Засварлах: ᠷᠢᠮᠠᠨ ᠊ᠤ ᠭᠧᠣᠮᠧᠲ᠋ᠧᠷ (хэсэгчилэн)

== ᠠᠻᠰᠢᠣᠮ == 
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|Text= ᠲᠤᠬᠠᠢ ‍ᠢᠢᠨ ᠰᠢᠯᠠᠭᠤᠨ ᠲᠠᠢ ᠲᠡᠭᠰᠢ ᠥᠨᠴᠦᠭ ‍ᠢᠢᠡᠷ ᠣᠭᠲᠤᠯᠤᠯᠴᠠᠵᠤ ᠪᠤᠢ ᠬᠣᠶᠠᠷ ᠰᠢᠯᠠᠭᠤᠨ ᠬᠣᠭᠤᠷᠤᠨᠳᠤ ᠪᠠᠨ ᠣᠭᠲᠤᠯᠤᠯᠴᠠᠨ᠎ ‍ᠠ᠋
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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>

ᠪᠠᠰᠠ᠄

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᠄ 

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᠃  

ᠲᠤᠬᠠᠢ ‍ᠢᠢᠨ ᠰᠢᠯᠠᠭᠤᠨ ‍ᠤ ᠨᠥᠭᠦᠭᠡ ᠲᠠᠯ ‍ᠠ᠋ ᠳ᠋ᠠᠬᠢ ᠫᠧᠷᠫᠧᠨ᠍ᠳᠢᠻᠦ᠋ᠯᠠᠷ ‍ᠤᠳ ᠴᠤ ᠮᠥᠨ ᠨᠢᠭᠡ ᠴᠡᠭ ᠲᠦ ᠣᠭᠲᠤᠯᠤᠯᠴᠠᠨ᠎ ‍ᠠ᠋᠃<br>

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 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 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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