From THE CHRONICLE of High Education March 12, 1999

WELL, it's finally happened. The fragrance industry has discovered "math appeal." Givenchy has a new men's cologne called Pi. In a recent National Public Radio segment, the reporter David Kestenbaurn attributed the name of this new scent to the public's growing love of technology, and the perception of technology--and hence mathematics and numbers--as cool.

But maybe we're not giving Givenchy enough credit. Was it just some marketing intuition on the company's part that brought about the fragrance Pi, or was it a more subtle appreciation of the number in and of itself9 Because if any number were poised to make a fashion statement, it would be pi.

To begin with, this is a number that has an exotic Greek name, and it's one-word appellation echoes the sexy Madonna, Cher, and Fabio. Of course, when we refer to pi in writing, we use a delicate and mysterious symbol, just as we do for the artist formerly known as Prince. In addition, pi is already famous to people around the world, recognized since 2000 B.C. as the ratio of the circumference of any circle to its diameter. That is, take any circle, and measure the distance around--that's the circumference. Then compare that to the diameter--the distance across when you go through the center. What you'll find is that you need just a little more than three times the diameter to get the circumference--and the exact number of diameters you need is pi. That is true for every circle. Pi is universal!

So exactly what number is pi?

 Well, as with many alluring things, pi is hard to pin down. You see, pi is an "irrational" number. That means that when you figure out pi's decimal expansion--that is, calculate its value beyond the decimal point--you find that pi is full of surprises. If pi were "rational"--in other words, a fraction--we would get either an expansion that stopped somewhere, such as 3.14, or one that repeated itself, such as 3.141414. But, instead, the list of digits that we get seems so arbitrary as to be almost whimsical. There is no telling what will come next, as you try to calculate its exact value. But to say simply that pi is irrational doesn't even begin to speak to the difficulty we have in describing pi. Its unpredict
ability is cabalistic and mysterious, for, even more than irrational, pi is "transcendental." Although some irrational numbers satisfy the simple relations of a polynomial (meaning that some combination of their powers add up to zero, in which case they are "algebraic"), the powers of pi are not subject to such simple coercion. One might even say, as mathematicians do, that they are independent!

Foreign, unpredictable, otherworldly, yet as common as a circle, the number pi teases and tempts us--it's easy to find, but hard to know. Why, among mathematicians there still rages a fierce, unsettled debate about whether pi is a "normal" number--that is, whether the digits 0 through 9 each occur on average one-tenth of the time in the never-ending decimal expansion of pi. The questions that surround pi's normalcy make it a veritable poster number for the fashion world's ambiguous and androgynous advertising campaigns.

So that's pi--an exotic, sensual paradox. Surely Givenchy must have known that this tiny name contained such a wealth of meaning and emotion. And, just think, there is an infinity of other numbers out there with similar qualities from which the fragrance and fashion world may choose. I suppose that if Pi is a hit, we may even begin to see fragrances named after functions. Of course, you need look no further than trigonometry to find two likely candidates: tan and sin.

Daniel Rockmore is an associate professor of mathematics and computer science at Dartmouth College.