A rancher hired an architect, an engineer, and a mathematician to design the largest animal pen possible using only a limited number of fence segments.

The architect arranged all the fence pieces in a perfect square. “Making all sides equal in length maximizes the space,” he explained to the farmer, who looked on with interest.
Next, the engineer took the fence pieces and arranged them in a large circle. “Eliminating sides and making the pen round produces a shape with even greater area than a square,” he told the farmer, who was even more impressed.
Finally, the mathematician took only three fence pieces and arranged them in a triangle with himself in the middle. “I am outside the pen,” he declared.

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