ᠷᠢᠮᠠᠨ ᠊ᠤ ᠭᠧᠣᠮᠧᠲ᠋ᠧᠷ: Засвар хоорондын ялгаа
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| (13 завсрын хувилбар ижил хэрэглэгч харагдахгүй байна) | |||
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= ᠷᠢᠮᠠᠨ ᠤ ᠭᠧᠣᠮᠧᠲ᠋ᠧᠷ = | = ᠷᠢᠮᠠᠨ ᠤ ᠭᠧᠣᠮᠧᠲ᠋ᠧᠷ = | ||
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|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 ᠡᠶᠡᠷᠭᠦ ᠮᠤᠷᠤᠶ᠋ᠢᠯᠲᠠ ᠲᠠᠢ ᠭᠠᠳᠠᠷᠭᠤ ᠪᠤᠶᠤ ᠵᠤᠤᠪᠠᠩ ᠭᠠᠳᠠᠷᠭᠤ ᠳᠡᠭᠡᠷᠡ 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᠃ | |||
ᠬᠠᠷᠢᠨ ᠷᠢᠮᠠᠨ ᠤ ᠭᠧᠣᠮᠧᠲ᠋ᠧᠷ ᠨᠢ ᠡᠶᠡᠷᠭᠦ ᠮᠤᠷᠤᠢᠢᠯᠲᠠ ᠲᠠᠢ ᠭᠦᠳᠦᠭᠦᠷ ᠣᠷᠤᠨ ᠵᠠᠢ ᠢᠢᠨ ᠵᠠᠭᠪᠤᠷ ᠪᠣᠯᠤᠨ ᠠ᠋᠃ | |||
ᠷᠢᠮᠠᠨ ᠥᠪᠡᠷ ᠦᠨ ᠪᠠᠢᠢᠭᠤᠯᠤᠭᠰᠠᠨ ᠭᠧᠣᠮᠧᠲ᠋ᠧᠷ ᠢ ᠬᠣᠶᠠᠷ ᠬᠡᠮᠵᠢᠭᠳᠠᠬᠦᠨᠲᠦ ᠬᠠᠪᠲᠠᠭᠠᠢ᠂ ᠭᠤᠷᠪᠠᠨ ᠬᠡᠮᠵᠢᠭᠳᠡᠬᠦᠨᠲᠦ ᠬᠢᠭᠡᠳ ᠲᠡᠭᠦᠨ ᠡᠴᠡ ᠳᠡᠭᠡᠭᠰᠢ ᠬᠡᠮᠵᠢᠭᠳᠡᠬᠦᠨᠲᠦ ᠣᠭᠲᠠᠷᠭᠤᠢ ᠳ᠋ᠤ ᠳᠦᠷᠰᠦᠯᠡᠭᠰᠡᠨ ᠪᠠᠢᠢᠳᠠᠭ᠃ <br><br> | |||
== ᠠᠻᠰᠢᠣᠮ == | == ᠠᠻᠰᠢᠣᠮ == | ||
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'''ᠲᠤᠬᠠᠢ ᠢᠢᠨ ᠰᠢᠯᠠᠭᠤᠨ ᠲᠠᠢ ᠨᠢᠭᠡ ᠬᠠᠪᠲᠠᠭᠠᠢ ᠳ᠋ᠤ ᠣᠷᠣᠰᠢᠵᠤ ᠪᠠᠢᠢᠭ ᠠ᠋ ᠰᠢᠯᠠᠭᠤᠨ ᠲᠤᠰ ᠪᠦᠷᠢ ᠲᠤᠬᠠᠢ ᠢᠢᠨ ᠰᠢᠯᠠᠭᠤᠨ ᠲᠠᠢ ᠣᠭᠲᠤᠯᠤᠯᠴᠠᠨ ᠠ᠋'''᠃ <ref>https://bigenc.ru/mathematics/text/2652171 Н. В. Ефимов. Неевклидовы геометрии. ᠬᠠᠨᠳᠤᠭᠰᠠᠨ 2021/02/23</ref> | '''ᠲᠤᠬᠠᠢ ᠢᠢᠨ ᠰᠢᠯᠠᠭᠤᠨ ᠲᠠᠢ ᠨᠢᠭᠡ ᠬᠠᠪᠲᠠᠭᠠᠢ ᠳ᠋ᠤ ᠣᠷᠣᠰᠢᠵᠤ ᠪᠠᠢᠢᠭ ᠠ᠋ ᠰᠢᠯᠠᠭᠤᠨ ᠲᠤᠰ ᠪᠦᠷᠢ ᠲᠤᠬᠠᠢ ᠢᠢᠨ ᠰᠢᠯᠠᠭᠤᠨ ᠲᠠᠢ ᠣᠭᠲᠤᠯᠤᠯᠴᠠᠨ ᠠ᠋'''᠃ <ref>[https://bigenc.ru/mathematics/text/2652171 Н. В. Ефимов. Неевклидовы геометрии]. ᠬᠠᠨᠳᠤᠭᠰᠠᠨ 2021/02/23</ref> | ||
ᠪᠠᠰᠠ᠄ | ᠪᠠᠰᠠ᠄ | ||
ᠬᠡᠷᠪᠡ g ᠰᠢᠯᠠᠭᠤᠨ ᠱᠤᠭᠤᠮ ᠪᠥᠭᠡᠳ P ᠴᠡᠭ ᠨᠢ ᠲᠡᠭᠦᠨ ᠦ ᠭᠠᠳᠠᠨ ᠠ ᠣᠷᠤᠰᠢᠵᠤ ᠪᠠᠢᠢᠭ ᠠ᠋ ᠪᠣᠯ g ᠰᠢᠯᠠᠭᠤᠨ ᠪᠠ P ᠴᠡᠭ ᠢ ᠳᠠᠮᠨᠠᠭᠰᠠᠨ ᠬᠠᠪᠲᠠᠭᠠᠢ ᠳ᠋ᠤ g ᠰᠢᠯᠠᠭᠤᠨ ᠲᠠᠢ ᠦᠯᠦ ᠣᠭᠲᠤᠯᠤᠯᠴᠠᠬᠤ ᠨᠢᠭᠡ ᠴᠦ ᠰᠢᠯᠠᠭᠤᠨ h ᠪᠠᠢᠢᠬᠤ ᠦᠭᠡᠢ᠃<ref>Benno Klotzek: . 1. Auflage. Harri Deutsch, Frankfurt am Main 2001, ISBN 3-8171-1583-0</ref> | ᠬᠡᠷᠪᠡ <math>g</math> ᠰᠢᠯᠠᠭᠤᠨ ᠱᠤᠭᠤᠮ ᠪᠥᠭᠡᠳ <math>P</math> ᠴᠡᠭ ᠨᠢ ᠲᠡᠭᠦᠨ ᠦ ᠭᠠᠳᠠᠨ ᠠ ᠣᠷᠤᠰᠢᠵᠤ ᠪᠠᠢᠢᠭ ᠠ᠋ ᠪᠣᠯ <math>g</math> ᠰᠢᠯᠠᠭᠤᠨ ᠪᠠ <math>P</math> ᠴᠡᠭ ᠢ ᠳᠠᠮᠨᠠᠭᠰᠠᠨ ᠬᠠᠪᠲᠠᠭᠠᠢ ᠳ᠋ᠤ <math>g</math> ᠰᠢᠯᠠᠭᠤᠨ ᠲᠠᠢ ᠦᠯᠦ ᠣᠭᠲᠤᠯᠤᠯᠴᠠᠬᠤ ᠨᠢᠭᠡ ᠴᠦ ᠰᠢᠯᠠᠭᠤᠨ <math>h</math> ᠪᠠᠢᠢᠬᠤ ᠦᠭᠡᠢ᠃<ref>Benno Klotzek: . 1. Auflage. Harri Deutsch, Frankfurt am Main 2001, ISBN 3-8171-1583-0</ref> | ||
