Re: how many dimensions do I need?

On Oct 29, 11:07 am, "narutocan...@xxxxxxxxx" <narutocan...@xxxxxxxxx>
wrote:
hi

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)

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)?

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)

(If m=4 I am sure only one layer is needed)
I need help with when m>4.

Thanks.

Your points form complete graphs K(n). Tetrahedron K(4) can be
compressed on one of its sides (without crossings), or bent to a
square with both diagonals. Complete graphs K(n) are
(n - 1) dimensional bodies and n dimensional planes. Therefore, we can
not see K(n) properly, without crossings or one of its edges going
through its body (trigonal bipyramide).
kunzmilan
.

Relevant Pages

  • Re: GIMP and MySQL
    ... in learning how to do this using several layers in Paint Shop Pro, ... gives me the flexibility I need to edit origins, dimensions, and colours, ... I have to go back and reconstruct hundreds of such images. ...
    (comp.graphics.apps.gimp)
  • Re: determining image dimensions/resizing precisely
    ... >> Lorem Ipsum wrote: ... >>> It remembers the last dimensions you used. ... I highlight one of the layers in the palette (if I ... If I am, then Yes sir, there is a way to change ...
    (comp.graphics.apps.photoshop)
  • Re: determining image dimensions/resizing precisely
    ... >> It remembers the last dimensions you used. ... >> Try automating from the file browser. ... layers in acccord. ...
    (comp.graphics.apps.photoshop)
  • Re: EasyPC Gerber "Dimensions" File Problem
    ... marked reference point and the dimensions to each side of the PCB ... soldermask layers, which their FreeDFM automatically creates from ... EasyPC had created. ... I'd never seen the inside of a Gerber file, before this, and don't ...
    (sci.electronics.cad)
  • 2 figures to be same height and size
    ... I have 2 graphs that are different ... dimensions and I would like them to print out side by side and to be ... number from the Herbert data after fitting Model 1 to cane yield.} ... Does anyne have any ideas? ...
    (comp.text.tex)