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The fencing problem.  

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The Fencing problem Introduction A farmer has 1000m of fencing. Wit this, he wants to enclose a field, of the maximum area possible, of any shape, which ill use all of his fencing, and have the greatest area possible. This means, any shaper can be used, but it must be flat, so with no height inside the perimeter. The task of this project is to investigate which shape of field would give the maximum area, using only 1000m of fencing as a perimeter. I will now outline some hypotheses, to give a structure to my investigation. Firstly, I believe that shapes of a regular nature, with sides of equal length will provide the greatest area. If I then prove this to be correct, I further believe that shapes with a greater number of sides will have the greatest area, and this leads to the idea of a circle enclosing...

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