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American Journal of Applied Science and Technology
It is known that the Poincaré interpretation of Lobachevsky’s geometry is used in solving many technical problems, in problems related to the theory of complex variable functions.In this article, we show the Poincaré interpretation of the Lobachevsky plane, which is interpreted in a circle in a plane, using one circle of a two-section hyperboloid ...
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It is known that the Poincaré interpretation of Lobachevsky’s geometry is used in solving many technical problems, in problems related to the theory of complex variable functions.In this article, we show the Poincaré interpretation of the Lobachevsky plane, which is interpreted in a circle in a plane, using one circle of a two-section hyperboloid ...
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Numerical Interpolation Methods for Solving Problems of Convex Geometry in the Lobachevsky Space
Journal of Mathematical Sciences, 2014hQ(x) of bounded one-dimensional sectional curvature. In this paper, such metrics are referred to as supporting functions of a convex set Q. If Q is a finite convex polyhedron in the Lobachevsky space, then the following formula holds: hQ(x) = mini{h i(x)}, where h i(x) are supporting functions of the (n − 1)-dimensional faces of the polyhedron Q.
M. V. Kurkina +2 more
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Foundations of Lobachevsky Geometry: Axiomatics, Models, Images in Euclidean Space
2014This first chapter is devoted to an exposition of the foundations of Lobachevsky geometry, formed by three classical components: axiomatics, model interpretations, and investigation of surfaces of constant negative curvature. The discussion of these parts is carried out keeping in mind what is required for their application to problems of contemporary ...
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On a Method of Construction of Partial Geometries and Partial Bolyai- Lobachevsky Planes
The American Mathematical Monthly, 1966Abstract : The concept of partial geometries was introduced by R. C. Bose (Strongly regular graphs, partial geometries and partially balanced block designs). The partial BolyaiLobachevsky planes were introduced by L. M. Graves (A finite Bolyai-Lobachevsky plane).
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On Simulating a Medium with Special Reflecting Properties by Lobachevsky Geometry
2017Lobachevsky geometry simulates a medium with special constitutive relations, Di = ϵ0ϵ ikEk ,Bi = μ0μikHk where two matrices coincide: ϵik(x) = μik(x). The situation is specified in quasi-cartesian coordinates (x, y, z). Exact solutions of the Maxwell equations in complex 3-vector E+iB form, extended to curved space models within the tetrad formalism ...
Ovsiyuk, E. M. +2 more
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Salih Zeki introduces Lobachevsky’s geometry: Two conferences in 1915
2005Salih Zeki (1864-1921) a Turkish mathematician known for his extensiveteaching of mathematics and the numerous textbooks he published inmathematical sciences for secondary and higher education. While he was actingas the director of the Istanbul Darülfünun (University), he delivered a series ofconferences in the years 1914-1916 aiming to introduce non ...
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Fermat Dynamics, Matrix Arithmetics, Finite Circles, and Finite Lobachevsky Planes
Functional Analysis and Its Applications, 2004V I Arnold
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