Rectangles

From: Graham Drabble (graham.drabble_at_lineone.net)
Date: 01/15/05 

Date: Sat, 15 Jan 2005 19:16:36 GMT

I was talking to a friend of mine the other day who is training to be
a primary teacher (5-9 year old). She mentioned an investigation that
the children were asked to do that consisted of drawing a rectangle
on squared paper, drawing the diagonl and then counting how many
squares it passes through (any square passed through conts as 1 even
if only partly touched so a 2x3 rectangle = 4).

I thought about this and decided there must be a way of solving this
mathematically. However I've not got far in solving it. What I've got
so far is:

if we define a rectangle with sides of length a and b then:

number of squares = f(a,b).

where b = na (n >=1 and is an integer)

f(a,b) = na

Where a and b share a common factor, m,

f(a,b) = m f(a/m,b/m)
ie f(4,6) = 2f(2,3)

Any suggestions? 

-- 
Graham Drabble
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