A farmer buys a truckload of fencing material, and is looking to pen in his cattle. So, he gets an engineer, a physicist, and a mathematician to look over the situation and says, "Whoever builds the fence that gives my cattle the most area to graze gets $1000 dollars."
The engineer thinks he's got it licked. He knows that with any amount of fencing material a circle will enclose the most area. He builds a circular fence and shows the farmer.
"That’s very good," says the farmer.
The physicist thinks he's got the engineer beat. He disassembles the circular fence and builds a new one. His fence is one long, straight line. He shows it to the farmer and explains, "The fence is so long that we can assume each end goes out to infinity. Therefore the enclosed area is half the earth. You can't do much better than that!"
The farmer says, "Well, that’s quite odd, but I suppose I can't argue with it."
The mathematician looks disapprovingly at the other two. He knocks down a small section of the physicist’s fence and builds a new one. It’s a very, very small fence that forms a circle around his feet. He looks up and triumphantly says, "I declare myself to be on the outside."
He collects his $1000 and goes home.