Results 281 to 290 of about 152,450 (318)
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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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The Hyperbolic Number Plane [PDF]
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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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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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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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.
Rochelle Boehning, William A. Miller
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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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Number of lattice points in the hyperbolic cross
Mathematical Notes, 1998An asymptotic formula for the number of points of an arbitrary lattice in the hyperbolic cross is obtained.
A. L. Roshchenya, N. M. Dobrovol'skii
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Hyperbolic Numbers, Genetics and Musicology
2020The article is devoted to applications of 2-dimensional hyperbolic numbers and their algebraic extensions in the form of 2n-dimensional hyperbolic numbers in bioinformatics, algebraic biology and musicology. These applications reveal hidden interconnections between structures of different biological phenomena.
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Geometrical Representation of Hyperbolic Numbers
2011A relevant property of Euclidean geometry is the Pythagorean distance between two points. From this definition the properties of analytical geometry follow. In a similar way the analytical geometry in Minkowski plane is introduced, starting from the invariant quantities of Special Relativity.
Dino Boccaletti +4 more
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