Teng yonli uchburchak

Geometriyada teng yonli uchburchak — tomonlaridan ikkitasi teng boʻlgan uchburchak. Teng tomonlari qarshisidagi burchaklari ham oʻzaro teng. Teng yonli uchburchaklarga teng yonli toʻgʻri burchakli uchburchak, oltin uchburchak va dipiramidalarni misol oʻlaroq koʻrsatish mumkin.

Teng yonli uchburchaklarni matematik oʻrganish qadimgi Misr matematikasi va Bobil matematikasiga borib taqaladi. Teng yonli uchburchaklar qadim zamonlardan buyon dekoratsiya oʻlaroq foydalanilgan hamda koʻpincha arxitektura va dizaynda, masalan, binolar frontonlarida paydo boʻlgandir.

Formulalar

Balandligini topish formulasi: $h={\frac {1}{2}}{\sqrt {4a^{2}-b^{2}}}$ .
Perimetrini topish formulasi: $p=2a+b$ .

Ichki chizilgan aylana radiusini topish formulalari:

$r={\frac {b}{2}}{\sqrt {\frac {2a-b}{2a+b}}}$
$r={\frac {bh}{b+{\sqrt {4h^{2}+b^{2}}}}}$
$r={\frac {h}{1+{\frac {a}{\sqrt {a^{2}-h^{2}}}}}}$
$r={\frac {b}{2}}\operatorname {tg} \left({\frac {\alpha }{2}}\right)$
$r=a\cdot \cos(\alpha )\cdot \operatorname {tg} \left({\frac {\alpha }{2}}\right)$

Yana qarang

Teng tomonli uchburchak

Manbalar

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Havolalar

Weisstein, Eric W., „Teng yonli uchburchak“, MathWorld ^(ingl.)