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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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MORE ABOUT CANTOR LIKE SETS IN HYPERBOLIC NUMBERS

, 2017
In this paper, we discuss the construction of new Cantor like sets in the hyperbolic plane. Also, we study the arithmetic sum of two of these Cantor like sets, as well as of those previously introduced in the literature.
G. Téllez-Sánchez, J. Bory‐Reyes
semanticscholar   +1 more source

Hyperbolic double-complex numbers

AIP Conference Proceedings, 2009
The 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, K. I. Krastev, B. Kiradjiev, George Venkov, Ralitza Kovacheva, Vesela Pasheva   +5 more
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Gaussian, Parabolic, and Hyperbolic Numbers

The Mathematics Teacher, 1968
In 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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On dual hyperbolic numbers with generalized Jacobsthal numbers components

Indian journal of pure and applied mathematics, 2022
Y. Soykan, E. Taşdemir, Inci Okumuş
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Number of lattice points in the hyperbolic cross

Mathematical Notes, 1998
An 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 complex numbers and nonlinear sigma models

International Journal of Theoretical Physics, 1987
We 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.
D. Lambert, Ph. Tombal
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n-Dimensional hyperbolic complex numbers

Advances in Applied Clifford Algebras, 1998
Direct product rings have received relatively little attention, perhaps because they are sometimes labeled “trivial” [8, p.6]. Nevertheless, the 2-dimensional direct product ring of the reals, when expressed in the “hyperbolic basis”, is analogous in many ways to the system of complex numbers and also has a physical interpretation.
Sorin G. Gal, Paul Fjelstad
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A representation of the Schrödinger and Klein–Gordon equations obtained using simple hyperbolic numbers

, 2003
We write the Bohm–Landau wave function in terms of simple hyperbolic numbers and apply this representation to the Schrodinger and Klein–Gordon equations. It is shown that the Schrodinger equation can be separated in one space dimension.
P. Bracken, James Hayes
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HILBERT SPACE OVER COMPLEX HYPERBOLIC NUMBERS AND HYPER-TRIGONOMETRIC INTERFERENCE

, 2009
This note is devoted to extension of quantum probability calculus to generalizations of complex Hilbert space. Starting with Hilbert space over complex hyperbolic numbers, we derive general hyper-trigonometric interference of probabilities.
A. Khrennikov
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