
Mathematic modelization
Hello,
I have thought of this math problem I haven't been able to solve, but it must have a simple solution.
We have an undefined (either even or odd) number of line segments and we want to connect their end dots except two of them (for all the set like if a fluid could get in by the unconnected dot, pass through all the segments and connections and them go out by the other unconnected dot).But there is an imposition: the connection cannot connect two segments that are side by side. Here is an uncompleted sketch
How can we know wherever it is better to have an odd number of line segments or an even one as to use the less length of connection?
What is, then, the best disposition of the connections (two by two and then the last one connects with the first one, three by three, etc)?
I guess the way to solve this problem is to create a Cartesian model of it, but I don't know what to do then.
Merry Christmas
Jaime