ᠫᠠᠷᠠᠪᠣᠯ: Засвар хоорондын ялгаа
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<span style="color:Blue; max-height: 30vh;">ᠡᠨᠡ ᠨᠡᠢᠢᠲᠡᠯᠡᠯ ᠢ ᠮᠡᠷᠭᠡᠵᠢᠯ ᠦᠨ ᠬᠦᠮᠦᠰ <br>(<span style="color:Red;">ᠮᠠᠲ᠋ᠾᠧᠮᠠᠲ᠋ᠢᠭᠴᠢᠳ᠂ ᠪᠠᠭᠰᠢ ᠨᠠᠷ</span>)<br> ᠬᠢᠨᠠᠨ ᠵᠠᠰᠠᠪᠤᠷᠢᠯᠠᠬᠤ ᠱᠠᠭᠠᠷᠳᠠᠯᠭᠠᠲᠠᠢ</span><br><br> | |||
<span style="color:Blue; writing-mode: horizontal-tb;">Энэ<br>нийтлэлийг<br>мэргэжлийн<br>хүмүүс<br>(<span style="color:Red;">математикчид,<br>багш нар</span>)<br>хянан<br>засварлах<br>шаардлагатай</span> | |||
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=ᠫᠠᠷᠠᠪᠣᠯ= | =ᠫᠠᠷᠠᠪᠣᠯ= | ||
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|[[File:Parabola animada.gif|thumb|center]] | |[[File:Parabola animada.gif|thumb|center]] | ||
|style = "height: 50px;"|ᠲᠥᠪ ᠴᠡᠭ ᠪᠠ ᠲᠤᠬᠠᠢ ᠢᠢᠨ | |style = "height: 50px;"|ᠲᠥᠪ ᠴᠡᠭ ᠪᠠ ᠲᠤᠬᠠᠢ ᠢᠢᠨ ᠰᠢᠯᠤᠭᠤᠨ ᠡᠴᠡ ᠠᠳᠠᠯᠢ ᠵᠠᠢ ᠳ᠋ᠤ ᠪᠠᠢᠢᠷᠢᠯᠠᠬᠤ ᠴᠡᠭ ᠦᠳ ᠦᠨ ᠣᠯᠠᠨᠯᠢᠭ ᠢ ᠫᠠᠷᠠᠪᠣᠯ ᠭᠡᠨ ᠡ᠋ ᠃ | ||
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ᠲᠣᠭᠤᠷᠢᠭ᠂ | ᠲᠤᠬᠠᠢ ᠢᠢᠨ ᠴᠡᠭ ᠪᠠ ᠲᠤᠬᠠᠢ ᠢᠢᠨ ᠰᠢᠯᠤᠭᠤᠨ ᠡᠴᠡ ᠠᠳᠠᠯᠢ ᠵᠠᠢ ᠳ᠋ᠤ ᠪᠠᠢᠢᠷᠢᠯᠠᠬᠤ ᠴᠡᠭ ᠦᠳ ᠦᠨ ᠣᠯᠠᠨᠯᠢᠭ ᠢ <b>ᠫᠠᠷᠠᠪᠣᠯ</b><sup>parabola</sup> ᠬᠡᠮᠡᠮᠦᠢ᠃ | ||
