N.I.LOBACHEVISKIY VA UNING GEOMETRIYASI
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noevklid geometriya, Lobachevskiy geometriyasi, parallel postulat, giperbolik fazo, trigonometrik formulalar, differensial geometriyaAbstrak
Ushbu maqolada noevklid geometriyaning asoschisi hisoblangan Nikolay Ivanovich Lobachevskiyning ilmiy merosi chuqur tahlil qilinadi. Asosan Evklid geometriyasining beshinchi postulatiga alternativ yondashuv sifatida yuzaga kelgan Lobachevskiy geometriyasining nazariy asoslari, matematik apparati va amaliy qo‘llanilish sohalari o‘rganiladi. Tadqiqot davomida parallel chiziqlar nazariyasi, giperbolik fazodagi uchburchaklar geometriyasi, trigonometrik formulalar hamda metrik xususiyatlar ilmiy asosda tahlil qilinadi. Shuningdek, ushbu geometriyaning zamonaviy matematika va fizika, xususan umumiy nisbiylik nazariyasidagi o‘rni ko‘rsatib beriladi. Maqola natijalari Lobachevskiy geometriyasining mustaqil va izchil matematik tizim sifatidagi ahamiyatini tasdiqlaydi.
Iqtiboslar
Nikolai Ivanovich Lobachevsky. Pangeometry. Kazan University Press, 1855.
Nikolai Ivanovich Lobachevsky. Geometrical Researches on the Theory of Parallels. Berlin, 1840.
Euclid. Elements. (Tarjimasi va sharhlari bilan turli nashrlar).
David Hilbert. Foundations of Geometry. Open Court Publishing, 1899.
Henri Poincaré. Science and Hypothesis. Dover Publications, 1902.
John G. Ratcliffe. Foundations of Hyperbolic Manifolds. Springer, 2006.
Marvin Jay Greenberg. Euclidean and Non-Euclidean Geometries: Development and History. W.H. Freeman, 2008.
William P. Thurston. Three-Dimensional Geometry and Topology. Princeton University Press, 1997.
Albert Einstein. The Meaning of Relativity. Princeton University Press, 1922.
Springer va Cambridge University Press nashrlaridagi zamonaviy ilmiy maqolalar va darsliklar.
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