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2007-03-14, 06:54   #12
mfgoode
Bronze Medalist

Jan 2004
Mumbai,India

40048 Posts

Quote:
 Originally Posted by m_f_h If I remember well, something looking like >-< where angles are 120° (?) I think you can get the result by using a "soap bubble computer"

If they are the angles the sum around the origin will be 4 x 120 = 480*
A point only has 360* around it.
I will say the four angles will be 90 * each if that is possible in this rectangle.
Mally

Last fiddled with by mfgoode on 2007-03-14 at 06:55

2007-03-14, 09:57   #13
davieddy

"Lucan"
Dec 2006
England

6,451 Posts

Quote:
 Originally Posted by mfgoode If they are the angles the sum around the origin will be 4 x 120 = 480* A point only has 360* around it. I will say the four angles will be 90 * each if that is possible in this rectangle. Mally
The network consists of a pair of linked nodes, each connected
to a pair of vertices. So each node has three roads.

If fixed width font were available, text diagrams would be easier
but I'll try. :>-<: should have been clear enough.

A B
\ /
+--+
/ \
D C

Last fiddled with by davieddy on 2007-03-14 at 10:01

 2007-03-14, 11:44 #14 davieddy     "Lucan" Dec 2006 England 6,451 Posts Conjecture The angle between routes in the minimum length network problem is never less than 120 degrees. I think this applies to any number of dimensions. David
2007-03-14, 12:54   #15
axn

Jun 2003

7×683 Posts

Quote:
 Originally Posted by davieddy If fixed width font were available...
Code:
A      B
\    /
+--+
/    \
D      C
Here you go. You're welcome

 2007-03-14, 14:04 #16 davieddy     "Lucan" Dec 2006 England 6,451 Posts THX I think even Mally might understand that
2007-03-14, 16:03   #17
mfgoode
Bronze Medalist

Jan 2004
Mumbai,India

22·33·19 Posts

Quote:
 Originally Posted by davieddy THX I think even Mally might understand that

Well Davie thats just what I was imagining.

I am not sure of any angle being = 120* for a minimum unless it is vigorously and mathematically proved. This is not as difficult as it seems. Just get a function involving angles or sides and deriving and solving for max , min. lengths. It will give you a test of your differentiating powers.

Come on Davie Im sure you can do it as I am not inclined to go to such a length.

Mally

 2007-03-14, 19:31 #18 davieddy     "Lucan" Dec 2006 England 6,451 Posts That's not the way I solved your original triangle problem, my rectangle or arrived at my conjecture. And it is not the simplest proof of my conjecture. It boils down to recognizing that 3 vertices linked by a "V" with angle <120 are linked more efficiently with a "Y" with 120 degree angles. It follows that no more than 3 routes meet at a node/vertex. The conjecture doesn't give a recipe for finding the best network though David
 2007-03-16, 10:18 #19 davieddy     "Lucan" Dec 2006 England 6,451 Posts It's like talking to a brick wall
 2007-03-19, 15:31 #20 davieddy     "Lucan" Dec 2006 England 144638 Posts Did you approve of my construction?

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