"ᠷᠢᠮᠠᠨ ᠊ᠤ ᠭᠧᠣᠮᠧᠲ᠋ᠧᠷ"-ны өөр хувилбарууд

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|Filename=Comparison_of_geometries.svg
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|Text=ᠡᠶᠡᠷᠡᠭ ᠮᠤᠷᠤᠢᠢᠯᠲᠠ ᠲᠠᠢ ᠣᠭᠲᠠᠷᠭᠤᠢ ‍ᠢᠢᠨ ᠳᠦᠷᠰᠦᠯᠡᠯ ᠨᠢ ᠷᠢᠮᠠᠨ ‍ᠤ ᠵᠤᠤᠪᠠᠩ ᠭᠠᠳᠠᠷᠭᠤ ‍ᠢᠢᠨ ᠭᠧᠣᠮᠧᠲ᠋ᠧᠷ ᠶᠤᠮ᠃  
|Text=ᠡᠶᠡᠷᠭᠦ ᠮᠤᠷᠤᠢᠢᠯᠲᠠ ᠲᠠᠢ ᠣᠭᠲᠠᠷᠭᠤᠢ ‍ᠢᠢᠨ ᠳᠦᠷᠰᠦᠯᠡᠯ ᠨᠢ ᠷᠢᠮᠠᠨ ‍ᠤ ᠵᠤᠤᠪᠠᠩ ᠭᠠᠳᠠᠷᠭᠤ ‍ᠢᠢᠨ ᠭᠧᠣᠮᠧᠲ᠋ᠧᠷ ᠶᠤᠮ᠃  
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ᠷᠢᠮᠠᠨ<sup>Riemann</sup>  ‍ᠤ ᠭᠧᠣᠮᠧᠲ᠋ᠷ<sup>geometry</sup> ᠨᠢ ᠲᠣᠭᠲᠠᠮᠠᠯ ᠡᠶᠡᠷᠡᠭ ᠮᠤᠷᠤᠶ᠋ᠢᠯᠲᠠ ᠲᠠᠢ ᠭᠠᠳᠠᠷᠭᠤ ᠪᠤᠶᠤ ᠵᠤᠤᠪᠠᠩ ᠭᠠᠳᠠᠷᠭᠤ ᠳᠡᠭᠡᠷ᠎ᠡ ᠬᠡᠷᠡᠭᠵᠢᠳᠡᠭ᠃<ref>[https://science.wikia.org/ru/wiki/%D0%93%D0%B5%D0%BE%D0%BC%D0%B5%D1%82%D1%80%D0%B8%D1%8F_%D0%A0%D0%B8%D0%BC%D0%B0%D0%BD%D0%B0 Наука. Геометрия Римана]. ᠬᠠᠨᠳᠤᠭᠰᠠᠨ 2021/02/28</ref>  
