## MatheMUSEments

Articles for kids about math in everyday life, written by Ivars Peterson for Muse magazine.

## April 11, 2007

### Ant Math

Imagine stepping into a pitch-black room. How might you figure out the room's size in the dark? You could, for example, carefully follow the walls and count how many steps you took going from one corner to the next all the way around. That would give you a rough idea of how big the room was.

Certain ants have their own method for estimating size in the dark. Ants of the species Leptothorax albipennis live in small, flat cracks in rocks. A typical colony consists of a single queen, her brood, and between 50 and 100 workers. When a nest happens to get wrecked, the colony sends out scouts to find places to start a new nest.

How does a scout estimate a crack's size so it can tell if it would make a good nest?

Experiments by mathematical biologists Eamonn Mallon and Nigel Franks of the University of Bath in England show that a scout usually visits a possible home twice. On its first visit, the scout spends about two minutes in the crack. As it scurries about, it lays down a trail of smell molecules, or pheromones. On its second visit, it follows a different path, repeatedly crossing its first track, slowing down each time it does.

The scout ant apparently smells each crossing. It can then estimate the crack's size from the number of crossings: the more crossings, the smaller the floor area.

As long as a scout explores the whole crack, the method works for different cracks and for cracks of different shapes. It also works in complete darkness. It's a neat example of how animals can use very simple rules of thumb to make good decisions.

Muse, December 2000, p. 23.