ᠥᠭᠡᠷ ᠡ᠋ ᠪᠡᠷ ᠬᠡᠯᠡᠪᠡᠯ ᠫᠠᠷᠠᠪᠣᠯ ᠠᠨᠤ ᠲᠥᠪ ᠴᠡᠭ ᠪᠤᠶᠤ ᠹᠣᠻᠦ᠋ᠰ<sup>focus</sup> ᠴᠡᠭ ᠪᠠ ᠳᠢᠷᠧᠻᠲ᠋ᠷᠢᠰ<sup>directrix</sup> ᠰᠢᠯᠤᠭᠤᠨ ᠡᠴᠡ ᠪᠠᠨ ᠠᠳᠠᠯᠢ ᠵᠠᠢ ᠳ᠋ᠤ ᠠᠯᠤᠰᠯᠠᠭᠳᠠᠭᠰᠠᠨ ᠴᠡᠭ ᠦᠨ ᠣᠯᠠᠨᠯᠢᠭ ᠪᠣᠯᠬᠤ ᠬᠠᠪᠲᠠᠭᠠᠢ ᠮᠤᠷᠤᠢ ᠱᠤᠭᠤᠮ ᠶᠤᠮ᠃<ref>[https://www.intmath.com/plane-analytic-geometry/4-parabola.php Interactive Mathematics. The Parabola]. ᠬᠠᠨᠳᠤᠭᠰᠠᠨ 2021/04/10</ref> | |||
ᠲᠡᠭᠦᠨᠴᠢᠯᠡᠨ ᠫᠠᠷᠠᠪᠣᠯ ᠨᠢ ᠳᠤᠭᠤᠢ ᠻᠣᠨᠦ᠋ᠰ ᠤᠨ<sup>конус</sup> ᠭᠠᠳᠠᠷᠭᠤ ᠪᠠ ᠬᠠᠪᠲᠠᠭᠠᠢ ᠢᠢᠨ ᠣᠭᠲᠤᠯᠤᠯᠴᠠᠯ ᠶᠤᠮ᠃<ref name=":0">[https://www.varsitytutors.com/hotmath/hotmath_help/topics/parabolas Varsity Tutors. Hotmath. Parabolas]. ᠬᠠᠨᠳᠤᠭᠰᠠᠨ 2021/04/10</ref> | |||
ᠲᠣᠭᠤᠷᠢᠭ᠂ ᠧᠯᠯᠢᠫᠰ<sup>ellipse</sup>᠂ [[ᠾᠢᠫᠧᠷᠪᠣᠯ]]<sup>hyperbola</sup>᠂ ᠫᠠᠷᠠᠪᠣᠯ - ᠡᠳᠡᠭᠡᠷ ᠨᠢ ᠻᠣᠨᠦ᠋ᠰ ᠤᠨ ᠣᠭᠲᠤᠯᠤᠯ ᠪᠠᠢᠢᠳᠠᠭ᠃ <ref>[https://www.mathsisfun.com/geometry/conic-sections.html Math is Fun. Conic Sections]. ᠬᠠᠨᠳᠤᠭᠰᠠᠨ 2021/04/10</ref> | |||
ᠫᠠᠷᠠᠪᠣᠯ ᠲᠣᠯᠢᠨ ᠲᠡᠭᠰᠢ ᠬᠡᠮᠲᠦ ᠳᠦᠷᠰᠦ ᠲᠡᠢ ᠮᠤᠷᠤᠢ ᠪᠢᠯᠡ᠃ | |||
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== | ==ᠲᠡᠭᠰᠢᠳᠬᠡᠯ== | ||
|[[File: | ᠻᠸᠠᠲᠷᠠᠲ<sup>quadratic</sup> ᠲᠡᠭᠰᠢᠳᠬᠡᠯ ᠦᠨ ᠭᠷᠠᠫᠾᠢᠻ<sup>graphic</sup> ᠨᠢ ᠨᠤᠮᠤ ᠬᠡᠯᠪᠡᠷᠢ ᠲᠡᠢ ᠫᠠᠷᠠᠪᠣᠯ ᠪᠠᠢᠢᠳᠠᠭ᠃<ref name=":0" /> | ||
