Into how many regions can you partition the plane with m n-sided
regular polygons?
For example, with two squares you can achieve up to 10 regions by choosing the right size and position of your squares.
(In reply to
re: I agree. Full explanation. by JLo)
Proof that there is no more cleverer solution.
[I’m sure there is a more formal proof in existence that
someone more learned can offer as a reference, but this is the best I can
offer].
<o:p></o:p>
In a 2D plane, 2 straight lines may intersect but do not
form a closed space.
Three straight lines will create just one.
Add to this a fourth. Should it pass through an already
formed intersection, then the previous space is divided into 2, however should
it cross all other lines at any other point then the regions are 3.
<o:p></o:p>
Here we have:
Lines Max Regions
2
0
3
1
4
3
5
6
<o:p></o:p>
Ah! that triangle series again, and it is replayed in every
one of Jer’s star points.
<o:p></o:p>
|
|
Posted by brianjn
on 2006-09-07 20:47:09 |
re(2): I agree. Full explanation. Attempted Proof
