ᠲᠣᠪᠴᠢᠯᠠᠯ᠄ \s911 ᠲᠡᠩᠴ ᠡᠳᠬ ᠡᠯ ᠪᠤᠰᠤ ᠵᠢ ᠴᠢ ᠲᠡ ᠭᠦᠨ ᠤ ᠬᠠᠷ ᠢᠭᠤ ᠴᠤᠭᠯ ᠠᠷᠠᠯ\sᠣᠷ ᠤᠯᠳ ᠤᠯᠭ ᠠ ᠶ᠋ᠢ ᠨ ᠬᠠᠭ ᠤᠳᠠᠰᠦ ᠠᠩ ᠭᠢ᠄ ᠨᠡᠷ ᠡ ᠄ ᠡᠳᠤᠷ ᠰᠠᠷ ᠠ ᠄ ᠣᠷ ᠤᠯᠳ ᠤᠯᠭ ᠠ ᠨᠢ ᠭᠡ ᠄ ᠢᠯᠡ ᠷᠬᠡ ᠢᠢᠯᠡᠵ ᠦ ᠦᠵᠡ 1 A ᠪᠣᠯ ᠡᠶᠡᠷ ᠭᠦ ᠲ ᠣᠭ ᠠ\s2 A ᠪᠣᠯ ᠰᠥ ᠭᠡᠷ ᠭᠦ ᠲ ᠣᠭ ᠠ\s3 A ᠪᠣᠯᠤᠨ 5 ᠶ᠋ᠢ ᠨ ᠨᠡᠢ ᠢᠯᠡᠪ ᠤᠷᠢ ᠨᠢ 7 ᠡᠴᠡ ᠪᠠᠭ ᠠ\s4 A ᠪᠣᠯᠤᠨ 2 ᠶ᠋ᠢ ᠨ ᠢᠯᠭᠠᠪ ᠤᠷᠢ ᠨᠢ

ᠲᠣᠪᠴᠢᠯᠠᠯ᠄ \sᠺ ᠦᠸᠠᠳ᠋ ᠢᠵᠠ ᠭᠤᠷ\sᠣᠷ ᠤᠯᠳ ᠤᠯᠭ ᠠ ᠶ᠋ᠢᠨ ᠬᠠ ᠭᠤᠳ ᠠᠰᠦ ᠠᠩᠭᠢ ᠄ ᠨ ᠡᠷ ᠡ ᠄ ᠡᠳ ᠤᠷ ᠰᠠᠷ ᠠ ᠄ ᠨᠢᠭ ᠡ ᠂ ᠪᠡᠯᠡᠳ ᠭᠡᠯ ᠰᠤᠷᠤᠯ ᠴᠠᠯᠭ ᠠ ᠪᠣ ᠳᠤ᠄ 1 1 2\s ᠂\s2\s−1\s2\s\s3\s 12\s2\s ᠂\s4\s− 12\s2\s ᠬᠤᠶᠡ ᠷ᠂ ᠠ ᠰᠠᠭ ᠤᠳᠠᠯ ᠤ ᠨ ᠣᠷ ᠴᠢᠨ 1ᠰ ᠤᠷᠭ ᠠᠭᠤᠯ ᠢ ᠤᠷ ᠠᠨ ᠵᠢᠷᠤᠭ ᠤ ᠨ ᠪᠦ ᠳᠦᠭᠡᠯ ᠤ ᠨ ᠤᠷ ᠤᠯᠳ ᠤᠭᠠ ᠨ ᠶᠠᠪᠤ ᠭ

ᠲᠣᠪᠴᠢᠯᠠᠯ᠄ ᠪᠤᠯᠪᠡᠰᠤᠷᠠᠯ ᠤ ᠋ᠨ᠋ᠬᠢᠴᠢᠶᠡ ᠯ ᠠᠩ ᠭᠢ᠄᠋᠋᠋ ᠋᠋᠋᠋ ᠋᠋᠋᠋᠋᠋᠋ ᠋᠋᠋ᠨ ᠡᠷ᠋ᠡ᠄᠋ ᠋᠋᠋᠋᠋ ᠋᠋᠋᠋᠋᠋᠋ ᠋᠋᠋᠋᠋᠋ᠡᠳᠤ ᠷ᠋ᠰᠠ ᠷ᠋ᠠ᠄ 1 ᠵᠢᠷᠤᠭ᠋ ᠮᠡᠲᠦ ᠂ A ⊥ C,B ⊥ C᠋᠂᠋ ᠪᠠᠲ ᠤᠯᠠᠭᠳ ᠠᠬᠤ᠋ᠨ ᠢ᠄ A // B᠋᠋\s2ᠵᠢᠷᠤᠭ᠋ ᠮᠡᠲᠦ ᠂᠋ᠲᠦ ᠷᠪᠡᠯ ᠵᠢᠨ AB CD ᠳ᠋ᠦ᠋ ᠂ ∠ C ∠D\s180 0᠂᠋ ᠪᠠᠲ ᠤᠯᠠᠭᠳᠠᠬᠤ᠋ ᠨᠢ᠄ ∠A\s∠B\s180 0᠃ 3ᠵᠢᠷᠤᠭ᠋ ᠮᠡᠲᠦ ᠂᠋ ᠥᠭᠭᠦᠭᠳᠡᠭᠰᠡᠨ᠋ ᠨᠢ ᠋ CD ᠋ᠨᠢ᠋ ∠A CE