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ᠻᠸᠠᠲᠷᠠᠲ ᠲᠡᠭᠰᠢᠳᠬᠡᠯ ᠨᠢ ᠳᠠᠷᠠᠭᠠᠬᠢ ᠪᠠᠢᠢᠳᠠᠯ ᠢᠢᠠᠷ ᠪᠢᠴᠢᠭᠳᠡᠳᠡᠭ᠄ | |||
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<math>y=ax^2+bx+c</math> | |||
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ᠡᠭᠦᠨ ᠳ᠋ᠦ᠄ | |||
<math>a, b, c \in \R,\ a \ne 0</math> ᠪᠤᠶᠤ <span style="writing-mode: horizontal-tb;">a, b, c</span> ᠨᠢ ᠪᠣᠳᠠᠲᠤ ᠲᠣᠭ ᠠ᠋ ᠪᠠᠢᠢᠨ ᠠ᠋᠃ | |||
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ᠮᠥᠨ <span style="writing-mode: horizontal-tb;">a</span> ᠨᠢ <span style="writing-mode: horizontal-tb;">0</span> ᠪᠤᠰᠤ ᠤᠳᠬ ᠠ᠋ ᠲᠠᠢ ᠪᠠᠢᠢᠨ ᠠ᠋᠃ | |||
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|[[File:Axis_of_symmetry_of_a_parabola.gif|thumb|center]] | |||
|style = "height: 100px;"|<span style="writing-mode: horizontal-tb;">b</span> ᠢᠢᠨ ᠤᠳᠬ ᠠ᠋ | |||
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<math>y=x^2</math> | |||
== | ᠬᠡᠯᠪᠡᠷᠢ ᠢᠢᠨ ᠹᠦᠨ᠍ᠻᠼᠢ ᠢᠢᠨ<sup>function</sup> ᠭᠷᠠᠫᠾᠢᠻ ᠴᠤ ᠫᠠᠷᠠᠪᠣᠯ ᠪᠠᠢᠢᠬᠤ ᠠᠭᠠᠳ ᠡᠨᠡ ᠨᠢ <math>a = 1</math> ᠪᠥᠭᠡᠳ <math>b = c = 0</math> ᠪᠠᠢᠢᠬᠤ ᠦᠶ ᠡ᠋ ᠢᠢᠨ ᠲᠣᠬᠢᠶᠠᠯᠳᠠ ᠶᠤᠮ᠃ | ||
ᠫᠠᠷᠠᠪᠣᠯ ᠤᠨ ᠲᠡᠭᠰᠢᠳᠬᠡᠯ ᠦᠨ ᠰᠣᠩᠭᠤᠳᠠᠭ ᠬᠡᠯᠪᠡᠷᠢ ᠨᠢ ᠳᠠᠷᠠᠭᠠᠬᠢ ᠪᠠᠢᠢᠳᠠᠯ ᠢᠢᠠᠷ ᠪᠢᠴᠢᠭᠳᠡᠳᠡᠭ᠄ | |||
