Results 291 to 300 of about 1,674,574 (315)

Complex and Hyperbolic Numbers

, 2013
The 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.
G. Sobczyk
semanticscholar   +3 more sources

Hyperbolic Numbers, Genetics and Musicology

, 2019
The 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.
S. Petoukhov
semanticscholar   +3 more sources

Hyperbolic Congruent Numbers

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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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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Geometrical Representation of Hyperbolic Numbers

, 2011
A 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.
F. Catoni, D. Boccaletti, Roberto Cannata, Vincenzo Catoni, P. Zampetti   +4 more
semanticscholar   +3 more sources

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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Number of lattice points in the hyperbolic cross

Mathematical Notes, 1998
For \(s\in \mathbb{N}\) with \(s\geq 2\) let \(\Lambda\subset \mathbb{R}^s\) be a complete lattice. For a real parameter \(T>0\) the domain \(K(T):= \{\underline{x}\in \mathbb{R}^s: \overline{x}_1 \overline{x_2}\cdots \overline{x}_s\leq T\}\), where \(\overline{\xi}:= \max \{1,|\xi|\}\) for all \(\xi\in \mathbb{R}\), is called a hyperbolic cross.
A. L. Roshchenya, N. M. Dobrovol'skii
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n-Dimensional hyperbolic complex numbers

Advances in Applied Clifford Algebras, 1998
In 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.
Sorin G. Gal, Paul Fjelstad
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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
semanticscholar   +1 more source