ᠲᠣᠪᠴᠢᠯᠠᠯ᠄ ᠥ ᠭᠦᠯᠡᠯ᠂ ᠪᠠᠲ ᠤᠶᠣᠰ ᠤ᠂ ᠪᠠᠲ ᠤᠯᠠᠯᠲ ᠠ\sᠣᠷ ᠤᠯᠳ ᠤᠯᠭ ᠠ ᠶ᠋ᠢ ᠨ ᠬᠠᠭ ᠤᠳᠠᠰᠦ ᠠᠩᠭᠢ ᠄ ᠨ ᠡᠷ ᠡ ᠄ ᠡᠳ ᠤᠷ ᠰᠠᠷ ᠠ ᠄ ᠨᠢ ᠭᠡ ᠂ ᠠ ᠰᠠᠭ ᠤᠳᠠᠯ ᠤ ᠨ ᠣᠷ ᠴᠢᠨ ᠵᠡᠷᠭᠡᠴᠡ ᠭᠡ ᠰᠢ ᠯᠤᠭ ᠤᠨ ᠤ ᠰ ᠢᠨᠵᠢ ᠴᠢ ᠨᠡᠷ᠄ 1 2 3 ᠵᠡᠷ ᠭᠡᠴᠡᠭ ᠡ ᠰᠢ ᠯᠤᠭᠤᠨ ᠤ ᠮᠠ ᠭᠠᠳᠯ ᠠᠯᠲ ᠠ᠄ 1 2 3 ᠬᠤᠶᠡ ᠷ᠂ ᠣᠷ ᠤᠯᠳ ᠤᠯᠭ ᠠ ᠨᠤ ᠳᠠᠯᠠᠯᠲ ᠠ 1᠂ ᠲᠠ ᠡᠳᠡ ᠭᠡᠷ ᠦᠭ ᠦᠯᠡᠪᠤ ᠷᠢ ᠢ ᠬ ᠤᠶᠡᠷ ᠬ

ᠲᠣᠪᠴᠢᠯᠠᠯ᠄ ᠵᠡᠷᠭᠡ ᠴᠡᠭ ᠡ ᠰᠢ ᠯᠤᠭᠤᠨ ᠤ ᠰᠢ ᠨᠵᠢ ᠴᠢ ᠨᠡᠷ\sᠣᠷ ᠤᠯᠳ ᠤᠯᠭ ᠠ ᠶ᠋ᠢ ᠨ ᠬᠠᠭ ᠤᠳᠠᠰ ᠦ ᠠᠩᠭᠢ ᠄ ᠨ ᠡᠷ ᠡ ᠄ ᠡᠳ ᠤᠷ ᠰᠠᠷ ᠠ ᠄ ᠭᠤ ᠷᠪᠡ ᠂ ᠰ ᠢᠨ ᠡ ᠳᠦ ᠷᠢ 1᠂ 2᠂ 3᠂ ᠳᠥ ᠷᠪᠡ ᠂ ᠰ ᠢᠨ ᠡ ᠳᠦ ᠷᠢ ᠶ᠋ᠢ ᠪᠠᠳ ᠤᠳᠬᠠᠬᠤ ᠪᠣᠯᠪ ᠠᠰᠤᠷ ᠠᠯ 1᠂ ᠵᠢᠷ ᠤᠭ ᠮᠡᠲ ᠦ᠂ A/ /B ᠂ C ᠪᠣᠯ ᠤᠭᠳᠤᠯᠤ ᠭᠴᠢ ᠱᠤ ᠭᠤᠮ ᠂ ᠪᠠᠳ ᠤᠯᠠᠭ ᠳᠠᠬ ᠤ ᠨ ᠢ᠄ ∠1\s∠3 ᠃ 2 A/ /B ᠂ C ᠪᠣᠯ ᠤᠭ ᠳᠤᠯᠤ ᠭᠴᠢ

