Drexel dragonThe Math ForumDonate to the Math Forum


Math Forum
 Ask Dr. Math
 Discussions
 Internet Newsletter
 MathTools
 Problems of the Week
 Teacher2Teacher
 Teacher Exchange
 Workshops

Search All of the Math Forum:
Browse our Internet Mathematics Library

Views expressed in these public forums are not endorsed by Drexel University or The Math Forum.


Math Forum » Discussions » Math Topics » geometry.college.independent

Topic: How many rectangles are in an n by n square array of dots?
Replies: 4   Last Post: Sep 9, 2006 11:14 PM

Advanced Search
Reply to this Topic Reply to this Topic

Back to Topic List Back to Topic List Jump to Tree View Jump to Tree View   Messages: [ Previous | Next ]
Oliver Stemforn

Posts: 48
Registered: 9/2/06
How many rectangles are in an n by n square array of dots?
Posted: Sep 8, 2006 9:56 PM
  Click to see the message monospaced in plain text Plain Text   Click to reply to this topic Reply

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?

*** For instance, if the dots were
(0,0),(0,1),(1,0), and (1,1), (meaning n = 2) then there would be a total of one rectangle for this array.
(In this case it would be described more specifically as a square if connected.)

Point your RSS reader here for a feed of the latest messages in this topic.

[Privacy Policy] [Terms of Use]

© Drexel University 1994-2015. All Rights Reserved.
The Math Forum is a research and educational enterprise of the Drexel University School of Education.