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Different lengths of lines on a pinboard
By Anonymous on Sunday, February 4, 2001 - 10:06 pm:

Hi All
I am trying to find out how many different lengths of lines can be found on square pinboards, in connection with the length of the square or as the nth term?

I know that:
2 by 2 square gives 2 lines
3 by 3 square gives 5 lines
4 by 4 square gives 9 lines
5 by 5 square gives 14 lines
6 by 6 square gives 19 lines

i have found that there is a formula for the no. of lines untill the 5 by 5 square, but this breaks down at the 6 by 6 square.
This is also the same between the 7 by 7 and 11 by 11 squares and the pattern once agian breaks at 12 by 12.
7 by 7 =26
8 by 8 =33
9 by 9 =41
10 by 10 = 50
11 by 11 = 60
12 by 12 = 70
13 by 13 = 82

If anyone can help me with a formula or in any other way please do help!

By James Lingard (Jchl2) on Monday, February 12, 2001 - 10:50 am:

I think that searching for an explicit 'formula' that's any better that what you know already may not get you anywhere.

How are you going about working out how many different lines there are? Do you know why the formula you've got almost works, and why it is not quite working exactly?

Can you write down what your formula is? It might be of interest to compare your formula with the actual numbers, and see how much difference there is between the two, for each size square.

James.