ᠲᠣᠪᠴᠢᠯᠠᠯ᠄ ᠵᠡᠷᠭᠡ ᠴᠡᠭ ᠡ ᠰᠢ ᠯᠤᠭᠤᠨ ᠤ ᠮᠠᠭᠠᠳᠯᠠᠯᠲᠠ\sᠣᠷ ᠤᠯᠳ ᠤᠯᠭ ᠠ ᠶ᠋ᠢ ᠨ ᠬᠠᠭ ᠤᠳᠠᠰ ᠦ ᠠᠩᠭᠢ ᠄ ᠨ ᠡᠷ ᠡ ᠄ ᠡᠳ ᠤᠷ ᠰᠠᠷ ᠠ ᠄ ᠨᠢ ᠭᠡ ᠂ ᠠ ᠰᠠᠭ ᠤᠳᠠᠯ ᠤ ᠨ ᠣᠷ ᠴᠢᠨ ⑴ ᠵ ᠢᠭᠠᠬ ᠤ ᠮᠠᠲ᠋ ᠧᠷᠢ ᠶᠠᠯ ᠤ ᠨ 14\s15 ᠳ᠋ ᠤᠭᠠᠷ ᠨ ᠢᠭᠤᠷ ᠤ ᠨ ᠠᠭᠤ ᠯᠭ ᠠ ᠶ᠋ᠢ ᠤᠩ ᠰᠢᠵ ᠤ᠂ ᠳᠤᠤᠷᠡᠬ ᠢ ᠰᠡᠳ ᠤᠪ ᠶ᠋ ᠢ ᠭ ᠦᠢᠴᠡ ᠳᠭᠡ ᠃ ᠵᠢᠷᠤᠭ ᠲ ᠦ ᠰᠢᠯᠤ ᠭᠤᠨ ᠤ ᠠᠠᠳ ᠠᠡᠡᠬ ᠢ ᠨᠢᠭᠡ ᠡᠡ ᠋ ᠠ ᠠᠭᠠᠷᠢᠭᠤ ᠯᠵᠦ

ᠲᠣᠪᠴᠢᠯᠠᠯ᠄ \sᠣᠷ ᠤᠯᠳ ᠤᠯᠭ ᠠ ᠶ᠋ᠢ ᠨ ᠬᠠᠭ ᠤᠳᠠᠰᠦ ᠠᠩᠭᠢ ᠄ ᠨ ᠡᠷ ᠡ ᠄ ᠡᠳ ᠤᠷ ᠰᠠᠷ ᠠ ᠄ ᠨᠢᠭ ᠡ ᠂ ᠪᠡᠯᠡᠳᠭ ᠡᠯ ᠰᠤᠷ ᠤᠯᠴ ᠠᠯᠭ ᠠ ᠄ ᠵᠢᠷᠤᠭ ᠮᠡᠲ ᠦ᠂ ᠰᠢᠯᠤᠭ ᠤᠨ DE ᠂ BC ᠨᠢ ᠰ ᠢᠯᠤᠭ ᠤᠨ AB ᠳ᠋ ᠦ ᠤᠭᠳᠤᠯᠤ ᠭᠳᠡᠵᠡᠢ᠂ ∠1 ᠪᠠ ∠4 ᠂ ∠2 ᠪᠠ ∠4 ᠂ ∠3 ᠪᠠ ∠4 ᠨᠢ ᠲᠤ ᠰ ᠲᠤ ᠰ ᠶ ᠠᠮᠠᠷ ᠥᠨ ᠴᠦᠭ ᠪᠣᠯᠬᠤ ᠪᠤᠢ ᠬᠤᠶᠡ ᠷ᠂ ᠠᠰ ᠠᠭᠤᠳᠠᠯ ᠤ ᠨ ᠣᠷ ᠴᠢᠨ ᠄ ᠱ ᠠᠭᠠᠷᠳᠠ ᠯᠭ ᠠ ᠶᠣᠰᠣᠭᠠ ᠷ ᠵᠢ ᠷᠤᠭ ᠵᠢ

ᠲᠣᠪᠴᠢᠯᠠᠯ᠄ 141     ,                      ,,,O,,,,,1 ,            3M    

ᠲᠣᠪᠴᠢᠯᠠᠯ᠄         ,2121  ,,,   1500DM2          10                    

ᠲᠣᠪᠴᠢᠯᠠᠯ᠄  ,,,,,,, ,         ,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,  ,,,  ,,,,,DCBAE     ABCDE  ,A,B,C,D,E,,         ,