ᠷᠢᠮᠠᠨ<sup>Riemann</sup>  ‍ᠤ ᠭᠧᠣᠮᠧᠲ᠋ᠷ<sup>geometry</sup> ᠨᠢ ᠲᠣᠭᠲᠠᠮᠠᠯ ᠡᠶᠡᠷᠭᠦ ᠮᠤᠷᠤᠶ᠋ᠢᠯᠲᠠ ᠲᠠᠢ ᠭᠠᠳᠠᠷᠭᠤ ᠪᠤᠶᠤ ᠵᠤᠤᠪᠠᠩ ᠭᠠᠳᠠᠷᠭᠤ ᠳᠡᠭᠡᠷ᠎ᠡ ᠬᠡᠷᠡᠭᠵᠢᠳᠡᠭ᠃<ref>[https://science.wikia.org/ru/wiki/%D0%93%D0%B5%D0%BE%D0%BC%D0%B5%D1%82%D1%80%D0%B8%D1%8F_%D0%A0%D0%B8%D0%BC%D0%B0%D0%BD%D0%B0 Наука. Геометрия Римана]. ᠬᠠᠨᠳᠤᠭᠰᠠᠨ 2021/02/28</ref>  


ᠤᠯᠠᠮᠵᠢᠯᠠᠯᠲᠤ ᠪᠤᠰᠤ ᠭᠧᠣᠮᠧᠲ᠋ᠧᠷ ‍ᠦᠨ ᠡᠨᠡ ᠬᠡᠯᠪᠡᠷᠢ ‍ᠢᠢ ᠮᠥᠨ ᠧᠯᠯᠢᠫᠰ ‍ᠦᠨ ᠭᠧᠣᠮᠧᠲ᠋ᠧᠷ<sup>elliptic geometry</sup> ᠭᠡᠳᠡᠭ᠃<ref>[https://www.booksite.ru/fulltext/1/001/008/080/804.htm Н. В. Ефимов. Неевклидовы геометрии]. ᠬᠠᠨᠳᠤᠭᠰᠠᠨ 2021/03/02 </ref> ᠧᠦ᠋ᠻ᠊ᠯᠢᠳ᠋<sup>Euclid</sup> ‍ᠦᠨ ᠪᠤᠶᠤ ᠤᠯᠠᠮᠵᠢᠯᠠᠲᠤ ᠭᠧᠣᠮᠧᠲ᠋ᠧᠷ ᠨᠢ ᠲᠡᠭ ᠮᠤᠷᠤᠢᠢᠯᠲᠠ ᠲᠠᠢ ᠬᠠᠪᠲᠠᠭᠠᠢ ᠣᠷᠤᠨ ᠵᠠᠢ ‍ᠢᠢᠨ ᠭᠧᠣᠮᠧᠲ᠋ᠡᠷ ᠪᠠᠢᠢᠳᠠᠭ ᠪᠣᠯ [[ᠯᠣᠪᠠᠴᠧᠹᠰᠻᠢ ᠊ᠢᠢᠨ ᠭᠧᠣᠮᠧᠲ᠋ᠧᠷ|ᠯᠣᠪᠠᠴᠧᠹᠰᠻᠢ]] ‍ᠢᠢᠨ<sup>Лобачевский</sup> ᠬᠢ ᠨᠢ ᠰᠥᠷᠭᠦ ᠮᠤᠷᠤᠢᠢᠯᠲᠠ ᠲᠠᠢ ᠣᠷᠤᠨ ᠵᠠᠢ ‍ᠢᠢ ᠳᠦᠷᠰᠦᠯᠡᠳᠡᠭ ᠪᠢᠯᠡ᠃  