ᠪᠠᠰᠠ᠄ | ᠪᠠᠰᠠ᠄ | ||
ᠲᠤᠬᠠᠢ ᠢᠢᠨ ᠰᠢᠯᠠᠭᠤᠨ ᠳ᠋ᠤ ᠫᠧᠷᠫᠧᠨ᠍ᠡᠳᠢᠻᠦ᠋ᠯᠠᠷ ᠬᠣᠶᠠᠷ ᠰᠢᠯᠠᠭᠤᠨ ᠬᠣᠭᠤᠷᠤᠨᠳᠤ ᠪᠠᠨ ᠣᠭᠲᠤᠯᠤᠯᠴᠠᠨ ᠠ᠋᠃ | ᠲᠤᠬᠠᠢ ᠢᠢᠨ ᠰᠢᠯᠠᠭᠤᠨ ᠳ᠋ᠤ ᠫᠧᠷᠫᠧᠨ᠍ᠡᠳᠢᠻᠦ᠋ᠯᠠᠷ<sup>perpendicular</sup> ᠬᠣᠶᠠᠷ ᠰᠢᠯᠠᠭᠤᠨ ᠬᠣᠭᠤᠷᠤᠨᠳᠤ ᠪᠠᠨ ᠣᠭᠲᠤᠯᠤᠯᠴᠠᠨ ᠠ᠋᠃ | ||
ᠶᠡᠷᠦ ᠨᠢ᠂ ᠲᠤᠬᠠᠢ ᠢᠢᠨ ᠰᠢᠯᠠᠭᠤᠨ ᠤ ᠨᠢᠭᠡ ᠲᠠᠯ ᠠ᠋ ᠳᠠᠬᠢ ᠪᠦᠬᠢ ᠫᠧᠷᠫᠧᠨ᠍ᠳᠢᠻᠦ᠋ᠯᠠᠷ ᠤᠳ ᠲᠡᠷᠡ ᠬᠦ ᠰᠢᠯᠠᠭᠤᠨ ᠤ "ᠦᠨᠡᠮᠯᠡᠬᠦᠢ ᠲᠤᠢᠢᠯ" ᠬᠡᠮᠡᠬᠦ ᠭᠠᠭᠴᠠ ᠴᠡᠭ ᠲᠦ ᠣᠭᠲᠤᠯᠤᠯᠴᠠᠨ ᠠ᠋᠃ | ᠶᠡᠷᠦ ᠨᠢ᠂ ᠲᠤᠬᠠᠢ ᠢᠢᠨ ᠰᠢᠯᠠᠭᠤᠨ ᠤ ᠨᠢᠭᠡ ᠲᠠᠯ ᠠ᠋ ᠳᠠᠬᠢ ᠪᠦᠬᠢ ᠫᠧᠷᠫᠧᠨ᠍ᠳᠢᠻᠦ᠋ᠯᠠᠷ ᠤᠳ ᠲᠡᠷᠡ ᠬᠦ ᠰᠢᠯᠠᠭᠤᠨ ᠤ "ᠦᠨᠡᠮᠯᠡᠬᠦᠢ ᠲᠤᠢᠢᠯ" ᠬᠡᠮᠡᠬᠦ ᠭᠠᠭᠴᠠ ᠴᠡᠭ ᠲᠦ ᠣᠭᠲᠤᠯᠤᠯᠴᠠᠨ ᠠ᠋᠃ | ||
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ᠲᠤᠬᠠᠢ ᠢᠢᠨ ᠰᠢᠯᠠᠭᠤᠨ ᠤ ᠨᠥᠭᠦᠭᠡ ᠲᠠᠯ ᠠ᠋ ᠳ᠋ᠠᠬᠢ ᠫᠧᠷᠫᠧᠨ᠍ᠳᠢᠻᠦ᠋ᠯᠠᠷ ᠤᠳ ᠴᠤ ᠮᠥᠨ ᠨᠢᠭᠡ ᠴᠡᠭ ᠲᠦ ᠣᠭᠲᠤᠯᠤᠯᠴᠠᠨ ᠠ᠋᠃<br> | ᠲᠤᠬᠠᠢ ᠢᠢᠨ ᠰᠢᠯᠠᠭᠤᠨ ᠤ ᠨᠥᠭᠦᠭᠡ ᠲᠠᠯ ᠠ᠋ ᠳ᠋ᠠᠬᠢ ᠫᠧᠷᠫᠧᠨ᠍ᠳᠢᠻᠦ᠋ᠯᠠᠷ ᠤᠳ ᠴᠤ ᠮᠥᠨ ᠨᠢᠭᠡ ᠴᠡᠭ ᠲᠦ ᠣᠭᠲᠤᠯᠤᠯᠴᠠᠨ ᠠ᠋᠃<br> | ||
ᠬᠣᠶᠠᠷ ᠡᠰᠡᠷᠭᠦ ᠲᠠᠯ | ᠬᠣᠶᠠᠷ ᠡᠰᠡᠷᠭᠦ ᠲᠠᠯ ᠠ᠋ ᠳ᠋ᠠᠬᠢ ᠲᠤᠢᠢᠯ ᠤᠳ ᠨᠢᠭᠡ ᠯᠡ ᠲᠤᠢᠢᠯ ᠪᠠᠢᠢᠨ᠌ ᠊ᠠ᠋᠃ | ||