ᠲᠣᠪᠴᠢᠯᠠᠯ᠄ ᠴᠢᠪᠠᠭ᠎ᠠ ᠲᠠᠪᠤᠳᠤᠭᠠᠷ ᠳᠤᠮᠳᠠᠳᠤ ᠰᠤᠷᠭᠠᠭᠤᠯᠢ , ᠬᠢᠴᠢᠶᠡᠯᠯᠡᠭᠴᠢ᠄ ᠤᠳᠤᠨᠳᠤᠶᠠᠭ᠎ᠠ , ᠦᠨᠳᠦᠷ ᠢ ᠴᠤᠠᠠᠯᠠᠭᠤᠯᠤᠠᠠᠰᠠᠨ ᠨᠢ ᠲᠤᠤᠷᠠᠬᠢ ᠮᠡᠳᠦ᠄ ᠪᠡᠯᠡᠳᠭᠡᠵᠦ ᠪᠠᠢᠨ᠎ᠠ᠃ 63 ᠰᠤᠷᠤᠠᠠᠴᠢ ᠶᠢᠨ ᠪᠡᠶ᠎ᠡ ᠶᠢᠨ ᠶᠢ ᠰᠣᠩᠭᠤᠨ ᠤᠷᠤᠯᠳᠤᠭᠠᠨ ᠳᠤ ᠤᠷᠤᠯᠴᠠᠭᠤᠯᠬᠤ ᠪᠠᠷ ᠢᠢᠨ ᠦᠨᠳᠦᠷ ᠨᠢ ᠲᠠᠮᠡᠢ ᠵᠦ᠋ᠷᠢᠬᠦ ᠦᠬᠡᠢ 40 ᠰᠤᠷᠤᠠᠠᠴᠢ ᠲᠦ᠋ᠯᠦᠬᠡ᠂ ᠲᠤᠯᠤᠳᠤᠭᠠᠷ ᠤᠨ ᠤ 63 ᠰᠤᠷᠤᠠᠠᠴᠢ ᠠᠴᠠ ᠪᠡᠶ᠎ᠡ ᠪᠡᠶ᠎ᠡ ᠲᠠᠮᠢᠷ ᠤᠨ ᠤᠷᠤᠯ

ᠲᠣᠪᠴᠢᠯᠠᠯ᠄ ᠲᠠᠯᠠᠪᠤᠷ ᠤᠷᠤᠯᠳᠤᠭᠠᠨ ᠳᠤ 16 ᠬᠤᠪᠢ ᠤᠯᠪᠠ᠃ ᠲᠠᠯᠠᠪᠤᠷ ᠢᠯᠬᠠᠳᠠᠪᠠᠯ 1 ᠬᠤᠪᠢ ᠤᠯᠭᠤᠨ᠎ᠠ᠃ ᠨᠢᠬᠡᠨ ᠠᠩᠬᠢ 10 ᠢᠯᠭᠠᠷᠠᠭᠤᠯᠵᠤ᠂ 1 ᠲᠠᠯᠠᠪᠤᠷ ᠢᠯᠠᠪᠠᠯ 2 ᠬᠤᠪᠢ ᠤᠯᠭᠤᠵᠤ᠂ 1 ᠰᠬᠠᠰᠤᠨ ᠪᠦᠮᠪᠦᠭᠡ ᠶᠢᠨ ᠤᠷᠤᠯᠳᠤᠭᠠᠨ ᠳᠤ ᠢᠯᠠᠵᠤ ᠢᠯᠬᠠᠳᠠᠬᠤ ᠶᠢ , ᠠᠰᠠᠭᠤᠳᠠᠯ ᠤᠨ ᠣᠷᠴᠢᠨ᠄ , ᠳᠠᠢᠴᠢᠯᠠᠬᠤ ᠠᠰᠠᠭᠤᠳᠠᠯ᠄ , ᠲᠠᠭᠠᠮᠠᠭᠯᠠᠯ ᠲᠦᠰᠦᠪᠯᠡᠯ᠄ , ᠲᠠᠯᠠᠪᠤᠷ ᠤᠨ ᠲᠤᠭ᠎ᠠ ᠨᠢ ᠲᠣᠰ ᠲᠤᠰ ᠬᠡᠳᠦᠢ ᠪᠣᠢ︖ ᠲᠡᠭᠡᠪᠡᠯ ᠡᠨᠡ