"ᠯᠣᠪᠠᠴᠧᠹᠰᠻᠢ ᠊ᠢᠢᠨ ᠭᠧᠣᠮᠧᠲ᠋ᠧᠷ"-ны өөр хувилбарууд
ᠯᠣᠪᠠᠴᠧᠹᠰᠻᠢ ᠊ᠢᠢᠨ ᠭᠧᠣᠮᠧᠲ᠋ᠧᠷ (кодоор харах)
19:37, 20 Хоёрдугаар сар 2021-ий байдлаарх засвар
, 20 Хоёрдугаар сар 2021Edit
(Edit) |
(Edit) |
||
| 1-р мөр: | 1-р мөр: | ||
<div style="max-height: 80vh; writing-mode: vertical-lr; font-family: 'Noto Sans Mongolian'"> | <div style="max-height: 80vh; writing-mode: vertical-lr; font-family: 'Noto Sans Mongolian'"> | ||
= ᠯᠣᠪᠠᠴᠧᠹᠰᠻᠢ ᠢᠢᠨ ᠭᠧᠣᠮᠧᠲ᠋ᠧᠷ = | = ᠯᠣᠪᠠᠴᠧᠹᠰᠻᠢ ᠢᠢᠨ ᠭᠧᠣᠮᠧᠲ᠋ᠧᠷ = | ||
ᠯᠣᠪᠠᠴᠧᠹᠰᠻᠢ<sup>Лобачевский</sup> ᠮᠠᠨ ᠤ ᠶᠢᠷᠲᠢᠨᠴᠦ ᠳ᠋ᠦ ᠧᠦ᠋ᠻ᠊ᠯᠢᠳ᠋ ᠦᠨ ᠬᠠᠪᠲᠠᠭᠠᠢ ᠭᠧᠣᠮᠧᠲ᠋ᠧᠷ<sup>geometry</sup>᠂ ᠮᠤᠷᠤᠶ᠋ᠢᠯᠲᠠ ᠲᠠᠢ ᠭᠧᠣᠮᠧᠲ᠋ᠧᠷ ᠬᠣᠶᠠᠷ ᠤᠨ ᠠᠯᠢ ᠨᠢ ᠪᠣᠳᠠ ᠲᠠᠢ ᠲᠣᠬᠢᠷᠠᠬᠤ ᠪᠤᠢ ᠭᠡᠰᠡᠨ ᠠᠰᠠᠭᠤᠯᠲᠠ ᠳᠡᠪᠰᠢᠭᠦᠯᠵᠡᠢ᠃<ref>http://tesseract-club.blogspot.com/2011/09/blog-post.html Орон зайн муруйлт ба цаг хугацааны гажилт᠃ ᠬᠠᠨᠳᠤᠭᠰᠠᠨ 2021/02/18</ref> <br> | ᠯᠣᠪᠠᠴᠧᠹᠰᠻᠢ<sup>Лобачевский</sup> ᠮᠠᠨ ᠤ ᠶᠢᠷᠲᠢᠨᠴᠦ ᠳ᠋ᠦ ᠧᠦ᠋ᠻ᠊ᠯᠢᠳ᠋ ᠦᠨ ᠬᠠᠪᠲᠠᠭᠠᠢ ᠭᠧᠣᠮᠧᠲ᠋ᠧᠷ<sup>geometry</sup>᠂ ᠮᠤᠷᠤᠶ᠋ᠢᠯᠲᠠ ᠲᠠᠢ ᠭᠧᠣᠮᠧᠲ᠋ᠧᠷ ᠬᠣᠶᠠᠷ ᠤᠨ ᠠᠯᠢ ᠨᠢ ᠪᠣᠳᠠ ᠲᠠᠢ ᠲᠣᠬᠢᠷᠠᠬᠤ ᠪᠤᠢ ᠭᠡᠰᠡᠨ ᠠᠰᠠᠭᠤᠯᠲᠠ ᠳᠡᠪᠰᠢᠭᠦᠯᠵᠡᠢ᠃<ref>[http://tesseract-club.blogspot.com/2011/09/blog-post.html Орон зайн муруйлт ба цаг хугацааны гажилт᠃] ᠬᠠᠨᠳᠤᠭᠰᠠᠨ 2021/02/18</ref> <br> | ||
ᠡᠭᠦᠪᠡᠷ ᠢᠢᠡᠨ ᠧᠦ᠋ᠻ᠊ᠯᠢᠳ᠋<sup>Euclid</sup> ᠦᠨ ᠪᠤᠰᠤ ᠭᠧᠣᠮᠧᠲ᠋ᠧᠷ ᠢ ᠦᠨᠳᠦᠰᠦᠯᠡᠵᠦᠬᠦᠢ᠃ | ᠡᠭᠦᠪᠡᠷ ᠢᠢᠡᠨ ᠧᠦ᠋ᠻ᠊ᠯᠢᠳ᠋<sup>Euclid</sup> ᠦᠨ ᠪᠤᠰᠤ ᠭᠧᠣᠮᠧᠲ᠋ᠧᠷ ᠢ ᠦᠨᠳᠦᠰᠦᠯᠡᠵᠦᠬᠦᠢ᠃ | ||
| 14-р мөр: | 14-р мөр: | ||
}} | }} | ||
<br> | <br> | ||
'''ᠲᠤᠬᠠᠢ ᠢᠢᠨ ᠰᠢᠯᠠᠭᠤᠨ ᠪᠠ ᠲᠡᠭᠦᠨ ᠳ᠋ᠤ ᠦᠯᠦ ᠬᠠᠷᠢᠶᠠᠯᠠᠭᠳᠠᠬᠤ ᠴᠡᠭ ᠦᠨ ᠣᠷᠣᠰᠢᠵᠤ ᠪᠠᠢᠢᠭ ᠠ᠋ ᠬᠠᠪᠲᠠᠭᠠᠢ ᠳ᠋ᠤ ᠲᠡᠷᠡ ᠴᠡᠭ ᠢᠢ ᠳᠠᠭᠠᠷᠢᠭᠤᠯᠤᠨ ᠲᠤᠬᠠᠢ ᠢᠢᠨ ᠰᠢᠯᠠᠭᠤᠨ ᠲᠠᠢ ᠦᠯᠦ ᠣᠭᠲᠠᠯᠠᠯᠴᠠᠬᠤ ᠨᠢᠭᠡ ᠡᠴᠡ ᠣᠯᠠᠨ ᠰᠢᠯᠠᠭᠤᠨ ᠲᠠᠲᠠᠵᠤ ᠪᠣᠯᠤᠨ ᠠ᠋'''᠃<ref>https://unistomlg.ru/mn/na-dne/gde-peresekayutsya-dve-parallelnye-pryamye-skolko Хоёр зэрэгцээ шугам огтлолцох | '''ᠲᠤᠬᠠᠢ ᠢᠢᠨ ᠰᠢᠯᠠᠭᠤᠨ ᠪᠠ ᠲᠡᠭᠦᠨ ᠳ᠋ᠤ ᠦᠯᠦ ᠬᠠᠷᠢᠶᠠᠯᠠᠭᠳᠠᠬᠤ ᠴᠡᠭ ᠦᠨ ᠣᠷᠣᠰᠢᠵᠤ ᠪᠠᠢᠢᠭ ᠠ᠋ ᠬᠠᠪᠲᠠᠭᠠᠢ ᠳ᠋ᠤ ᠲᠡᠷᠡ ᠴᠡᠭ ᠢᠢ ᠳᠠᠭᠠᠷᠢᠭᠤᠯᠤᠨ ᠲᠤᠬᠠᠢ ᠢᠢᠨ ᠰᠢᠯᠠᠭᠤᠨ ᠲᠠᠢ ᠦᠯᠦ ᠣᠭᠲᠠᠯᠠᠯᠴᠠᠬᠤ ᠨᠢᠭᠡ ᠡᠴᠡ ᠣᠯᠠᠨ ᠰᠢᠯᠠᠭᠤᠨ ᠲᠠᠲᠠᠵᠤ ᠪᠣᠯᠤᠨ ᠠ᠋'''᠃<ref>[https://unistomlg.ru/mn/na-dne/gde-peresekayutsya-dve-parallelnye-pryamye-skolko Хоёр зэрэгцээ шугам огтлолцох үед]᠃ ᠬᠠᠨᠳᠤᠭᠰᠠᠨ 2021/02/18</ref> | ||
