In the most simple case, take a very long rectangle and rotate it. There can be 
an infinity of horizontal rectangles inside it all having the same biggest area.

> -----Original Message-----
> From: [email protected] [mailto:postgis-users-
> [email protected]] On Behalf Of Pierre Racine
> Sent: Wednesday, December 04, 2013 9:42 AM
> To: PostGIS Users Discussion
> Subject: Re: [postgis-users] biggest rectangle contained within another
> polygon
> 
> You will have to define "biggest" more precisely. Biggest in terms of area?
> There might be many inner rectangles having the same biggest area. How to
> choose one over the other?
> 
> Pierre
> 
> > -----Original Message-----
> > From: [email protected] [mailto:postgis-users-
> > [email protected]] On Behalf Of tommaso
> > Sent: Wednesday, December 04, 2013 5:07 AM
> > To: PostGIS Users Discussion
> > Subject: [postgis-users] biggest rectangle contained within another
> polygon
> >
> > Hello, I need to calculate the biggest rectangle which is contained
> > within another polygon. A sort of inner envelope or inner bounding box.
> > I found this interesting article:
> > http://cgm.cs.mcgill.ca/~athens/cs507/Projects/2003/DanielSud/
> > Is it possible in Postgis?
> >
> > I have attached a picture with a example of what I need.
> >
> > Tom
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