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<math>y^2=2px</math> ᠡᠭᠦᠨ ᠳ᠋ᠦ᠄ <math>p > 0</math> ᠪᠠᠢᠢᠬᠤ ᠠᠭᠠᠳ ᠹᠣᠻᠦ᠋ᠰ ᠪᠠ ᠳ᠋ᠢᠷᠧᠻᠲ᠋ᠷᠢᠰ ᠦᠨ ᠬᠣᠭᠤᠷᠤᠨᠳᠤᠬᠢ ᠵᠠᠢ ᠲᠠᠢ ᠲᠡᠩᠴᠡᠨ ᠡ᠋᠃ | |||
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|[[File:Parts of a Parabola.JPG|thumb|center]] | |||
|style = "height: 100px;"|<math>p</math> ᠨᠢ ᠹᠣᠻᠦ᠋ᠰ ᠪᠠ ᠳ᠋ᠢᠷᠧᠻᠲ᠋ᠷᠢᠰ ᠦᠨ ᠬᠣᠭᠤᠷᠤᠨᠳᠤᠬᠢ ᠵᠠᠢ ᠲᠠᠢ ᠲᠡᠩᠴᠡᠨ ᠡ᠋ | |||
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==ᠨᠡᠷ ᠡ᠋ ᠲᠣᠮᠢᠶᠠᠯᠠᠯ== | |||
ᠫᠠᠷᠠᠪᠣᠯ - parabola - парабола | |||
ᠴᠡᠭ - point - точка | |||
ᠣᠯᠠᠨᠯᠢᠭ - set - множество | |||
ᠮᠤᠷᠤᠢ - curve - кривая | |||
ᠲᠡᠭᠰᠢᠳᠬᠡᠯ - equation - уравнение | |||
ᠲᠡᠩᠴᠡᠳᠬᠡᠯ ᠪᠢᠰᠢ - inequality - неравенство | |||
ᠲᠣᠮᠢᠶ ᠠ᠋ - formula - формула | |||
ᠹᠦᠨ᠍ᠻᠼᠢ - function - функция | |||
ᠹᠣᠻᠦ᠋ᠰ - focus - фокус | |||
ᠳ᠋ᠢᠷᠧᠻᠲ᠋ᠷᠢᠰ - directrix - директриса | |||
ᠲᠡᠭᠰᠢ ᠬᠡᠮ - symmetry - симметрия | |||
==ᠤᠶᠠᠯᠳᠤᠭ ᠠ᠋ ᠲᠠᠢ ᠨᠡᠢᠢᠲᠡᠯᠡᠯ== | |||
[[ᠾᠢᠫᠧᠷᠪᠣᠯ]]<br><br> | |||
==ᠡᠬᠢ ᠰᠤᠷᠪᠤᠯᠵᠢ== | ==ᠡᠬᠢ ᠰᠤᠷᠪᠤᠯᠵᠢ== | ||
< | <span style="writing-mode: horizontal-tb; "><references/> | ||
17:52, 10 Дөрөвдүгээр сар 2021-ий байдлаарх одоогийн засвар
ᠡᠨᠡ ᠨᠡᠢᠢᠲᠡᠯᠡᠯ ᠢ ᠮᠡᠷᠭᠡᠵᠢᠯ ᠦᠨ ᠬᠦᠮᠦᠰ
(ᠮᠠᠲ᠋ᠾᠧᠮᠠᠲ᠋ᠢᠭᠴᠢᠳ᠂ ᠪᠠᠭᠰᠢ ᠨᠠᠷ)