ᠤᠯᠠᠮᠵᠢᠯᠠᠯᠲᠤ ᠪᠤᠰᠤ ᠭᠧᠣᠮᠧᠲ᠋ᠧᠷ ‍ᠦᠨ ᠡᠨᠡ ᠬᠡᠯᠪᠡᠷᠢ ‍ᠢᠢ ᠮᠥᠨ ᠧᠯᠯᠢᠫᠰ ‍ᠦᠨ ᠭᠧᠣᠮᠧᠲ᠋ᠧᠷ<sup>elliptic geometry</sup> ᠭᠡᠳᠡᠭ᠃<ref>[https://www.booksite.ru/fulltext/1/001/008/080/804.htm Н. В. Ефимов. Неевклидовы геометрии]. ᠬᠠᠨᠳᠤᠭᠰᠠᠨ 2021/03/02 </ref> ᠧᠦ᠋ᠻ᠊ᠯᠢᠳ᠋<sup>Euclid</sup> ‍ᠦᠨ ᠪᠤᠶᠤ ᠤᠯᠠᠮᠵᠢᠯᠠᠲᠤ ᠭᠧᠣᠮᠧᠲ᠋ᠧᠷ ᠨᠢ ᠲᠡᠭ ᠮᠤᠷᠤᠢᠢᠯᠲᠠ ᠲᠠᠢ ᠬᠠᠪᠲᠠᠭᠠᠢ ᠣᠷᠤᠨ ᠵᠠᠢ ‍ᠢᠢᠨ ᠭᠧᠣᠮᠧᠲ᠋ᠡᠷ ᠪᠠᠢᠢᠳᠠᠭ ᠪᠣᠯ [[ᠯᠣᠪᠠᠴᠧᠹᠰᠻᠢ ᠊ᠢᠢᠨ ᠭᠧᠣᠮᠧᠲ᠋ᠧᠷ|ᠯᠣᠪᠠᠴᠧᠹᠰᠻᠢ]] ‍ᠢᠢᠨ<sup>Лобачевский</sup> ᠬᠢ ᠨᠢ ᠰᠥᠷᠭᠦ ᠮᠤᠷᠤᠢᠢᠯᠲᠠ ᠲᠠᠢ ᠣᠷᠤᠨ ᠵᠠᠢ ‍ᠢᠢ ᠳᠦᠷᠰᠦᠯᠡᠳᠡᠭ ᠪᠢᠯᠡ᠃  


ᠬᠠᠷᠢᠨ ᠷᠢᠮᠠᠨ ‍ᠤ ᠭᠧᠣᠮᠧᠲ᠋ᠧᠷ ᠨᠢ ᠡᠶᠡᠷᠡᠭ ᠮᠤᠷᠤᠢᠢᠯᠲᠠᠲᠠᠢ ᠭᠦᠳᠦᠭᠦᠷ ᠣᠷᠤᠨ ᠵᠠᠢ ‍ᠢᠢᠨ ᠵᠠᠭᠪᠤᠷ ᠪᠣᠯᠤᠨ᠎ ‍ᠠ᠋᠃  
ᠬᠠᠷᠢᠨ ᠷᠢᠮᠠᠨ ‍ᠤ ᠭᠧᠣᠮᠧᠲ᠋ᠧᠷ ᠨᠢ ᠡᠶᠡᠷᠭᠦ ᠮᠤᠷᠤᠢᠢᠯᠲᠠ ᠲᠠᠢ ᠭᠦᠳᠦᠭᠦᠷ ᠣᠷᠤᠨ ᠵᠠᠢ ‍ᠢᠢᠨ ᠵᠠᠭᠪᠤᠷ ᠪᠣᠯᠤᠨ᠎ ‍ᠠ᠋᠃  


ᠷᠢᠮᠠᠨ ᠥᠪᠡᠷ ‍ᠦᠨ ᠪᠠᠢᠢᠭᠤᠯᠤᠭᠰᠠᠨ ᠭᠧᠣᠮᠧᠲ᠋ᠧᠷ ‍ᠢ ᠬᠣᠶᠠᠷ ᠬᠡᠮᠢᠵᠳᠠᠬᠦᠨᠲᠦ ᠬᠠᠪᠲᠠᠭᠠᠢ᠂ ᠭᠤᠷᠪᠠᠨ ᠬᠡᠮᠵᠢᠭᠳᠡᠬᠦᠨ ᠲᠦ ᠬᠢᠭᠡᠳ ᠲᠡᠭᠦᠨ ᠡᠴᠡ ᠳᠡᠭᠡᠰᠢ ᠬᠡᠮᠵᠢᠭᠳᠡᠬᠦᠨᠲᠦ ᠣᠭᠲᠠᠷᠭᠤᠢ ᠳ᠋ᠤ ᠳᠦᠷᠰᠦᠯᠡᠭᠰᠡᠨ ᠪᠠᠢᠢᠳᠠᠭ᠃  <br><br>
ᠷᠢᠮᠠᠨ ᠥᠪᠡᠷ ‍ᠦᠨ ᠪᠠᠢᠢᠭᠤᠯᠤᠭᠰᠠᠨ ᠭᠧᠣᠮᠧᠲ᠋ᠧᠷ ‍ᠢ ᠬᠣᠶᠠᠷ ᠬᠡᠮᠵᠢᠭᠳᠠᠬᠦᠨᠲᠦ ᠬᠠᠪᠲᠠᠭᠠᠢ᠂ ᠭᠤᠷᠪᠠᠨ ᠬᠡᠮᠵᠢᠭᠳᠡᠬᠦᠨᠲᠦ ᠬᠢᠭᠡᠳ ᠲᠡᠭᠦᠨ ᠡᠴᠡ ᠳᠡᠭᠡᠭᠰᠢ ᠬᠡᠮᠵᠢᠭᠳᠡᠬᠦᠨᠲᠦ ᠣᠭᠲᠠᠷᠭᠤᠢ ᠳ᠋ᠤ ᠳᠦᠷᠰᠦᠯᠡᠭᠰᠡᠨ ᠪᠠᠢᠢᠳᠠᠭ᠃  <br><br>


