The sweet quest for pi

March 14, 2015

Saturday is the day when the circle gets squared — or at least gets expressed with as much clarity as the calendar can provide. This day comes along once in a century.

It’s 3/14/15, and those five digits signify one of the most mystical numbers in the universe.

That number, of course, is the infinite sequence of pi, which is a deceptively simple idea: the ratio of a circle’s circumference to its diameter.

This is the numeric expression of a perfect curve — a line endlessly looping. And as the nation pauses (or not) to celebrate Pi Day, it’s worth reflecting on the importance of this eternally hiccuping number usually expressed in a shape that looks like an end table: π.

The Babylonians and the ancient Egyptians were beguiled by pi 4,000 years ago. The Bible tells the story of King Solomon building a circular pool “ten cubits from the one brim to the other” and “thirty cubits did compass it round about,” meaning that the ancient Hebrews understood the number to be close to three.

Leonardo da Vinci suggested that ideal human proportions — the full extensions of arms and legs — decipher this divine puzzle.

Dutch mathematician Ludolph van Ceulen devoted much of his life to calculating digits of pi. By the time of his death in 1610, he had correctly determined 35 digits.

It wasn’t until the 18th century that Swiss mathematician Johann Heinrich Lambert proved that pi is “irrational,” meaning that the pattern of its ever-advancing digits never ceases and never repeats.

This didn’t stop the Indiana legislature in 1897 from trying to declare the number a simple 3.2. The lobbying of one professor C.A. Waldo of Purdue University kept the romance alive, however.

He persuaded a senator to declare that the government lacked the power to “establish mathematical truth.”

The quest to compute evermore digits of pi continues. The current record of more than 12 trillion is held by Alexander Yee and Shigeru Kondo; they had to stop in 2013 because they ran out of disk space.

On the other hand, NASA assures us that 16 digits are enough to ensure that the International Space Station stays in its correct orbit. Just 39 digits allow us to compute the volume of the observable universe to the nearest atom.

So why do we continue the push past 12 trillion? On the practical side, we can use our knowledge of pi to test supercomputers for accuracy and speed. We can analyze the effectiveness of new algorithms.

But the real reason is human nature: We’re satisfying our curiosity of what is possible, even if it means following a rope ever farther into the darkness. Be it the actual digits of pi or the properties the number exhibits, this thirst for knowledge turns mathematicians into treasure hunters.

So stop today — a once-in-a-century Super Pi Day, as it happens — and pay tribute to this weird number so intertwined with the workings of our universe. You’ll have plenty of company.

Thousands of published articles and books have pi in the title. It is a number with its own 324-page biography and 797-page source book. As for me, today at 9:26 a.m. and 53 seconds (the next five numbers in the sequence), my children tucked into a piece of pie.

It also bears mentioning that, in most of the rest of the world, where people put the month after the day when writing dates, there is no 3/14 — it would represent the third day of a nonexistent 14th month. If you’ll permit some circular reasoning on my part, that means today is as American as apple π.

Holm is an associate professor of mathematics at Cornell University.

© 2015, The Washington Post

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