Re: How to increase area of irregular polygon?

*To*: mathgroup at smc.vnet.net*Subject*: [mg39339] Re: How to increase area of irregular polygon?*From*: Steve Gray <stevebg at adelphia.net>*Date*: Wed, 12 Feb 2003 03:51:37 -0500 (EST)*References*: <b2ahjq$pk7$1@smc.vnet.net>*Sender*: owner-wri-mathgroup at wolfram.com

On Tue, 11 Feb 2003 10:00:26 +0000 (UTC), Garry Helzer <gah at math.umd.edu> wrote: >Steve, > >If you operate on an object with a linear transformation the >area/volume of the image is the original area/volume multiplied by the >determinant of the matrix of the linear transformation. [snip] >You now have rescaled the object without moving its center of gravity. >This is the "fix" mentioned below. Gray: Right. I knew that but the poster didn't say he wanted the centroid invariant. Rather than think of the determinant, I find it much simpler just to use the fact that the area of anything with constant shape goes as the square of its linear dimensions. This would also work for 3-D (with the cube), etc., and one can find the centroid in the same way.