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Re: How many rectangles are in an n by n square array of dots?
Posted:
Sep 9, 2006 1:35 AM
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On Sep 8, 2006, at 8:13 PM, Oliver Stemforn wrote:
> Let the n by n dots be in one plane, and let n be equal to or
> greater than 2. Rectangles here are understood to be squares or
> non-square rectangles. A rectangle counts only when each of its
> four vertices coincides with one of the dots of the array.***
>
> Can you come up with a polynomial in terms of n for the total
> number of rectangles for a general n by n array?
You are going to have to be more careful about when a rectangle
counts. Must the sides be horizontal/vertical? Or does the
rectangle formed by, say, (0,7), (4,10), (10,3), (6, 0) count when n
= 10? If so, the problem may be considerably more difficult than you
thought
--Lou Talman
Department of Mathematical and Computer Sciences
Metropolitan State College of Denver
<http://clem.mscd.edu/%7Etalmanl>
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