Spying pi in the sky.

It's calculated in the stars.

In the April 20 Nature, Robert A.J. Matthews of the applied mathematics and computer science department at the University of Aston in Birmingham, England, describes how to use the distribution of bright stars across the night sky to deduce a surprisingly accurate value of pi (p), the ratio of the circumference of a circle to its diameter.

"My aim was to extract something mathematically interesting from something we're all familiar with," Matthews says.

This result follows from an application of certain theorems in number theory. These hold that, given any pair of whole numbers chosen from a large, random collection of numbers, the probability that the two numbers have no common factor other than 1 is 6/[pi]2 (about 0.61). For example, in a set of numbers including 8, 9, and 27, 9 and 27 have the common factor 3, whereas 8 and 27, as well as 8 and 9, have no common factor apart from 1. It's possible to calculate the value of pi by determining what proportion of pairs of whole numbers selected from a large, random sample has no common factors.

As the source of random numbers for his "celestial" estimate of pi, Matthews used the angular separation between the positions of pairs of the 100 brightest stars. He checked a million pairs of these numbers for factors and obtained a value of 3.12772 for pi, which is within 0.5 percent of the actual value of 3.14159.... "The ancient Greeks used to believe that numbers lie at the root of all things," Matthews notes. "I guess this result tends to support that idea."