Services & Resources / Wolfram Forums
-----
 /
MathGroup Archive
2003
*January
*February
*March
*April
*May
*June
*July
*August
*September
*October
*November
*December
*Archive Index
*Ask about this page
*Print this page
*Give us feedback
*Sign up for the Wolfram Insider

MathGroup Archive 2003

[Date Index] [Thread Index] [Author Index]

Search the Archive

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.


  • Prev by Date: Factoring Methods
  • Next by Date: Re: Getting rid of the symbol -> after finding the root
  • Previous by thread: Re: Re: How to increase area of irregular polygon?
  • Next by thread: Re: triangles