Amazing Trips

From a distance, the picture looks like a pen-and-ink study of a super famous painting, the Mona Lisa, by Leonardo da Vinci. Up close, all you see is a squiggly mess of connected lines that form a jagged but continuous path.

- By Ivars Peterson

Robert Bosch, a mathematician at Oberlin College in Ohio, created the image. It is not only an artwork but also a solution to a particular math problem.

Suppose you're planning a trip that takes you to, say, five cities scattered across the country.

You want to visit each city once, following a route that adds up to the shortest possible distance. In this case, there are 120 (5x4x3x2x1 = 120) routes that take you to each of the five cities in turn. You could add up the distances for each route to see which trip would be the shortest.