ᠬᠢᠨᠠᠨ ᠵᠠᠰᠠᠪᠤᠷᠢᠯᠠᠬᠤ ᠱᠠᠭᠠᠷᠳᠠᠯᠭᠠᠲᠠᠢ
Энэ
нийтлэлийг
мэргэжлийн
хүмүүс
(математикчид,
багш нар)
хянан
засварлах
шаардлагатай
ᠫᠠᠷᠠᠪᠣᠯ[засварлах | кодоор засварлах]
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ᠲᠥᠪ ᠴᠡᠭ ᠪᠠ ᠲᠤᠬᠠᠢ ᠢᠢᠨ ᠰᠢᠯᠤᠭᠤᠨ ᠡᠴᠡ ᠠᠳᠠᠯᠢ ᠵᠠᠢ ᠳ᠋ᠤ ᠪᠠᠢᠢᠷᠢᠯᠠᠬᠤ ᠴᠡᠭ ᠦᠳ ᠦᠨ ᠣᠯᠠᠨᠯᠢᠭ ᠢ ᠫᠠᠷᠠᠪᠣᠯ ᠭᠡᠨ ᠡ᠋ ᠃ |
ᠲᠤᠬᠠᠢ ᠢᠢᠨ ᠴᠡᠭ ᠪᠠ ᠲᠤᠬᠠᠢ ᠢᠢᠨ ᠰᠢᠯᠤᠭᠤᠨ ᠡᠴᠡ ᠠᠳᠠᠯᠢ ᠵᠠᠢ ᠳ᠋ᠤ ᠪᠠᠢᠢᠷᠢᠯᠠᠬᠤ ᠴᠡᠭ ᠦᠳ ᠦᠨ ᠣᠯᠠᠨᠯᠢᠭ ᠢ ᠫᠠᠷᠠᠪᠣᠯparabola ᠬᠡᠮᠡᠮᠦᠢ᠃
ᠥᠭᠡᠷ ᠡ᠋ ᠪᠡᠷ ᠬᠡᠯᠡᠪᠡᠯ ᠫᠠᠷᠠᠪᠣᠯ ᠠᠨᠤ ᠲᠥᠪ ᠴᠡᠭ ᠪᠤᠶᠤ ᠹᠣᠻᠦ᠋ᠰfocus ᠴᠡᠭ ᠪᠠ ᠳᠢᠷᠧᠻᠲ᠋ᠷᠢᠰdirectrix ᠰᠢᠯᠤᠭᠤᠨ ᠡᠴᠡ ᠪᠠᠨ ᠠᠳᠠᠯᠢ ᠵᠠᠢ ᠳ᠋ᠤ ᠠᠯᠤᠰᠯᠠᠭᠳᠠᠭᠰᠠᠨ ᠴᠡᠭ ᠦᠨ ᠣᠯᠠᠨᠯᠢᠭ ᠪᠣᠯᠬᠤ ᠬᠠᠪᠲᠠᠭᠠᠢ ᠮᠤᠷᠤᠢ ᠱᠤᠭᠤᠮ ᠶᠤᠮ᠃[1]
ᠲᠡᠭᠦᠨᠴᠢᠯᠡᠨ ᠫᠠᠷᠠᠪᠣᠯ ᠨᠢ ᠳᠤᠭᠤᠢ ᠻᠣᠨᠦ᠋ᠰ ᠤᠨконус ᠭᠠᠳᠠᠷᠭᠤ ᠪᠠ ᠬᠠᠪᠲᠠᠭᠠᠢ ᠢᠢᠨ ᠣᠭᠲᠤᠯᠤᠯᠴᠠᠯ ᠶᠤᠮ᠃[2]
ᠲᠣᠭᠤᠷᠢᠭ᠂ ᠧᠯᠯᠢᠫᠰellipse᠂ ᠾᠢᠫᠧᠷᠪᠣᠯhyperbola᠂ ᠫᠠᠷᠠᠪᠣᠯ - ᠡᠳᠡᠭᠡᠷ ᠨᠢ ᠻᠣᠨᠦ᠋ᠰ ᠤᠨ ᠣᠭᠲᠤᠯᠤᠯ ᠪᠠᠢᠢᠳᠠᠭ᠃ [3]
ᠫᠠᠷᠠᠪᠣᠯ ᠲᠣᠯᠢᠨ ᠲᠡᠭᠰᠢ ᠬᠡᠮᠲᠦ ᠳᠦᠷᠰᠦ ᠲᠡᠢ ᠮᠤᠷᠤᠢ ᠪᠢᠯᠡ᠃
ᠲᠡᠭᠰᠢᠳᠬᠡᠯ[засварлах | кодоор засварлах]
ᠻᠸᠠᠲᠷᠠᠲquadratic ᠲᠡᠭᠰᠢᠳᠬᠡᠯ ᠦᠨ ᠭᠷᠠᠫᠾᠢᠻgraphic ᠨᠢ ᠨᠤᠮᠤ ᠬᠡᠯᠪᠡᠷᠢ ᠲᠡᠢ ᠫᠠᠷᠠᠪᠣᠯ ᠪᠠᠢᠢᠳᠠᠭ᠃[2]
ᠻᠸᠠᠲᠷᠠᠲ ᠲᠡᠭᠰᠢᠳᠬᠡᠯ ᠨᠢ ᠳᠠᠷᠠᠭᠠᠬᠢ ᠪᠠᠢᠢᠳᠠᠯ ᠢᠢᠠᠷ ᠪᠢᠴᠢᠭᠳᠡᠳᠡᠭ᠄
$ y=ax^{2}+bx+c $
ᠡᠭᠦᠨ ᠳ᠋ᠦ᠄
$ a,b,c\in \mathbb {R} ,\ a\neq 0 $ ᠪᠤᠶᠤ a, b, c ᠨᠢ ᠪᠣᠳᠠᠲᠤ ᠲᠣᠭ ᠠ᠋ ᠪᠠᠢᠢᠨ ᠠ᠋᠃
ᠮᠥᠨ a ᠨᠢ 0 ᠪᠤᠰᠤ ᠤᠳᠬ ᠠ᠋ ᠲᠠᠢ ᠪᠠᠢᠢᠨ ᠠ᠋᠃
