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[EMHL] Re: Areal center

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  • Jeffrey Brooks
    Dear Francois, S is simply a point but I suppose it could be viewed as an area in a dual sense? Sincerely, Jeff
    Message 1 of 5 , Apr 1, 2009
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      Dear Francois,
      S is simply a point but I suppose it could be viewed as an area in a dual sense?
      Sincerely, Jeff

      > You are not doing wrong.
      > Area(S, A', A") = Area( S, B', B") = Area(S, C', C") ( where S is a
      > signed area) is just the definition of the areal center S of
      > triangles A'B'C' and A"B"C".
      > Friendly
      > Francois
      >
      > On Wed, Mar 11, 2009 at 1:33 AM, Jeffrey Brooks <cu1101@...> wrote:
      >
      > > Oops. I accidentally reversed a couple of midpoints.
      > > Sorry.
      > > Sincerely, Jeff
      > >
      > >
      > > --- In Hyacinthos@yahoogroups.com <Hyacinthos%
      > > 40yahoogroups.com>, "Jeffrey Brooks" <cu1101@> wrote:
      > >
      > > > Can someone please remind me the definition of areal center?
      > > > Something is not right here; that is I construct the areal
      > > > center following Quim Castellsaguer's The Triangles Web
      > > >
      > > > 1) Let A'B'C', A"B"C" be the two inscribed triangles, La the
      > > > line through A parallel to the line joining the midpoints of
      > > > B'C" and B"C'.
      > > > 2) Construct analogously Lb, Lc.
      > > > 3) The lines La, Lb, Lc intersect at the areal center S.
      > > >
      > > > Then I try Francois' choo-choo way from a previous message.
      > > > Both methods give a center S where Area(S,A',A")=Area(S,B',B")>
      > > > =Area(S,C',C").
      > > >
      > > > What am I doing wrong?
      > > > Sincerely, Jeff
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