重心列表

描述	图形	${\bar {x}}$	${\bar {y}}$	面积
三角形		${\frac {b}{3}}$	${\frac {h}{3}}$	${\frac {bh}{2}}$
四分之一圆		${\frac {4r}{3\pi }}$	${\frac {4r}{3\pi }}$	${\frac {\pi r^{2}}{4}}$
半圆		$\,\!0$	${\frac {4r}{3\pi }}$	${\frac {\pi r^{2}}{2}}$
四分之一椭圆		${\frac {4a}{3\pi }}$	${\frac {4b}{3\pi }}$	${\frac {\pi ab}{4}}$
半椭圆	椭圆 ${\frac {x^{2}}{a^{2}}}+{\frac {y^{2}}{b^{2}}}=1$ 与 $\,\!x$ 轴所围成的图形	$\,\!0$	${\frac {4b}{3\pi }}$	${\frac {\pi ab}{2}}$
扇形	曲线 $\,\!r=\rho$ ，直线 $\,\!\theta =-\alpha$ 与直线 $\,\!\theta =\alpha$ 所围成的图形	${\frac {2\rho \sin(\alpha )}{3\alpha }}$	$\,\!0$	$\,\!\alpha \rho ^{2}$
四分之一圆弧	第一象限内的曲线 $\,\!x^{2}+y^{2}=r^{2}$	${\frac {2r}{\pi }}$	${\frac {2r}{\pi }}$	${\frac {\pi r}{2}}$
半圆弧	$\,\!x$ 轴上方的曲线 $\,\!x^{2}+y^{2}=r^{2}$	$\,\!0$	${\frac {2r}{\pi }}$	$\,\!\pi r$
圆弧	从 $\,\!\theta =-\alpha$ 到 $\,\!\theta =\alpha$ 的曲线 $\,\!r=\rho$	${\frac {\rho \sin(\alpha )}{\alpha }}$	$\,\!0$	$\,\!2\alpha \rho$

参见

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