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: Who dares: Not I by Jer)
If I have this concept correct, I can manage 17 bounded regions and then the external using two intersecting quadrilaterals.
I trust that this description conveys what I mean.
Draw a hexagon with all internal angles about 120 deg.
Label the vertices A through F in a cyclic manner.
Join A to C and C to F. Join E to B and B to D.
[So far I have to triangles and a quadrilateral].
Now locate point X within the triangle bounded by the angle FCA. I complete this quadrilateral by joining Y to A and then to F.
Similarly I locate Y within the triangle bounded by angle EBD and join it to E and D.
Vertices X and C of quad. ACFX lie on the same side of BD.
Vertices B and Y of quad . BDYE lie on the same side of AC.
I haven't thought beyond that.
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Posted by brianjn
on 2006-09-11 23:32:55 |
re(2): Who dares: Not I
