Geometrical centre

1. Dec 2, 2011

anigeo

Could anyone tell me what actually the geometric centre of a body is?
please don't cite references from centre of mass or gravity.i want to know what it is in terms of its geometricity.

2. Dec 2, 2011

HallsofIvy

Staff Emeritus
You might want to google or otherwise look up "centroid". If you can find formulas describing the body it is the the x, y, and z coordinates given by
$$\overline{x}= \frac{\int\int\int xdV}{\int\int\int dV}$$
$$\overline{y}= \frac{\int\int\int ydV}{\int\int\int dV}$$
$$\overline{z}= \frac{\int\int\int zdV}{\int\int\int dV}$$

The denominator is, of course, the volume of the body.

If you don't mind my using dirty words, that is, in fact, the "center of mass" or "center of gravity" assuming a constant density where you replace $dV$ with $\rho dV$, $\rho$ being the density. Since it is constant it can be taken out of the integrals, and, since it is in both numerator and denominator, will cancel.