1686-:d:422653
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