Fencing in Cattle Three gentleman who excel in their respective fields are invited to compete in a competition. Competing are: a top Engineer, a shrewd Businessman, and an award-winning Mathematician. The judges, in turn ask each gentleman to fence in a herd of cattle using the shortest length of fence. The engineer goes first. He takes out a large sheet of graph paper, and maps out the outermost foot of each of the outermost cows. He then measures exactly how much fence is required to create a polygon around the herd, and erects the fence. He is particularly pleased with his job, and has used only 451.39m of fence. Next it is the businessman's turn. He takes a long length of fence, and quickly runs it around the herd with no particular care. He then uses all his strength to tighten, and tighten, and tighten until all of the cows are squished together nearly on top of one another. The cows are clearly in extreme pain, but he has completed his task, and done so using only 110m of fence. The judges are revolted by the sight, but admit that it seems the businessman has won, as the cows could not be fenced in any tighter. Nonetheless, it is only fair to give the mathematician a turn. At this point, the mathematician has wandered off solving differential equations or trying to prove P =/= NP, but eventually they find him, and explain the rules. The mathematician thinks for a few seconds, then grabs 2 meters of fence. He wraps it around himself and declares, ""I'm on the outside"".