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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 ᠴᠢᠩᠬᠠ 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᠄ | |||
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<math>L = \pi r</math> | |||
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ᠡᠭᠦᠨ ᠳ᠋ᠦ᠄ <br><span style="writing-mode: horizontal-tb;">L</span> ᠨᠢ ᠰᠢᠯᠠᠭᠤᠨ ᠤ ᠤᠷᠲᠤ᠂ <br><span style="writing-mode: horizontal-tb;">r</span> ᠨᠢ ᠬᠡᠭᠡᠰᠦ (ᠷᠠᠳᠢᠦ᠋ᠰ<sup>radius</sup>)᠃ | |||
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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᠃ | |||
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==ᠠᠴᠢ ᠬᠣᠯᠪᠤᠭᠳᠠᠯ== | ==ᠠᠴᠢ ᠬᠣᠯᠪᠤᠭᠳᠠᠯ== | ||
<br> | <br> | ||
{{ImageX | {{ImageX | ||
|Filename=Euclidian_and_non_euclidian_geometry.png | |Filename=Euclidian_and_non_euclidian_geometry.png | ||
|Text=<span style="writing-mode: horizontal-tb; "><b>1</b>.</span> ᠲᠤᠬᠠᠢ ᠢᠢᠨ ᠰᠢᠯᠠᠭᠤᠨ ᠳᠤ ᠦᠯᠦ | |Text=<span style="writing-mode: horizontal-tb; "><b>1</b>.