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Old 2007-03-14, 06:54   #12
mfgoode
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Question

Quote:
Originally Posted by m_f_h View Post
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
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Old 2007-03-14, 09:57   #13
davieddy
 
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Quote:
Originally Posted by mfgoode View Post

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
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Old 2007-03-14, 11:44   #14
davieddy
 
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Default 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
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Old 2007-03-14, 12:54   #15
axn
 
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Quote:
Originally Posted by davieddy View Post
If fixed width font were available...
Code:
A      B
 \    / 
  +--+
 /    \
D      C
Here you go. You're welcome
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Old 2007-03-14, 14:04   #16
davieddy
 
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THX
I think even Mally might understand that
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Old 2007-03-14, 16:03   #17
mfgoode
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Smile linked nodes

Quote:
Originally Posted by davieddy View Post
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
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Old 2007-03-14, 19:31   #18
davieddy
 
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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
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Old 2007-03-16, 10:18   #19
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It's like talking to a brick wall
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Old 2007-03-19, 15:31   #20
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Did you approve of my construction?
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