Re: how many dimensions do I need?



William Elliot wrote:
On Wed, 29 Oct 2008, narutocanada@xxxxxxxxx wrote:

1. I have n points, each point needs to connect with all the other
points (total of (n-1)! lines), how many diemensions do I need in
general so that no lines are crossed. (lines do not have to be
straight)

3 if n > 3; 2 if n = 3; 1 if n = 2; 0 if n < 2.

When n = 1, you don't need (n - 1)! = 1, but 0 lines.

2. If each point is allowed only m lines (going out or coming in),
what is the minimum dimensions needed (of the n points, two of them
are fully connected to all the other points)?

Impossible if m < n - 1. If m >= n - 1, then as above, except
. . when n = 1 and m >= 1; 2 dimensions.

Note that when n = 0, m = 0 is the only possible value for m.

3. (related to 2) let's say each point is actually some electronic
component and has only a maximum of m lines going out or in, how many
layers of PCB board are needed? (there are only two points represent
power and ground that connect with every other points)

You need to modify the problem accordingly. Be sure
to note that the power and ground aren't connected.

(If m=4 I am sure only one layer is needed)

If m = 4 = n the number of components, then two layers are needed.

I need help with when m>4.

Is n > m?

In general yes, n is usually a lot greater than m. (I can assume m is
some fixed number say 4,5,6...) (n is usually very very big)


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