== ᠠᠻᠰᠢᠣᠮ ==  
== ᠠᠻᠰᠢᠣᠮ ==  
41-р мөр: 41-р мөр:
ᠬᠣᠶᠠᠷ ᠡᠰᠡᠷᠭᠦ ᠲᠠᠯ ‍ᠠ᠋ ᠳ᠋ᠠᠬᠢ ᠲᠤᠢᠢᠯ ‍ᠤᠳ ᠨᠢᠭᠡ ᠯᠡ ᠲᠤᠢᠢᠯ ᠪᠠᠢᠢᠨ᠌ ᠊ᠠ᠋᠃
ᠬᠣᠶᠠᠷ ᠡᠰᠡᠷᠭᠦ ᠲᠠᠯ ‍ᠠ᠋ ᠳ᠋ᠠᠬᠢ ᠲᠤᠢᠢᠯ ‍ᠤᠳ ᠨᠢᠭᠡ ᠯᠡ ᠲᠤᠢᠢᠯ ᠪᠠᠢᠢᠨ᠌ ᠊ᠠ᠋᠃


ᠤᠯᠠᠮᠵᠢᠯᠠᠯᠲᠤ ᠭᠧᠣᠮᠧᠲ᠋ᠧᠷ ᠲᠦ ᠰᠢᠯᠠᠭᠤᠨ ᠨᠢ ᠬᠣᠶᠠᠷ ᠵᠦᠭ ᠲᠦ ᠬᠢᠵᠠᠭᠠᠷ ᠦᠭᠡᠢ ᠪᠠᠢᠢᠳᠠᠭ ᠪᠣᠯ ᠷᠢᠮᠠᠨ ‍ᠤ ᠭᠧᠣᠮᠧᠲ᠋ᠧᠷ ᠲᠦ ᠰᠢᠯᠠᠭᠤᠨ ᠨᠢ ᠪᠢᠲᠠᠭᠦ ᠪᠠᠢᠢᠳᠠᠭ᠂ ᠥᠭᠡᠷ ‍ᠡ᠋ ᠪᠠᠡ ᠬᠡᠯᠡᠪᠡᠯ ᠬᠣᠶᠠᠷ ᠦᠵᠦᠭᠦᠷ ᠨᠢ ᠠᠭᠤᠯᠵᠠᠨ ᠨᠡᠢᠢᠯᠡᠳᠡᠭ᠃<ref name=":0">[http://www.e-osnova.ru/PDF/osnova_3_24_3845.pdf О.А.Старова. Геометрия Римана. 2012/12]. ᠬᠠᠨᠳᠤᠭᠰᠠᠨ 2021/03/02]</ref>
ᠤᠯᠠᠮᠵᠢᠯᠠᠯᠲᠤ ᠭᠧᠣᠮᠧᠲ᠋ᠧᠷ ᠲᠦ ᠰᠢᠯᠠᠭᠤᠨ ᠨᠢ ᠬᠣᠶᠠᠷ ᠵᠦᠭ ᠲᠦ ᠬᠢᠵᠠᠭᠠᠷ ᠦᠭᠡᠢ ᠪᠠᠢᠢᠳᠠᠭ ᠪᠣᠯ ᠷᠢᠮᠠᠨ ‍ᠤ ᠭᠧᠣᠮᠧᠲ᠋ᠧᠷ ᠲᠦ ᠰᠢᠯᠠᠭᠤᠨ ᠨᠢ ᠪᠢᠲᠠᠭᠦᠦ ᠪᠠᠢᠢᠳᠠᠭ᠂ ᠥᠭᠡᠷ ‍ᠡ᠋ ᠪᠠᠡ ᠬᠡᠯᠡᠪᠡᠯ ᠬᠣᠶᠠᠷ ᠦᠵᠦᠭᠦᠷ ᠨᠢ ᠠᠭᠤᠯᠵᠠᠨ ᠨᠡᠢᠢᠯᠡᠳᠡᠭ᠃<ref name=":0">[http://www.e-osnova.ru/PDF/osnova_3_24_3845.pdf О.А.Старова. Геометрия Римана. 2012/12]. ᠬᠠᠨᠳᠤᠭᠰᠠᠨ 2021/03/02]</ref>