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b ᠢᠢᠨ ᠤᠳᠬ ᠠ᠋ |
$ y=x^{2} $
ᠬᠡᠯᠪᠡᠷᠢ ᠢᠢᠨ ᠹᠦᠨ᠍ᠻᠼᠢ ᠢᠢᠨfunction ᠭᠷᠠᠫᠾᠢᠻ ᠴᠤ ᠫᠠᠷᠠᠪᠣᠯ ᠪᠠᠢᠢᠬᠤ ᠠᠭᠠᠳ ᠡᠨᠡ ᠨᠢ $ a=1 $ ᠪᠥᠭᠡᠳ $ b=c=0 $ ᠪᠠᠢᠢᠬᠤ ᠦᠶ ᠡ᠋ ᠢᠢᠨ ᠲᠣᠬᠢᠶᠠᠯᠳᠠ ᠶᠤᠮ᠃
ᠫᠠᠷᠠᠪᠣᠯ ᠤᠨ ᠲᠡᠭᠰᠢᠳᠬᠡᠯ ᠦᠨ ᠰᠣᠩᠭᠤᠳᠠᠭ ᠬᠡᠯᠪᠡᠷᠢ ᠨᠢ ᠳᠠᠷᠠᠭᠠᠬᠢ ᠪᠠᠢᠢᠳᠠᠯ ᠢᠢᠠᠷ ᠪᠢᠴᠢᠭᠳᠡᠳᠡᠭ᠄
$ y^{2}=2px $ ᠡᠭᠦᠨ ᠳ᠋ᠦ᠄ $ p>0 $ ᠪᠠᠢᠢᠬᠤ ᠠᠭᠠᠳ ᠹᠣᠻᠦ᠋ᠰ ᠪᠠ ᠳ᠋ᠢᠷᠧᠻᠲ᠋ᠷᠢᠰ ᠦᠨ ᠬᠣᠭᠤᠷᠤᠨᠳᠤᠬᠢ ᠵᠠᠢ ᠲᠠᠢ ᠲᠡᠩᠴᠡᠨ ᠡ᠋᠃
 |
$ p $ ᠨᠢ ᠹᠣᠻᠦ᠋ᠰ ᠪᠠ ᠳ᠋ᠢᠷᠧᠻᠲ᠋ᠷᠢᠰ ᠦᠨ ᠬᠣᠭᠤᠷᠤᠨᠳᠤᠬᠢ ᠵᠠᠢ ᠲᠠᠢ ᠲᠡᠩᠴᠡᠨ ᠡ᠋ |
ᠨᠡᠷ ᠡ᠋ ᠲᠣᠮᠢᠶᠠᠯᠠᠯ[засварлах | кодоор засварлах]
ᠫᠠᠷᠠᠪᠣᠯ - parabola - парабола
ᠴᠡᠭ - point - точка
ᠣᠯᠠᠨᠯᠢᠭ - set - множество
ᠮᠤᠷᠤᠢ - curve - кривая
ᠲᠡᠭᠰᠢᠳᠬᠡᠯ - equation - уравнение
ᠲᠡᠩᠴᠡᠳᠬᠡᠯ ᠪᠢᠰᠢ - inequality - неравенство
ᠲᠣᠮᠢᠶ ᠠ᠋ - formula - формула
ᠹᠦᠨ᠍ᠻᠼᠢ - function - функция
ᠹᠣᠻᠦ᠋ᠰ - focus - фокус
ᠳ᠋ᠢᠷᠧᠻᠲ᠋ᠷᠢᠰ - directrix - директриса
ᠲᠡᠭᠰᠢ ᠬᠡᠮ - symmetry - симметрия
ᠤᠶᠠᠯᠳᠤᠭ ᠠ᠋ ᠲᠠᠢ ᠨᠡᠢᠢᠲᠡᠯᠡᠯ[засварлах | кодоор засварлах]
ᠡᠬᠢ ᠰᠤᠷᠪᠤᠯᠵᠢ[засварлах | кодоор засварлах]
- ↑ Interactive Mathematics. The Parabola. ᠬᠠᠨᠳᠤᠭᠰᠠᠨ 2021/04/10
- ↑ 2.0 2.1 Varsity Tutors. Hotmath. Parabolas. ᠬᠠᠨᠳᠤᠭᠰᠠᠨ 2021/04/10
- ↑ Math is Fun. Conic Sections. ᠬᠠᠨᠳᠤᠭᠰᠠᠨ 2021/04/10