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Cut Wire (Posted on 2005-05-20) Difficulty: 3 of 5
A piece of wire is to be cut into two pieces (one bent into the shape of a regular p-gon and the other a regular q-gon).

If

1) p = 2*q,
2) 2*perimeter(q-gon) = 3*perimeter(p-gon), and
3) the sum of the two areas is minimized;

then what is the value of q?

See The Solution Submitted by Bractals    
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intuition | Comment 4 of 6 |
This looks like a great problem, the kind I love.  Haven't read any other responses yet.  But I won't have time to work on it until tomorrow.  But before any work is done, it seems to me that if we were making circles instead of polygons, we would want the 2 pieces of wire to be equal in order to enclose the minimum total area.  For any given piece of wire, a circle maximizes the area for that amount of perimeter, so I would assume a triangle minimizes the area.  So my first intuition is that q=3.   But tomorrow, I'll try to utilize what I learned from college tuition, rather than intuition, and figure it out;  see if I get the same as Charlie.
  Posted by Larry on 2005-05-20 22:31:26
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