Search All of the Math Forum:

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

Notice: We are no longer accepting new posts, but the forums will continue to be readable.

Topic: Continous path on square grid
Replies: 15   Last Post: Feb 6, 2013 7:04 PM

 Messages: [ Previous | Next ]
 Willem Posts: 9 Registered: 12/29/10
Re: Continous path on square grid
Posted: Feb 1, 2013 10:23 AM

Willem wrote:
) clive tooth wrote:
) ) Let a P(n,s) be a continuous path, made of s straight sections, which
) ) passes exactly once through each of n^2 points arranged in a square
) ) array.
) )
) ) So, here is a P(3,4)...
) ) http://www.flickr.com/photos/lhc_logs/8435448440/in/photostream
) )
) ) I know of a P(4,6). But I cannot find a P(5,8). Any takers?
)
) IIRC, I figured out a way to get P(n,n*2-2) by beginning at P(4,6) in
) such a way that adding a row and column required two extra lines.
)
) I can't remember exactly what that beginning sequence was though.

Ah yes, now I remember. If you take the 3x3 solution you posted, the last
line can be extended upward, and then you can draw lines right and down,
adding a row and column to the top and right respectively. From there on
you can keep on spiraling outward.

(Fixed width)

8-O-O-O-O-9
| |
O 4-O-O-5 O
| | | |
O 1-O-O-2 O
| |\ /| |
O O O O O O
| | X | |
O O O # O O
| |/ | |
7-3-O-O-6 10

SaSW, Willem
--
Disclaimer: I am in no way responsible for any of the statements
made in the above text. For all I know I might be
drugged or something..
No I'm not paranoid. You all think I'm paranoid, don't you !
#EOT