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: <email@example.com>
- 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:
>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.
>You now have rescaled the object without moving its center of gravity.
>This is the "fix" mentioned below.
Right. I knew that but the poster didn't say he wanted the
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
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