</span> ᠲᠤᠬᠠᠢ ᠢᠢᠨ ᠰᠢᠯᠠᠭᠤᠨ ᠳᠤ ᠦᠯᠦ ᠬᠠᠮᠢᠶᠠᠷᠬᠤ ᠴᠡᠭ ᠢ ᠳᠠᠭᠠᠷᠢᠬᠤ ᠨᠢᠭᠡ ᠯᠡ ᠰᠢᠯᠠᠭᠤᠨ ᠲᠤᠬᠠᠢ ᠢᠢᠨ ᠰᠢᠯᠠᠭᠤᠨ ᠳ᠋ᠤ ᠫᠠᠷᠠᠯᠯᠧᠯ ᠪᠠᠢᠢᠨ ᠠ᠋᠃ (ᠧᠦ᠋ᠻ᠊ᠯᠢᠳ᠋ ᠦᠨ ᠭᠧᠣᠮᠧᠲ᠋ᠧᠷ) <br><span style="writing-mode: horizontal-tb; "><b>2</b>.</span> ᠲᠤᠬᠠᠢ ᠢᠢᠨ ᠰᠢᠯᠠᠭᠤᠨ ᠳᠤ ᠦᠯᠦ ᠬᠠᠮᠢᠶᠠᠷᠬᠤ ᠴᠡᠭ ᠢ ᠳᠠᠭᠠᠷᠢᠬᠤ ᢩᠪᠥᠭᠡᠳ ᠲᠤᠬᠠᠢ ᠢᠢᠨ ᠰᠢᠯᠠᠭᠤᠨ ᠳ᠋ᠤ ᠫᠠᠷᠠᠯᠯᠧᠯ ᠣᠷᠤᠰᠢᠬᠤ ᠬᠢᠵᠠᠭᠠᠷ ᠦᠭᠡᠢ ᠣᠯᠠᠨ ᠰᠢᠯᠠᠭᠤᠨ ᠪᠠᠢᠢᠨ ᠠ᠋᠃ (ᠷᠢᠮᠠᠨ ᠤ ᠭᠧᠣᠮᠧᠲ᠋ᠧᠷ) <br><span style="writing-mode: horizontal-tb; "><b>3</b>.</span> ᠲᠤᠬᠠᠢ ᠢᠢᠨ ᠰᠢᠯᠠᠭᠤᠨ ᠳᠤ ᠦᠯᠦ ᠬᠠᠮᠢᠶᠠᠷᠬᠤ ᠴᠡᠭ ᠢ ᠳᠠᠭᠠᠷᠢᠬᠤ ᠬᠣᠶᠠᠷ ᠰᠢᠯᠠᠭᠤᠨ ᠤ ᠠᠯᠢ ᠨᠢ ᠴᠤ ᠲᠤᠬᠠᠢ ᠢᠢᠨ ᠰᠢᠯᠠᠭᠤᠨ ᠲᠠᠢ ᠣᠭᠲᠤᠯᠤᠯᠴᠠᠬᠤ ᠦᠭᠡᠢ᠃ (ᠯᠣᠪᠠᠴᠧᠹᠰᠻᠢ ᠢᠢᠨ ᠭᠧᠣᠮᠧᠲ᠋ᠧᠷ) | ||
|Height=50 | |Height=50 | ||
}} | }} | ||
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ᠷᠢᠮᠠᠨ ᠤ ᠭᠧᠣᠮᠧᠲ᠋ᠷ ᠧᠦ᠋ᠻ᠊ᠯᠢᠳ᠋᠂ | ᠷᠢᠮᠠᠨ ᠤ ᠭᠧᠣᠮᠧᠲ᠋ᠷ ᠧᠦ᠋ᠻ᠊ᠯᠢᠳ᠋᠂ ᠭᠠᠦ᠋ᠰᠰ<sup>Gauss</sup>᠂ ᠪᠣᠯᠢᠶᠠᠢ<sup>Boliay</sup>᠂ ᠯᠣᠪᠠᠴᠧᠹᠰᠻᠢ ᠨᠠᠷ ᠤᠨ ᠣᠨᠣᠯ ᠢ ᠪᠦᠭᠦᠳᠡ ᠶᠢ ᠨᠢᠭᠡ ᠳᠡᠭᠡᠪᠦᠷ ᠳᠣᠣᠷᠠ ᠣᠷᠣᠭᠤᠯᠵᠤ ᠥᠭᠭᠦᠭᠰᠡᠨ ᠪᠠᠶ᠋ᠢᠨᠠ᠃ <br> | ||
ᠲᠡᠭᠦᠨᠴᠢᠯᠡᠨ᠂ ᠲᠡᠳᠡᠭᠡᠷ ᠢ ᠦᠯᠡᠮᠵᠢ ᠥᠷᠭᠡᠳᠬᠡᠵᠦ᠂ ᠡᠮᠦᠨᠡ ᠨᠢ ᠬᠡᠨ ᠦ ᠴᠤ ᠲᠥᠰᠦᠭᠡᠯᠡᠵᠦ ᠪᠠᠶ᠋ᠢᠭᠠᠳᠦᠢ | ᠲᠡᠭᠦᠨᠴᠢᠯᠡᠨ᠂ ᠲᠡᠳᠡᠭᠡᠷ ᠢ ᠦᠯᠡᠮᠵᠢ ᠥᠷᠭᠡᠳᠬᠡᠵᠦ᠂ ᠡᠮᠦᠨᠡ ᠨᠢ ᠬᠡᠨ ᠦ ᠴᠤ ᠲᠥᠰᠦᠭᠡᠯᠡᠵᠦ ᠪᠠᠶ᠋ᠢᠭᠠᠳᠦᠢ ᠨᠡᠩ ᠰᠢᠨ ᠡ ᠪᠣᠯᠤᠮᠵᠢ ᠶᠢ ᠬᠦᠮᠦᠨ ᠲᠥᠷᠥᠯᠬᠢᠲᠡᠨ ᠦ ᠣᠶᠤᠨ ᠤᠬᠠᠭᠠᠨ ᠳᠤ ᠨᠡᠭᠡᠭᠡᠵᠦ ᠥᠭᠴᠡᠢ᠃ <br> | ||
