# Mathematical Digest

### Short Summaries of Articles about Mathematics

in the Popular Press

Articles on mathematics and cicada behavior:

"Mathematicians explore cicada's mysterious link with primes," by Michael Stroh. *The Baltimore Sun*, 17 May 2004.

"Big buzz as cicadas arrive after 17-year gap," by Laura Nelson. *Nature*, 20 May 2004, page 233.

"The 17-Year Itch," by Tabitha M. Powledge. *Scientific American*, June 2004, pages 32-33.

"Bugs That Count," by Brian Hayes. *American Scientist*, September-October 2004, pages 401-405.

Residents in the eastern United States have recently witnessed the arrival of trillions of cicadas. The insects spend most of their time underground, but emerge for six weeks every 13 or 17 years, depending on the species, to reproduce. This year it is the 17-year cicadas that are now above ground. A natural question is, Why are the lengths of the cycles of both species prime numbers? No one knows for sure, but Stroh interviewed Glenn Webb of Vanderbilt University, who said that the prime-numbered lengths make it unlikely that the cicada cycle will coincide with a predator's cycle. The *Nature* article points out that the two different prime-year lengths for the two cicada species also make hybridization of the two species unlikely. The article in *Scientific American* casts doubt on the theories about the reasons for the prime periodicity, noting that "true periodicity is rare in cicadas."

Hayes' article goes into more depth about cicadas' cycles and runs some simulations to analyze population behavior.

*--- Mike Breen*