ᠰᠢᠯᠠᠭᠤᠨ ᠭᠡᠵᠦ ᠷᠢᠮᠠᠨ ‍ᠤ ᠭᠧᠣᠮᠧᠲ᠋ᠧᠷ ᠲᠦ ᠪᠥᠮᠪᠦᠷᠴᠡᠭ ‍ᠦᠨ ᠪᠦᠰᠡᠯᠡᠭᠦᠷ ᠲᠣᠭᠤᠷᠢᠭ ‍ᠤᠳ ‍ᠢ ᠬᠡᠯᠡᠳᠡᠭ ᠪᠥᠭᠡᠳ ᠡᠨᠡ ᠨᠢ ᠴᠢᠩᠬ᠎ᠠ ᠡᠰᠡᠷᠭᠦ ᠲᠠᠯ ‍᠋ᠠ᠋ ᠳ᠋ᠤ ᠪᠠᠢᠢᠷᠢᠯᠠᠬᠤ ᠴᠡᠭ ‍ᠦᠳ ‍ᠦᠨ ᠣᠯᠤᠨᠯᠢᠭ ᠪᠣᠯᠵᠤ ᠪᠠᠢᠢᠨ᠎ ‍ᠠ᠋᠃  
ᠰᠢᠯᠠᠭᠤᠨ ᠭᠡᠵᠦ ᠷᠢᠮᠠᠨ ‍ᠤ ᠭᠧᠣᠮᠧᠲ᠋ᠧᠷ ᠲᠦ ᠪᠥᠮᠪᠦᠷᠴᠡᠭ ‍ᠦᠨ ᠪᠦᠰᠡᠯᠡᠭᠦᠷ ᠲᠣᠭᠤᠷᠢᠭ ‍ᠤᠳ ‍ᠢ ᠬᠡᠯᠡᠳᠡᠭ ᠪᠥᠭᠡᠳ ᠡᠨᠡ ᠨᠢ ᠴᠢᠩᠬ᠎ᠠ ᠡᠰᠡᠷᠭᠦ ᠲᠠᠯ ‍᠋ᠠ᠋ ᠳ᠋ᠤ ᠪᠠᠢᠢᠷᠢᠯᠠᠬᠤ ᠴᠡᠭ ‍ᠦᠳ ‍ᠦᠨ ᠣᠯᠠᠨᠯᠢᠭ ᠪᠣᠯᠵᠤ ᠪᠠᠢᠢᠨ᠎ ‍ᠠ᠋᠃  


ᠰᠢᠯᠠᠭᠤᠨ ‍ᠢ ᠢᠩᠭᠢᠵᠦ ᠲᠣᠳᠤᠷᠬᠠᠶ᠋ᠢᠯᠠᠭᠰᠠᠨ ‍ᠢᠢᠠᠷ ᠰᠢᠯᠠᠭᠤᠨ ‍ᠤ ᠤᠷᠲᠤ ᠨᠢ ᠳᠠᠷᠠᠭᠠᠬᠢ ᠲᠡᠭᠰᠢᠳᠬᠡᠯ ‍ᠢᠢᠡᠷ ᠲᠣᠮᠢᠶᠠᠯᠠᠭᠳᠠᠨ᠎ ‍ᠠ᠋᠄   
ᠰᠢᠯᠠᠭᠤᠨ ‍ᠢ ᠢᠩᠭᠢᠵᠦ ᠲᠣᠳᠤᠷᠬᠠᠶ᠋ᠢᠯᠠᠭᠰᠠᠨ ‍ᠢᠢᠠᠷ ᠰᠢᠯᠠᠭᠤᠨ ‍ᠤ ᠤᠷᠲᠤ ᠨᠢ ᠳᠠᠷᠠᠭᠠᠬᠢ ᠲᠡᠭᠰᠢᠳᠬᠡᠯ ‍ᠢᠢᠡᠷ ᠲᠣᠮᠢᠶᠠᠯᠠᠭᠳᠠᠨ᠎ ‍ᠠ᠋᠄   
55-р мөр: 55-р мөр:
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ᠧᠯᠯᠢᠫᠰ ᠭᠧᠣᠮᠧᠲ᠋ᠷ ᠲᠦ ᠭᠤᠷᠪᠠᠯᠵᠢᠨ ‍ᠤ ᠥᠨᠴᠦᠭ ‍ᠦᠳ ‍ᠦᠨ ᠨᠡᠢᠢᠯᠡᠪᠦᠷᠢ ᠢᠮᠠᠭᠲᠠ <span style="writing-mode: horizontal-tb;">180°</span> ᠡᠴᠡ ᠶᠡᠬᠡ ᠪᠠᠢᠢᠨ᠎ ‍ᠠ᠋᠃<ref>[https://mathworld.wolfram.com/EllipticGeometry.html WolframMathWorld. Elliptic Geometry]. ᠬᠠᠨᠳᠤᠭᠰᠠᠨ 2021/03/02</ref>