ᠡᠨᠡ ᠪᠣᠯ ᠯᠣᠪᠠᠴᠧᠣᠰᠻᠢ ᠢᠢᠨ ᠳᠡᠪᠰᠢᠭᠦᠯᠦᠭᠰᠡᠨ ᠫᠣᠰᠲ᠋ᠦ᠋ᠯᠠᠲ<sup>postulate</sup>᠃ | ᠡᠨᠡ ᠪᠣᠯ ᠯᠣᠪᠠᠴᠧᠣᠰᠻᠢ ᠢᠢᠨ ᠳᠡᠪᠰᠢᠭᠦᠯᠦᠭᠰᠡᠨ ᠫᠣᠰᠲ᠋ᠦ᠋ᠯᠠᠲ<sup>postulate</sup>᠃ | ||
| 44-р мөр: | 44-р мөр: | ||
ᠨᠢᠭᠡᠨ ᠲᠾᠧᠣᠷᠧᠮ ᠨᠢ ᠭᠤᠷᠪᠠᠯᠵᠢᠨ ᠤ <math>\alpha</math>᠂ <math>\beta</math>᠂ <math>\gamma</math> ᠥᠨᠴᠦᠭ ᠦᠳ ᠦᠨ ᠨᠡᠢᠢᠯᠡᠪᠦᠷᠢ ᠲᠡᠭᠰᠢ ᠥᠨᠴᠦᠭ ᠡᠴᠡ ᠢᠠᠮᠠᠭᠲᠠ ᠪᠠᠭ ᠠ᠋ ᠪᠠᠢᠢᠨ ᠠ᠋ ᠭᠡᠳᠡᠭ᠃ | ᠨᠢᠭᠡᠨ ᠲᠾᠧᠣᠷᠧᠮ ᠨᠢ ᠭᠤᠷᠪᠠᠯᠵᠢᠨ ᠤ <math>\alpha</math>᠂ <math>\beta</math>᠂ <math>\gamma</math> ᠥᠨᠴᠦᠭ ᠦᠳ ᠦᠨ ᠨᠡᠢᠢᠯᠡᠪᠦᠷᠢ ᠲᠡᠭᠰᠢ ᠥᠨᠴᠦᠭ ᠡᠴᠡ ᠢᠠᠮᠠᠭᠲᠠ ᠪᠠᠭ ᠠ᠋ ᠪᠠᠢᠢᠨ ᠠ᠋ ᠭᠡᠳᠡᠭ᠃ | ||
ᠲᠡᠭᠰᠢ ᠥᠨᠴᠦᠭ ᠪᠠ ᠭᠤᠷᠪᠠᠯᠵᠢᠨ ᠤ ᠥᠨᠴᠦᠭ ᠦᠳ ᠦᠨ ᠨᠡᠢᠢᠯᠡᠪᠦᠷᠢ ᠢᠢᠨ ᠢᠯᠭᠠᠭ ᠠ᠋ ᠭᠤᠷᠪᠠᠯᠵᠢᠨ ᠤ ᠳ᠋ᠧᠹᠧᠻᠲ ᠭᠡᠨ ᠡ᠋᠃<ref>https://www.maa.org/press/periodicals/loci/joma/hyperbolic-geometry-triangles-angles-and-area Andrew G. Bennett. Hyperbolic Geometry - Triangles, Angles, and Area. ᠬᠠᠨᠳᠤᠭᠰᠠᠨ 2021/02/20</ref> | ᠲᠡᠭᠰᠢ ᠥᠨᠴᠦᠭ ᠪᠠ ᠭᠤᠷᠪᠠᠯᠵᠢᠨ ᠤ ᠥᠨᠴᠦᠭ ᠦᠳ ᠦᠨ ᠨᠡᠢᠢᠯᠡᠪᠦᠷᠢ ᠢᠢᠨ ᠢᠯᠭᠠᠭ ᠠ᠋ ᠭᠤᠷᠪᠠᠯᠵᠢᠨ ᠤ ᠳ᠋ᠧᠹᠧᠻᠲ ᠭᠡᠨ ᠡ᠋᠃<ref>[https://www.maa.org/press/periodicals/loci/joma/hyperbolic-geometry-triangles-angles-and-area Andrew G. Bennett. Hyperbolic Geometry - Triangles, Angles, and Area.] ᠬᠠᠨᠳᠤᠭᠰᠠᠨ 2021/02/20</ref> | ||
ᠭᠤᠷᠪᠠᠯᠵᠢᠨ ᠤ ᠲᠠᠯᠠᠪᠠᠢ ᠨᠢ ᠳᠠᠷᠠᠭᠠᠬᠢ ᠪᠠᠢᠢᠳᠠᠯ ᠢᠢᠠᠷ ᠲᠣᠭᠠᠴᠠᠭᠠᠯᠠᠭᠳᠠᠨ ᠠ᠋᠄ <br><br> | ᠭᠤᠷᠪᠠᠯᠵᠢᠨ ᠤ ᠲᠠᠯᠠᠪᠠᠢ ᠨᠢ ᠳᠠᠷᠠᠭᠠᠬᠢ ᠪᠠᠢᠢᠳᠠᠯ ᠢᠢᠠᠷ ᠲᠣᠭᠠᠴᠠᠭᠠᠯᠠᠭᠳᠠᠨ ᠠ᠋᠄ <br><br> | ||
| 56-р мөр: | 56-р мөр: | ||
</span><br><br> | </span><br><br> | ||
ᠪᠠᠰᠠ ᠨᠢᠭᠡ | ᠪᠠᠰᠠ ᠨᠢᠭᠡ ᠮᠥᠷᠳᠡᠯᠭᠡ ᠨᠢ "ᠬᠣᠶᠠᠷ ᠲᠥᠰᠦᠲᠠᠢ ᠭᠤᠷᠪᠠᠯᠵᠢᠨ ᠣ ᠲᠠᠯᠠᠪᠠᠢ ᠲᠡᠩᠴᠡᠭᠦᠦ ᠪᠠᠢᠢᠨ ᠠ᠋" ᠬᠡᠮᠡᠨ ᠡ᠋᠃ ᠥᠭᠡᠷ ᠡ᠋ ᠢᠢᠡᠷ ᠬᠡᠯᠡᠪᠡᠯ ᠲᠥᠰᠦᠲᠠᠢ ᠭᠤᠷᠪᠠᠯᠵᠢᠨ ᠨᠤᠭᠤᠳ ᠻᠣᠨ᠍ᠭ᠌ᠷᠦ᠋ᠧᠨ᠍ᠲ<sup>congruent</sup> ᠪᠠᠢᠢᠨ ᠠ᠋᠃ | ||
ᠡᠨᠡ ᠮᠡᠲᠦ ᠪᠡᠷ ᠯᠣᠪᠠᠴᠧᠹᠰᠻᠢ ᠢᠢᠨ ᠭᠧᠣᠮᠧᠲ᠋ᠧᠷ ᠦᠨ ᠮᠥᠷᠳᠡᠯᠭᠡ ᠨᠦᠭᠦᠳ ᠬᠡᠳᠦᠢ ᠡᠲᠡᠭᠡᠳ ᠭᠠᠵᠢ᠂ ᠫᠠᠷᠠᠳᠣᠻᠰ<sup>paradox</sup> ᠶᠤᠮ ᠰᠢᠭ ᠪᠣᠯᠪᠠᠴᠤ ᠤᠯᠠᠮᠵᠢᠯᠠᠯᠲᠤ ᠭᠧᠣᠮᠧᠲ᠋ᠧᠷ ᠲᠡᠢ ᠪᠦᠷᠢᠨ ᠠᠳᠠᠯᠢ ᠡᠷᠬᠡ ᠲᠡᠢ ᠠᠵᠡᠢ᠃ | |||
ᠰᠢᠨ ᠡ᠋ ᠭᠧᠣᠮᠧᠲ᠋ᠧᠷ ᠨᠢ ᠣᠷᠤᠨ ᠵᠠᠢ ᠢᠢᠨ ᠮᠥᠨ ᠴᠢᠨᠠᠷ ᠤᠨ ᠲᠤᠬᠠᠢ ᠣᠢᠢᠯᠠᠭᠠᠯᠲᠠ ᠳᠤ ᠰᠠᠭᠤᠷᠢ ᠥᠭᠡᠷᠡᠴᠢᠯᠡᠯᠲᠡ ᠢᠢ ᠠᠪᠴᠢᠷᠠᠭᠰᠠᠨ ᠪᠠᠢᠢᠨ ᠠ᠋᠃<br><br> | |||
== ᠨᠡᠷ ᠡ᠋ ᠲᠣᠮᠢᠶᠠᠯᠠᠯ == | == ᠨᠡᠷ ᠡ᠋ ᠲᠣᠮᠢᠶᠠᠯᠠᠯ == | ||