Results 231 to 240 of about 30,262 (267)
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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.
Francesco Catoni +4 more
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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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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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On the Heesch number for the hyperbolic plane
Mathematical Notes, 2010The article deals with the Heesch number on the hyperbolic (Lobachevski) plane. It is defined as the maximum possible order of a corona for a given polygon. It is shown that there exists a polygon with arbitrary Heesch number on the hyperbolic plane.
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On the Dual Hyperbolic Numbers and the Complex Hyperbolic Numbers
Journal of Computer Science & Computational Mathematics, 2018Şahin, Serdal +2 more
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A Generalized Face Number for Regular Hyperbolic Honeycombs
Geometriae Dedicata, 2000A generalized face number, typically taking negative rational values for a regular hyperbolic honeycomb, is constructed in three different ways -- via differential geometry, combinatorics, and divergent series.
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Hyperbolic Flows and Linking Numbers for Closed Orbits
Journal of the London Mathematical Society, 1986We consider a similar setting to that of Franks and consider how the linking numbers are related to the least periods of the closed orbits. In particular, we show that the ''chaotic'' behaviour of an axiom A flow means that although the appropriate linking numbers may vary erratically for individual closed orbits of progressively longer lengths we can ...
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Hyperbolic metamaterials: fusing artificial structures to natural 2D materials
ELight, 2022Minkyung Kim, Hanlyun Cho, Sunae So
exaly
The number theory of a system of hyperbolic complex numbers.
1949[...] Although much has been written and a great deal of elegent theory developed for numbers of the form x + iy, where i2 = -1 and x and y are real numbers, viz, the ordinary complex numbers; very little has been said concerning an analogous system of numbers of the form x + jy where j2 = 1.
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