RATIONALIZATION OF THE MATHEMATICAL DESCRIPTION OF LOXODROME IN MERCATOR MAPS

Autor:	Eugene Mihaylovith Lushnikov, Elena Evgenevna Alekseeva
Rok vydání:	2015
Předmět:	Logarithm media_common.quotation_subject Hyperbolic function Geometry Function (mathematics) Physics::Geophysics law.invention law Rhumb line Astrophysics::Earth and Planetary Astrophysics Eccentricity (behavior) Mercator projection Logarithmic spiral Sign (mathematics) media_common Mathematics
Zdroj:	V mire nauchnykh otkrytiy. :400
ISSN:	2307-9428 2072-0831
DOI:	10.12731/wsd-2015-4-20
Popis:	In article problems of scientific and didactic character in the mathematical description of the most important and characteristic line in a mercator projection – a loxodrome are described. This line taking into account terrestrial eccentricity is described by the equation of a logarithmic spiral in function from isometric width. Rather difficult functional dependence creates problems of scientific and didactic character especially around high latitudes. The developed transition in calculations on mercator cards from logarithmic functions to hyperbolic functions significantly simplifies calculation process the loksodromicheskikh of courses and bearings, meridional parts, differences of latitudes and differences of longitudes, does it more evident and convenient for programming. The new way of record of the equation of a loxodrome, in the form of function of a hyperbolic tangent from a sign of geographic latitude and from terrestrial eccentricity is offered. Such record allows applying decomposition in a row of Taylor that couldn’t be done in a classical formula. It is shown that the new equation of a loxodrome allows solving very effectively existing problems, including in polar areas.
Databáze:	OpenAIRE
Externí odkaz:	https://explore.openaire.eu/search/publication?articleId=doi_________::8778ed0015a566371b802e060946ba5a https://doi.org/10.12731/wsd-2015-4-20 Zobrazit plný text záznamu