## Re: Areal center

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• Oops. I accidentally reversed a couple of midpoints. Sorry. Sincerely, Jeff
Message 1 of 5 , Mar 10, 2009
Oops. I accidentally reversed a couple of midpoints.
Sorry.
Sincerely, Jeff

--- In Hyacinthos@yahoogroups.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
>
• 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
Message 2 of 5 , Mar 11, 2009
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
> >
>
>
>

[Non-text portions of this message have been removed]
• Dear Francois, Next time I ll screw up better, I promise. :-) I reversed two sets of midpoints and still got an S with
Message 3 of 5 , Mar 11, 2009
Dear Francois,
Next time I'll screw up better, I promise. :-)
I reversed two sets of midpoints and still got an S with Area(S,A',A")=Area(S,B',B")=Area(S,C',C")
Sincerely, Jeff

--- In Hyacinthos@yahoogroups.com, Francois Rideau <francois.rideau@...> wrote:
>
> 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
• Dear Francois, S is simply a point but I suppose it could be viewed as an area in a dual sense? Sincerely, Jeff
Message 4 of 5 , Apr 1, 2009
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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