Finding a formula for a sum
- To: mathgroup at smc.vnet.net
- Subject: [mg35104] Finding a formula for a sum
- From: Matthias.Bode at oppenheim.de
- Date: Tue, 25 Jun 2002 03:39:48 -0400 (EDT)
- Sender: owner-wri-mathgroup at wolfram.com
when trying to find the number of diagonals in a convex polygon (all corners
on the perimeter of a circle) with n corners I came across that sum:
+(n-3) ; up to here = diagonals in a triangle.
+(n-3) ; up to here = diagonals in a quadrangle.
+(n-4) ; up to here = diagonals in a pentagon.
+(n-5) ; up to here = diagonals in a hexagon.
+(n-6) ; up to here = diagonals in a heptagon.
and so on.
I found the general formula (n*n -3*n)/2 with pencil and paper.
How could I coax MATHEMATICA into helping me to find the generalization in
this case - and of course for more difficult ones as well?
Sal. Oppenheim jr. & Cie. KGaA
Koenigsberger Strasse 29
D-60487 Frankfurt am Main
Tel.: +49(0)69 71 34 53 80
Mobile: +49(0)172 6 74 95 77
Fax: +49(0)69 71 34 95 380
E-mail: matthias.bode at oppenheim.de
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