ᠧᠯᠯᠢᠫᠰ ᠭᠧᠣᠮᠧᠲ᠋ᠧᠷ ᠲᠦ ᠭᠤᠷᠪᠠᠯᠵᠢᠨ ‍ᠤ ᠥᠨᠴᠦᠭ ‍ᠦᠳ ‍ᠦᠨ ᠨᠡᠢᠢᠯᠡᠪᠦᠷᠢ ᠢᠮᠠᠭᠲᠠ <span style="writing-mode: horizontal-tb;">180°</span> ᠡᠴᠡ ᠶᠡᠬᠡ ᠪᠠᠢᠢᠨ᠎ ‍ᠠ᠋᠃<ref>[https://mathworld.wolfram.com/EllipticGeometry.html WolframMathWorld. Elliptic Geometry]. ᠬᠠᠨᠳᠤᠭᠰᠠᠨ 2021/03/02</ref>


ᠮᠥᠨ ᠲᠥᠰᠦᠲᠠᠢ ᠭᠤᠷᠪᠠᠯᠵᠢᠨ ᠨᠤᠭᠤᠳ ᠵᠠᠪᠠᠯ ᠻᠣᠨ᠍ᠭ᠌ᠷᠦ᠋ᠧᠨ᠍ᠲ<sup>congruent</sup> ᠪᠠᠢᠢᠨ᠎ ‍ᠠ᠋᠃
ᠮᠥᠨ ᠲᠥᠰᠦᠲᠠᠢ ᠭᠤᠷᠪᠠᠯᠵᠢᠨ ᠨᠤᠭᠤᠳ ᠵᠠᠪᠠᠯ ᠻᠣᠨ᠍ᠭ᠌ᠷᠦ᠋ᠧᠨ᠍ᠲ<sup>congruent</sup> ᠪᠠᠢᠢᠨ᠎ ‍ᠠ᠋᠃
77-р мөр: 77-р мөр:
ᠡᠭᠦᠪᠡᠷ  ‍ᠢᠶ᠋ᠡᠨ ᠧᠦᠻ᠊ᠯᠢᠳ᠋  ᠦᠨ ᠪᠤᠰᠤ ᠭᠧᠣᠮᠧᠡᠲ᠋ᠧᠷ  ᠦᠨ ᠣᠯᠠᠨ ᠬᠡᠯᠪᠡᠷᠢ ᠪᠠᠶ᠋ᠢᠵᠤ᠂ ᠣᠭᠲᠠᠷᠭᠤᠢ ᠶᠢᠨ ᠬᠢᠵᠠᠭᠠᠷ ᠦᠭᠡᠢ ᠣᠯᠠᠨ ᠥᠭᠡᠷ ‍ᠠ᠋ ᠪᠦᠲᠦᠴᠡ ᠶᠢ ᠲᠣᠳᠣᠷᠬᠠᠶ᠋ᠢᠯᠠᠵᠤ ᠪᠣᠯᠬᠤ ᠶᠢ ᠲᠤᠩᠬᠠᠭᠯᠠᠭᠰᠠᠨ ᠪᠠᠶ᠋ᠢᠨ᠎ᠠ᠃
ᠡᠭᠦᠪᠡᠷ  ‍ᠢᠶ᠋ᠡᠨ ᠧᠦᠻ᠊ᠯᠢᠳ᠋  ᠦᠨ ᠪᠤᠰᠤ ᠭᠧᠣᠮᠧᠡᠲ᠋ᠧᠷ  ᠦᠨ ᠣᠯᠠᠨ ᠬᠡᠯᠪᠡᠷᠢ ᠪᠠᠶ᠋ᠢᠵᠤ᠂ ᠣᠭᠲᠠᠷᠭᠤᠢ ᠶᠢᠨ ᠬᠢᠵᠠᠭᠠᠷ ᠦᠭᠡᠢ ᠣᠯᠠᠨ ᠥᠭᠡᠷ ‍ᠠ᠋ ᠪᠦᠲᠦᠴᠡ ᠶᠢ ᠲᠣᠳᠣᠷᠬᠠᠶ᠋ᠢᠯᠠᠵᠤ ᠪᠣᠯᠬᠤ ᠶᠢ ᠲᠤᠩᠬᠠᠭᠯᠠᠭᠰᠠᠨ ᠪᠠᠶ᠋ᠢᠨ᠎ᠠ᠃


