Kut paralelnosti v geometriyi Lobachevskogo kut mizh perpendikulyarom do danoyi pryamoyi i asimptotichno paralelnoyu pryamoyu provedenoyu z tochki sho ne lezhit na danij pryamij Kut paralelnosti 8 pryami x displaystyle mathcal x i y displaystyle mathcal y asimptotichno paralelni do pryamoyi ℓ displaystyle ell V evklidovij geometriyi kut paralelnosti zavzhdi pryamij U geometriyi Lobachevskogo kut paralelnosti zavzhdi gostrij Na ploshini Lobachevskogo z krivinoyu 1 kut paralelnosti dlya tochki na vidstani a displaystyle a vid pryamoyi zazvichaj poznachayetsya P a displaystyle Pi a Zmist 1 Vlastivosti ta spivvidnoshennya 2 Istoriya 3 Primitki 4 LiteraturaVlastivosti ta spivvidnoshennya RedaguvatiP a displaystyle Pi a nbsp ye gostrim kutom pri kateti rivnomu a displaystyle a nbsp u pryamokutnomu giperbolichnomu trikutniku yakij maye dvi asimptotichni paralelni storoni lim a 0 P a 1 2 p i lim a P a 0 displaystyle lim a to 0 Pi a tfrac 1 2 cdot pi quad text i quad lim a to infty Pi a 0 nbsp sin P a sech a 1 ch a 2 e a e a displaystyle sin Pi a operatorname sech a frac 1 operatorname ch a frac 2 e a e a nbsp cos P a th a e a e a e a e a displaystyle cos Pi a operatorname th a frac e a e a e a e a nbsp t g P a csch a 1 sh a 2 e a e a displaystyle operatorname rm tg Pi a operatorname csch a frac 1 operatorname sh a frac 2 e a e a nbsp t g 1 2 P a e a displaystyle operatorname rm tg left tfrac 1 2 cdot Pi a right e a nbsp P a 1 2 p gd a displaystyle Pi a tfrac 1 2 cdot pi operatorname gd a nbsp de s h displaystyle operatorname rm sh nbsp c h displaystyle operatorname rm ch nbsp t h displaystyle operatorname rm th nbsp s e c h displaystyle operatorname rm sech nbsp i c s c h displaystyle operatorname rm csch nbsp giperbolichna funkciya a g d displaystyle operatorname rm gd nbsp funkciya Gudermana Istoriya RedaguvatiKut paralelnosti rozglyadav Lobachevskij 1 Zokrema vin viviv spivvidnoshennya c t g 1 2 P a e a displaystyle operatorname rm ctg left tfrac 1 2 cdot Pi a right e a nbsp Primitki Redaguvati Lobachevsky N I Geometrische Untersuchungen zur Theorie der Parallellinien Berlin 1840 Literatura RedaguvatiD Morduhaj Boltovskoj O geometricheskih postroeniyah v prostranstve Lobachevskogo In mem Lobatschevskii 1927 T 2 13 oktyabrya S 67 82 Lobachevskij Nikolaj Ivanovich Geometricheskie issledovaniya po teorii parallelnyh linij M L izd vo Akademii Nauk SSSR 1945 176 s Arhivovano z dzherela 26 grudnya 2021 Otrimano z https uk wikipedia org w index php title Kut paralelnosti amp oldid 35121951
