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Dick Klingens
Posts:
19
From:
Rotterdam (The Netherlands)
Registered:
12/3/04
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[HM] An Arbitrary Quadrilateral
Posted:
Jun 22, 2006 8:40 AM
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Dear Sam,
You wrote:
> Date: Wed, 21 Jun 2006 19:43:46 -0400
> From: Sam Kutler <reltuk@comcast.net>
> Subject: [HM] An Arbitrary Quadrilateral
>
> I just came across this geometrical theorem:
>
> Consider the centers of squares drawn outward he on the sides of
> an arbitrary quadrilateral.
> Join the opposite centers with line segments.
>
> Then, the line segments are equal and cut each other orthogonally.
>
> This seems to me a beautiful result. Have you seen it,
> and if so, how far back can you trace it?
In Dutch literature the theorem is know as: Van Aubel's theorem (Henri van Aubel,
1830-1906).
See:
http://www.pandd.demon.nl/lemoine/vanaubel.htm (in Dutch)
And, in English:
"Dual generalizations of Van Aubel's theorem" by Michael de Villiers.
(http://mzone.mweb.co.za/residents/profmd/aubel2.pdf)
Regards,
Dick Klingens
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