From the September 2008 issue

Bob Berman’s strange universe: A piece of π

November 2008: Intelligent beings throughout the galaxy remain obsessed with 3.14.
By | Published: September 22, 2008

Knowing pi to a mere 39 places is good enough to calculate the circumference of the universe accurate to the diameter of an atom.

Read more of Bob Berman’s strange universe
October 2008: Astro-humiliation
December 2008: Plenty of nothing
See an archive of Bob Berman’s strange universe

Ever “chew on” a portion of π? It’s not a piece of cake. Pi has obsessed and tortured minds for centuries. This Greek letter, of course, represents the relationship between a circle and its diameter. It’s certainly known by smart aliens throughout the universe, since disks and spheres are everywhere.

Pi is a rock-solid “word” in the extraterrestrial lingua franca. Other numbers that tattooed Andromedan school-kids have memorized no doubt include the four-to-one mass ratio of hydrogen to helium, the speed of light, and the location of the nearest major galaxy (us) sitting dreamily 13° from the milky “Andromeda Way” crossing their sky.

The Old Testament repeatedly expressed the pi ratio as exactly three: A round altar (in 1 Kings 7:23 and 2 Chronicles 4:2) is said to be “ten cubits from edge to edge and 30 cubits around.” (A more correct circumference figure would have been 31½, but maybe they were seriously rounding off.) Jump ahead a half millennium to Archimedes, and we get a big official improvement to 3.1418.

Still no cigar. Pi is fascinating because it never evens out or ends. My 18-year-old daughter memorized its value to 75 decimal places. I went even further after a friend gave me a “Pi Pan” dish with 87 places inscribed around its edge. This neurosis-inducing item beckons daily. How far can you go? If you’re obsessive — and unemployed — you can probably recite at least the first six digits. All I can recall is 3.1415926535897932384626433832795028841971693993751058209749445923078164. I’ll mercifully stop there.

A wonderful feature of this perfectly random number pattern is that it’s accurately computed using a simple and interesting equation: π precisely equals 4 multiplied by 1 − 1/3 + 1/5 − 1/7 + 1/9 − 1/11 + 1/13 and on and on. Astoundingly simple, and the more of these fractions you include, the greater the accuracy.

Einstein seems to have been the first to point out that rivers obey pi. The ratio of a river’s straight-line distance from source to sea, when divided into its loopy path over the ground, is roughly equal to π.
Rivers acquire a meandering path because any small curve creates faster currents on the outer edge, where erosion then carves out a sharper bend. This in turn produces an even faster flow and accelerated material loss, since the mass of earth a river carries away is proportional to the sixth power of water speed.

So a river’s bend keeps sharpening. But a natural process limits this watery desire toward circularity: Too much of a curve makes the river double back on itself, forming a lake. We’re left with an average of half-circles and an overall value of 3.14. You can see this from the air or on a map. Simon Singh, in his 1998 book Fermat’s Enigma, explains that the ratio varies from river to river, with the appear­ance of pi being “the result of a battle between order and chaos.” Rivers that flow across gently sloping terrain are the ones most likely to follow the exact ratio of pi. A river cascading down steep topography moves too quickly for the pi effect to work.

We’d expect to see this on other worlds as well, except no other planet has rivers or streams of flowing water. It remains to be seen whether rivers of methane on Titan or elsewhere follow the same erosive pi-model.
Mars had flowing water millions of years ago, but no one’s yet sure whether they stuck around for a long time, or else were sudden, temporary, explosive events. The fluvial channels along the martian surface are ghosts from a long-ago era, and some appear π-curvy indeed. The only other liquid water within 4 light-years of the Mississippi is not the flowing variety, but oceans under satellite ice-surfaces.

Pi is fun. You can use it for quick astro-reckoning. Say you already know Jupiter’s width as nearly 90,000 miles (145,000 kilometers). Mentally multiply by three and you get its circumference: about 270,000 miles (435,000 km).

Knowing Jupiter rotates in 10 hours instantly tells you its equator moves at a screaming 27,000 mph (43,500 km/h) — the planet’s circumference divided by 10.

Jove’s waistline thus whizzes with amazing velocity, beating our own planet’s spin-speed 25 times over. No wonder its main features are horizontal streaks. Also no wonder whirling globs and chaotic eddies appear where zooming cloud belts rub against their neighbors. Suddenly a lot of things make sense. All from using pi.

In a class at a local high school, they plastered pi to 75 big digits around the room, forcing students to look at it hour after hour. In real life, its practical value requires only a few decimal places.

According to Singh, knowing pi to a mere 39 places is good enough to calculate the circumference of the universe accurate to the diameter of an atom. Anything more is clearly an annoying waste of time. So why do geeks keep going? Beats me. You’ll have to, er, find one and ask.