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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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Calculus? | Comment 1 of 6

This doesn't seem like calculus to me.   If you want to minimize the area for a given perimeter, make the polygon have as few sides as possible. 

So q=3

I thought at first I wanted to maximize the area sum, so I came up with a formula in terms of q [perimeter(q-gon) = 1]

1/(2b*tan(180/b)) + 9/(16b*tan(90/b))

but this function strictly increases anyway.


  Posted by Jer on 2005-05-20 19:07:25
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