<br> | ᠪᠣᠳᠠᠲᠤ ᠹᠢᠽᠢᠻ<sup>physic</sup> ᠣᠷᠤᠨ ᠵᠠᠢ᠂ ᠴᠠᠭ ᠬᠤᠭᠤᠴᠠᠭᠠᠨ ᠤ ᠭᠧᠣᠮᠧᠲ᠋ᠧᠷ ᠴᠢᠨᠠᠷ ᠤᠳ ᠨᠢ [[ᠧᠦ᠋ᠻ᠊ᠯᠢᠳ᠋ ᠊ᠦᠨ ᠭᠧᠣᠮᠧᠲ᠋ᠧᠷ|ᠧᠦ᠋ᠻ᠊ᠯᠢᠳ᠋ ᠦᠨ ᠭᠧᠣᠮᠧᠲ᠋ᠧᠷ ᠲᠦ]] ᠪᠢᠰᠢ ᠬᠠᠷᠢᠨ ᠷᠢᠮᠠᠨ ᠤ ᠭᠧᠣᠮᠧᠲ᠋ᠧᠷ ᠲᠦ ᠬᠠᠷᠠᠭᠠᠯᠵᠠᠳᠠᠭ ᠪᠠᠢᠢᠨ ᠠ᠋᠃<ref>В.А.Фок. Теория пространства, времени и тяготения. ГИТТЛ. Москва 1955. с. 253 </ref> | ||
ᠲᠡᠦᠬᠡᠨ ᠳᠠᠷᠠᠭᠠᠯᠠᠯ ᠤᠨ ᠬᠤᠪᠢ ᠳᠤ ᠷᠢᠮᠠᠨ ᠤ ᠭᠧᠣᠮᠧᠲ᠋ᠧᠷ ᠨᠢ ᠯᠣᠪᠠᠴᠧᠹᠰᠻᠢ ᠢᠢᠨ ᠭᠧᠣᠮᠧᠲ᠋ᠧᠷ ᠡᠴᠡ ᠬᠣᠵᠢᠭᠤ᠂ 1854 ᠣᠨ ᠳᠤ ᠭᠠᠷᠴᠤ ᠢᠷᠡᠭᠰᠡᠨ᠃ | |||
ᠧᠦ᠋ᠻ᠊ᠯᠢᠳ᠋ ᠦᠨ ᠭᠧᠣᠮᠧᠲ᠋ᠧᠷ ᠦᠨ ᠰᠠᠭᠤᠷᠢ ᠶᠢ ᠷᠢᠮᠠᠨ ᠪᠥᠷᠢᠨ ᠬᠢᠨᠠᠵᠤ ᠦᠵᠠᠭᠡᠳ᠂ ᠲᠡᠭᠦᠨ ᠦ ᠣᠷᠣᠨ ᠳᠤ ᠭᠧᠣᠮᠧᠲ᠋ᠧᠷ ᠪᠠᠢᠢᠭᠤᠯᠬᠤ ᠥᠪᠡᠷ ᠦᠨ ᠵᠠᠷᠴᠢᠮ ᠤᠳ ᠢ ᠰᠠᠨᠠᠯ ᠪᠣᠯᠭᠠᠵᠠᠢ᠃ | |||
ᠡᠭᠦᠪᠡᠷ ᠢᠶ᠋ᠡᠨ ᠧᠦᠻ᠊ᠯᠢᠳ᠋ ᠦᠨ ᠪᠤᠰᠤ ᠭᠧᠣᠮᠧᠡᠲ᠋ᠧᠷ ᠦᠨ ᠣᠯᠠᠨ ᠬᠡᠯᠪᠡᠷᠢ ᠪᠠᠶ᠋ᠢᠵᠤ᠂ ᠣᠭᠲᠠᠷᠭᠤᠢ ᠶᠢᠨ ᠬᠢᠵᠠᠭᠠᠷ ᠦᠭᠡᠢ ᠣᠯᠠᠨ ᠥᠭᠡᠷ ᠠ᠋ ᠪᠦᠲᠦᠴᠡ ᠶᠢ ᠲᠣᠳᠣᠷᠬᠠᠶ᠋ᠢᠯᠠᠵᠤ ᠪᠣᠯᠬᠤ ᠶᠢ ᠲᠤᠩᠬᠠᠭᠯᠠᠭᠰᠠᠨ ᠪᠠᠶ᠋ᠢᠨᠠ᠃ | |||
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> | |||
==ᠨᠡᠷ ᠡ᠋ ᠲᠣᠮᠢᠶᠠᠯᠠᠯ== | ==ᠨᠡᠷ ᠡ᠋ ᠲᠣᠮᠢᠶᠠᠯᠠᠯ== | ||
