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Quaestiones Mathematicae, 2020
AbstractWe introduce the notion of hyperbolic congruent numbers which is a hyperbolic analogue of congruent numbers, and investigate the relations between congruent numbers and hyperbolic congruent...
Injo Hur, Jang Hyun Jo
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AbstractWe introduce the notion of hyperbolic congruent numbers which is a hyperbolic analogue of congruent numbers, and investigate the relations between congruent numbers and hyperbolic congruent...
Injo Hur, Jang Hyun Jo
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n-Dimensional hyperbolic complex numbers
Advances in Applied Clifford Algebras, 1998In this contribution is deduced a generalisation of the 2-dimensional complex number system. The construction of a hyperbolic basis is one of the main topics in this paper. By the aid of this basis the authors succeed in a nice description of an \(n\)-dimensional direct product ring of reals.
Fjelstad, Paul, Gal, Sorin G.
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Hyperbolic double-complex numbers
AIP Conference Proceedings, 2009The algebra of bicomplex numbers and the corresponding bicomplex holomorphic functions are well known ([1] and others). The hyperbolic bicomplex numbers were used by Dominic Rochon in different aspects (for instance [2]). The algebra of double‐complex numbers (in the sense of [3]) gives a parallel treatement closely related with the classical theory of
L. N. Apostolova +5 more
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CANTOR-TYPE SETS IN HYPERBOLIC NUMBERS
Fractals, 2016The construction of the ternary Cantor set is generalized into the context of hyperbolic numbers. The partial order structure of hyperbolic numbers is revealed and the notion of hyperbolic interval is defined. This allows us to define a general framework of the fractal geometry on the hyperbolic plane.
A. S. BALANKIN +3 more
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$${f}$$ f -Algebra Structure on Hyperbolic Numbers
Advances in Applied Clifford Algebras, 2016zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Gargoubi, Hichem, Kossentini, Sayed
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Bicomplex and Hyperbolic Numbers
2014The main properties of bicomplex and hyperbolic numbers are considered, in particular, the three conjugations on them generate the corresponding moduli of a bicomplex number which are not real valued: two of them are complex valued and one is hyperbolic valued. The notion of a positive hyperbolic number allows to introduce a partial order on the set of
Daniel Alpay +3 more
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The College Mathematics Journal, 1995
(1995). The Hyperbolic Number Plane. The College Mathematics Journal: Vol. 26, No. 4, pp. 268-280.
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(1995). The Hyperbolic Number Plane. The College Mathematics Journal: Vol. 26, No. 4, pp. 268-280.
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Gaussian, Parabolic, and Hyperbolic Numbers
The Mathematics Teacher, 1968In the November 1966 issue of THE MATHEMATICS TEACHER, Willerding developed the structure of the “Gaussian integers.” Two number systems that have a parallel structure, but which are less well known, are the parabolic complex and hyperbolic Complex numbers.
William Miller, Rochelle Boehning
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Hyperbolic complex numbers and nonlinear sigma models
International Journal of Theoretical Physics, 1987We show that the hyperbolic complex numbers or double numbers can be used to generate solutions of two-dimensional Minkowskian sigma models with values on noncompact manifolds.
Lambert, Dominique, TOMBAL,, Philippe
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Complex and Hyperbolic Numbers
2012The complex numbers were grudgingly accepted by Renaissance mathematicians because of their utility in solving the cubic equation.1 Whereas the complex numbers were discovered primarily for algebraic reasons, they take on geometric significance when they are used to name points in the plane.
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