FINDING THE SURFACE OF TRIANGLES USING ELEMENTS OF GALILEY GEOMETRY
Keywords:
triangle, triangle's surface, angle, height, parabola, cycle, Galilean geometryAbstract
In this article, with the helpof the usage of the elements of Galilean geometry, a number of properties are given for shapeson the ground, ie triangles. It is noted that the formulas are similar to the formulas in Euclidean geometry. New formulas similar to Euclidean geometry were found, given the Galilean meanings of some concepts. Although the concepts in Euclidean geometry are used in the concepts in this article, their geometric meanings are radically different. The properties created in the article will greatly help to solve new problems in planimetry and also to understand Galilean geometry.
References
Хачатурян А.В. Геометрия галилея Москва 2005.( Galileo geometry)
Jaglom I.M. The principle of relativity of of Galilean and non-Euclidean geometry. Nauka, Moscow, (1996).
Артыкбаев А. Соколов Д.Д. Геометрия в целом в плоском пространстве времени.- Ташкент: “Фан”, 1990 г. (Geometry as a whole in space-time)
Андреева З.И, Шеремет Г.Г. Псевдоевклидова плоскость (плоскость Минковского) //в сб. Актуальные проблемы обучения математике т.3: Материалы Всероссийской научно-практической конференции.- Орел: Изд. ОГУ,2002.( Pseudo-Euclidean plane (Minkowski plane) // in Sat. Actual problems of teaching mathematics vol. 3: Materials of the All-Russian scientific-practical conference)
Розенфельд Б.А. Неевклидовы пространства.-М.:Наука,1978. (Non-euclidean spaces)
Бахвалов С.В., Моденов П.С., Пархоменко А.С. “Сборник задач по аналитической геометрии” Наука, 1964. – 440с (Collection of problems in analytic geometry)
Султанов Б.М. Поверхности, определяемые символами Кристоффеля. Современные проблемы геометрии и топологии и ее приложения. 21-23 ноября, Ташкент, Узбекистан, 2019. pp 180-181.( Surfaces defined by Christoffel symbols).
Алексей Васильевич Погорелов “Элементарная Геометрия Планиметрия” Москва 1972 Г.-210 с. (Elementary Geometry Planimetry)
A.Artykbayev, B.M.Sultanov/ Invariants of surface indicatrix in a Special linear transformation. Mathematics and statistics. USA 7(4):106-115.2019
A.Artykbayev, B.M.Sultanov Research of parabolic surface points in Galilean space. Bulletin of National University of Uzbekistan: Mathematics and Natural Sciences.