ᠷᠢᠮᠠᠨ ᠡᠳᠡᠭᠡᠷ ᠪᠣᠯᠤᠮᠵᠢᠲᠤ ᠬᠤᠪᠢᠯᠪᠤᠷᠢ ᠨᠤᠭᠤᠳ ᠠᠴᠠ ᠡᠩ  ᠦᠨ ᠨᠢᠭᠡᠨ ᠲᠣᠬᠢᠶᠠᠯᠳᠤᠯ ᠪᠣᠯᠬᠤ ᠲᠣᠭᠲᠠᠮᠠᠯ ᠡᠶᠡᠷᠡᠭ ᠮᠤᠷᠤᠶ᠋ᠢᠯᠲᠠ ᠲᠠᠢ ᠣᠷᠣᠨ ᠵᠠᠢ ᠶᠢ ᠳᠦᠷᠰᠦᠯᠡᠭᠰᠡᠨ ᠭᠧᠣᠮᠧᠲ᠋ᠧᠷ  ᠢ ᠲᠠᠨᠢᠯᠴᠠᠭᠤᠯᠤᠭᠰᠠᠨ ᠪᠢᠯᠡ᠃᠎<ref name=":0" />
ᠷᠢᠮᠠᠨ ᠡᠳᠡᠭᠡᠷ ᠪᠣᠯᠤᠮᠵᠢᠲᠤ ᠬᠤᠪᠢᠯᠪᠤᠷᠢ ᠨᠤᠭᠤᠳ ᠠᠴᠠ ᠡᠩ  ᠦᠨ ᠨᠢᠭᠡᠨ ᠲᠣᠬᠢᠶᠠᠯᠳᠤᠯ ᠪᠣᠯᠬᠤ ᠲᠣᠭᠲᠠᠮᠠᠯ ᠡᠶᠡᠷᠭᠦ ᠮᠤᠷᠤᠶ᠋ᠢᠯᠲᠠ ᠲᠠᠢ ᠣᠷᠣᠨ ᠵᠠᠢ ᠶᠢ ᠳᠦᠷᠰᠦᠯᠡᠭᠰᠡᠨ ᠭᠧᠣᠮᠧᠲ᠋ᠧᠷ  ᠢ ᠲᠠᠨᠢᠯᠴᠠᠭᠤᠯᠤᠭᠰᠠᠨ ᠪᠢᠯᠡ᠃᠎<ref name=":0" />


[[ᠬᠠᠷᠢᠴᠠᠩᠭᠤᠢ ᠊ᠢᠢᠨ ᠶᠡᠷᠦᠩᠬᠡᠢ ᠣᠨᠤᠯ|ᠬᠠᠷᠢᠴᠠᠩᠭᠤᠢ ‍ᠢᠢᠨ ᠶᠡᠷᠦᠩᠬᠡᠢ ᠣᠨᠤᠯ]] ‍ᠢ ᠪᠠᠢᠢᠭᠤᠯᠤᠭᠰᠠᠨ ᠧᠢᠢᠨ᠍ᠱᠲ᠋ᠠᠢᠢᠨ<sup>Einstein</sup> ᠥᠪᠡᠷ ᠲᠦ ᠪᠡᠨ ᠬᠡᠷᠡᠭ ᠲᠡᠢ ᠦᠨᠡᠨ ᠵᠥᠪ ᠮᠠᠲᠾᠧᠮᠠᠲᠢᠻ<sup>mathematic</sup> ᠬᠡᠷᠡᠭᠰᠡᠯ ‍ᠢ ᠷᠢᠮᠠᠨ ‍ᠤ ᠭᠧᠣᠮᠧᠲ᠋ᠧᠷ ᠡᠴᠡ ᠣᠯᠵᠤ<ref>Max Born. Physics in My Generation (Springer, 1969), <nowiki>ISBN 0-387-90008-X</nowiki>. p. 329</ref>᠂ ᠲᠡᠭᠦᠨ ‍ᠳᠤ ᠲᠦᠰᠢᠭᠯᠡᠭᠰᠡᠨ ᠪᠢᠯᠡ᠃<br><br>
