Measuring Cattle
A physics teacher, a businessman and a university mathematician were all challenged to build the shortest possible fence around a small herd of resting cattle. The physics teacher went first. He took out a piece of graph paper and plotted the position of each cow. Next he introduced an xy-axes and gave each cow a pair of coordinates. Then he determined the lines connecting all the points. Finally he constructed a fence based on his diagram. When he finished he turned to the others and said "I'm done. And since the interior region bounded by the line segments connecting the cattle-points is convex, it follows that the boundary is minimal. Q.E.D." Then it was the businessman's turn. He began by calling the physicist an idiot and saying that it was no wonder young people entering the work force were useless with teachers like him. And if the physicist worked in his company, then he would fire him and fire the man who hired him. Finally he calmed down and went to work. First he secured a strong fence-pole near the cattle. Next he attached one end of a six-foot-high roll of wire fence to the pole and walked around the cows slowly letting out the roll of wire fence until he came back to the post. Then he gave the roll to his assistant and told him to start pulling. The businessman ran around the outside of the fence kicking the cows, flailing his arms, and screaming at them to make them get up and move into the middle. All the while he was yelling to his assistant "Pull the Fence tighter!" "Pull the Fence tighter!" Finally the cows were shoved so close together that they couldn't move and the fence was wrapped around them so tightly that it was leaving marks on their hides. The businessman nailed the other end of the fence to the post, cut away the roll and said "There, that is the shortest fence." Finally it was the mathematician's turn. He had been solving differential equations in his head and had wandered away and had forgotten about the problem. So they had to find him and explain it to him all over again. Then he asked questions that nobody could understand like "Am I allowed to assume the Pythagorean metric over a Euclidean space?". Finally the businessman threatened to hit him if he didn't get started. "Okay, okay, but I think the restraints are ill-stated" he said. Then he walked over to the roll of wire fence, cut off a small piece, wrapped it around himself and said "I'm on the outside."