# فهرست مرکزهای هندسی

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نام نگاره ${\displaystyle {\bar {x}}}$ ${\displaystyle {\bar {y}}}$ مساحت
مثلث راست‌گوشه ${\displaystyle {\frac {-b}{3}}}$ ${\displaystyle {\frac {h}{3}}}$ ${\displaystyle {\frac {bh}{2}}}$
ربع دایره ${\displaystyle {\frac {4r}{3\pi }}}$ ${\displaystyle {\frac {4r}{3\pi }}}$ ${\displaystyle {\frac {\pi r^{2}}{4}}}$
نیم‌دایره | align="center"|${\displaystyle \,\!0}$ ${\displaystyle {\frac {4r}{3\pi }}}$ ${\displaystyle {\frac {\pi r^{2}}{2}}}$
ربع بیضی | align="center"|${\displaystyle {\frac {4a}{3\pi }}}$ ${\displaystyle {\frac {4b}{3\pi }}}$ ${\displaystyle {\frac {\pi ab}{4}}}$
نیم‌بیضی ${\displaystyle \,\!0}$ ${\displaystyle {\frac {4b}{3\pi }}}$ ${\displaystyle {\frac {\pi ab}{2}}}$
نیمه سهمی گون The area between the curve ${\displaystyle y={\frac {h}{b^{2}}}x^{2}}$ and the ${\displaystyle \,\!y}$ axis, from ${\displaystyle \,\!x=0}$ to ${\displaystyle \,\!x=b}$ ${\displaystyle {\frac {3b}{8}}}$ ${\displaystyle {\frac {3h}{5}}}$ ${\displaystyle {\frac {2bh}{3}}}$
سهمی The area between the curve ${\displaystyle \,\!y={\frac {h}{b^{2}}}x^{2}}$ and the line ${\displaystyle \,\!y=h}$ ${\displaystyle \,\!0}$ ${\displaystyle {\frac {3h}{5}}}$ ${\displaystyle {\frac {4bh}{3}}}$
Parabolic spandrel The area between the curve ${\displaystyle \,\!y={\frac {h}{b^{2}}}x^{2}}$ and the ${\displaystyle \,\!x}$ axis, from ${\displaystyle \,\!x=0}$ to ${\displaystyle \,\!x=b}$ ${\displaystyle {\frac {3b}{4}}}$ ${\displaystyle {\frac {3h}{10}}}$ ${\displaystyle {\frac {bh}{3}}}$
General spandrel The area between the curve ${\displaystyle y={\frac {h}{b^{n}}}x^{n}}$ and the ${\displaystyle \,\!x}$ axis, from ${\displaystyle \,\!x=0}$ to ${\displaystyle \,\!x=b}$ ${\displaystyle {\frac {n+1}{n+2}}b}$ ${\displaystyle {\frac {n+1}{4n+2}}h}$ ${\displaystyle {\frac {bh}{n+1}}}$
قاچ دایره The area between the curve (in polar coordinates) ${\displaystyle \,\!r=\rho }$ and the pole, from ${\displaystyle \,\!\theta =-\alpha }$ to ${\displaystyle \,\!\theta =\alpha }$ ${\displaystyle {\frac {2\rho \sin(\alpha )}{3\alpha }}}$ ${\displaystyle \,\!0}$ ${\displaystyle \,\!\alpha \rho ^{2}}$
قطعه دایره ${\displaystyle \,\!0}$ ${\displaystyle {\frac {4R\sin ^{3}{\frac {\theta }{2}}}{3(\theta -\sin {\theta })}}}$ ${\displaystyle {\frac {R^{2}}{2}}(\theta -sin{\theta })}$
Quarter-circular arc The points on the circle ${\displaystyle \,\!x^{2}+y^{2}=r^{2}}$ and in the first quadrant ${\displaystyle {\frac {2r}{\pi }}}$ ${\displaystyle {\frac {2r}{\pi }}}$ ${\displaystyle {\frac {\pi r}{2}}}$
کمان نیم دایره The points on the circle ${\displaystyle \,\!x^{2}+y^{2}=r^{2}}$ and above the ${\displaystyle \,\!x}$ axis ${\displaystyle \,\!0}$ ${\displaystyle {\frac {2r}{\pi }}}$ ${\displaystyle \,\!\pi r}$
کمان دایره The points on the curve (in polar coordinates) ${\displaystyle \,\!r=\rho }$ØŒ from ${\displaystyle \,\!\theta =-\alpha }$ to ${\displaystyle \,\!\theta =\alpha }$ ${\displaystyle {\frac {\rho \sin(\alpha )}{\alpha }}}$ ${\displaystyle \,\!0}$ ${\displaystyle \,\!2\alpha \rho }$

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