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three strategies for fencing in area

Question

A farmer challenges an engineer, a physicist, and a mathematician to fence off the largest amount of area using the least amount of fence.

The engineer made his fence in a circle and said it was the most efficient.

The physicist made a long line and said that the length was infinite. Then he said that fencing half of the Earth was the best.

The mathematician laughed at the others and with his design, beat the others. What did he do?

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