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Cutting planes with polygons (Posted on 2006-09-06) Difficulty: 3 of 5
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.

See The Solution Submitted by JLo    
Rating: 4.0000 (2 votes)

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re(2): Who dares: Not I | Comment 13 of 17 |
(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.


  Posted by brianjn on 2006-09-11 23:32:55

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