[[ᠬᠠᠷᠢᠴᠠᠩᠭᠤᠢ ᠊ᠢᠢᠨ ᠶᠡᠷᠦᠩᠬᠡᠢ ᠣᠨᠤᠯ|ᠬᠠᠷᠢᠴᠠᠩᠭᠤᠢ ‍ᠢᠢᠨ ᠶᠡᠷᠦᠩᠬᠡᠢ ᠣᠨᠤᠯ]] ‍ᠢ ᠪᠠᠢᠢᠭᠤᠯᠤᠭᠰᠠᠨ ᠧᠢᠢᠨ᠍ᠱᠲ᠋ᠠᠢᠢᠨ<sup>Einstein</sup> ᠥᠪᠡᠷ ᠲᠦ ᠪᠡᠨ ᠬᠡᠷᠡᠭ ᠲᠡᠢ ᠦᠨᠡᠨ ᠵᠥᠪ ᠮᠠᠲᠾᠧᠮᠠᠲᠢᠻ<sup>mathematic</sup> ᠬᠡᠷᠡᠭᠰᠡᠯ ‍ᠢ ᠷᠢᠮᠠᠨ ‍ᠤ ᠭᠧᠣᠮᠧᠲ᠋ᠧᠷ ᠡᠴᠡ ᠣᠯᠵᠤ<ref>Max Born. Physics in My Generation (Springer, 1969), <nowiki>ISBN 0-387-90008-X</nowiki>. p. 329</ref>᠂ ᠲᠡᠭᠦᠨ ‍ᠳᠤ ᠲᠦᠰᠢᠭᠯᠡᠭᠰᠡᠨ ᠪᠢᠯᠡ᠃<br><br>
87-р мөр: 87-р мөр:
ᠪᠥᠮᠪᠦᠷᠴᠦᠭ ‍ᠦᠨ ᠭᠧᠣᠮᠧᠲ᠋ᠧᠷ - spherical geometry - сферическая геометрия
ᠪᠥᠮᠪᠦᠷᠴᠦᠭ ‍ᠦᠨ ᠭᠧᠣᠮᠧᠲ᠋ᠧᠷ - spherical geometry - сферическая геометрия


ᠡᠶᠡᠷᠡᠭ ᠮᠤᠷᠤᠢᠢᠯᠲᠠ - positive curvature - положительная кривизна
ᠡᠶᠡᠷᠭᠦ ᠮᠤᠷᠤᠢᠢᠯᠲᠠ - positive curvature - положительная кривизна


ᠰᠥᠷᠭᠦ ᠮᠤᠷᠤᠢᠢᠯᠲᠠ - negative curvature - отрицательная кривизна
ᠰᠥᠷᠭᠦ ᠮᠤᠷᠤᠢᠢᠯᠲᠠ - negative curvature - отрицательная кривизна
109-р мөр: 109-р мөр:
<br>
<br>
== ᠡᠬᠢ ᠰᠤᠷᠪᠤᠯᠵᠢ ==
== ᠡᠬᠢ ᠰᠤᠷᠪᠤᠯᠵᠢ ==
<references />
[[Ангилал:ᠮᠠᠲ᠋ᠾᠧᠮᠠᠲᠢᠭ]]
[[Ангилал:ᠭᠧᠣᠮᠧᠲ᠋ᠧᠷ]]
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