ᠷᠢᠮᠠᠨ ᠤ ᠭᠧᠣᠮᠧᠲ᠋ᠧᠷ - Riemannian geometry - геометрия Римана | |||
ᠧᠯᠯᠢᠫᠰ ᠭᠧᠣᠮᠧᠲ᠋ᠧᠷ - elliptic geometry - эллиптическая геометрия | |||
ᠪᠥᠮᠪᠦᠷᠴᠡᠭ ᠦᠨ ᠭᠧᠣᠮᠧᠲ᠋ᠧᠷ - spherical geometry - сферическая геометрия | |||
ᠡᠶᠡᠷᠭᠦ ᠮᠤᠷᠤᠢᠢᠯᠲᠠ - positive curvature - положительная кривизна | |||
ᠰᠥᠷᠭᠦ ᠮᠤᠷᠤᠢᠢᠯᠲᠠ - negative curvature - отрицательная кривизна | |||
ᠫᠧᠷᠫᠧᠨ᠍ᠳᠢᠻᠦ᠋ᠯᠠᠷ - perpendicular - перпендикуляр | |||
ᠫᠠᠷᠠᠯᠯᠧᠯ - parallel - параллель | |||
ᠣᠭᠲᠤᠯᠤᠯᠴᠠᠬᠤ - intersect - пересекаться | |||
ᠬᠠᠪᠲᠠᠭᠠᠢ - plane - плоскость | |||
ᠣᠭᠲᠠᠷᠭᠤᠢ᠂ ᠣᠷᠤᠨ ᠵᠠᠢ - space - пространство<br>ᠦᠨᠡᠮᠯᠡᠬᠦᠢ ᠲᠤᠢᠢᠯ - absolute pole - абсолютный полюс | |||
ᠪᠥᠮᠪᠦᠷᠴᠡᠭ - sphere - сфера | |||
ᠲᠣᠭᠤᠷᠢᠭ - circle - окружность | |||
ᠬᠡᠮᠵᠢᠭᠳᠡᠬᠦᠨ - dimension - измерение | |||
<br><br> | <br><br> | ||
==ᠤᠶᠠᠯᠳᠤᠭ ᠠ᠋ ᠨᠡᠢᠢᠲᠡᠯᠡᠯ== | |||
[[ᠧᠦ᠋ᠻ᠊ᠯᠢᠳ᠋ ᠊ᠦᠨ ᠭᠧᠣᠮᠧᠲ᠋ᠧᠷ]]<br> | |||
[[ᠯᠣᠪᠠᠴᠧᠹᠰᠻᠢ ᠊ᠢᠢᠨ ᠭᠧᠣᠮᠧᠲ᠋ᠧᠷ]] | |||
<br> | |||
== ᠡᠬᠢ ᠰᠤᠷᠪᠤᠯᠵᠢ == | == ᠡᠬᠢ ᠰᠤᠷᠪᠤᠯᠵᠢ == | ||
<references /> | |||
[[Ангилал:ᠮᠠᠲ᠋ᠾᠧᠮᠠᠲᠢᠭ]] | |||
[[Ангилал:ᠭᠧᠣᠮᠧᠲ᠋ᠧᠷ]] | |||