The geometry geeks (or space aliens, if you prefer) who stamp out intricate designs on the fields of the U.K. may have topped themselves this time.
British astrophysicist Mike Reed said last week that the giant formation that appeared outside the village of Wroughton in early June, and had stumped scientists and amateur enthusiasts attempting to decode it, has a simple explanation: Pi. That’s right. The world’s most popular irrational number, 3.14159 and so on, holds the key, Reed says. Starting from the circle in the center, a line spirals out toward the edge. The length of each segment, before it juts out, corresponds to a digit in pi. The smaller circle near the middle is the decimal point, Reed says, while the three larger dots near the edge are an ellipsis, indicating that the number never ends. Check out Wired‘s blog for a graph of the numerical progression.
The surprise for many was that it took so long for somebody to figure out the Wroughton crop circle. After all, crop circles tend to be based on geometric patterns—another circle that appeared in the same county of Wiltshire in 2002 clearly demonstrated the spiral shape of the Fibonacci sequence. The late Gerald Hawkins of Boston University popularized the idea that the geometric patterns were tied to the diatonic relationship of musical notes in the Western scale. Many patterns feature repeating fractals. But what many experts consider to be the most elaborate and complex crop circle design even seen in Britain seems to have hidden one of mathematics’ best-known number sequences in plain sight.
Well done, whoever you are. What’s next—the square root of two?