Pi (π), the symbol used to describe the ratio of a circle’s circumference to its diameter, has fascinated and puzzled mathematicians for nearly four thousand years. In this work, Alan Rath, ever the math nerd, celebrates that obsession by building and programming a sculpture that counts π to 808 digits, which refers to a milestone in the calculation of π: the first time a mechanical calculator was used for the computation, in 1947.
The first known reference to π comes from an Egyptian scribe 3,650 years ago. Ancient Greeks offered values for π starting about 2,500 years ago. China’s Ch’ang Hong implied a π ratio of 3.162 about 1,800 years ago. 1,500 years ago, in India, Aryabhata approximated π at 3.1416. At about the same time, the Chinese astronomer Tsu Ch’ungchih and his son, Tsu Keng-chih deduced that π is approximately 3.1415929 – within 8-millionths of 1 percent difference from the now-accepted value.
In 1579 French lawyer and mathematician Francois Viète described π using an infinite product for the first time, one of the first steps in the evolution of mathematics toward trigonometry and calculus.
German mathematician Ludolf van Ceulen spent most of his adult life on the problem, and by 1610 had calculated 35 decimals. His π value was engraved on his tombstone. By 1699, Englishman Abraham Sharp found 72 decimals of π. In 1844, Zacharias Dase and Strassnitzky calculated 205 digits of π, but only 200 digits were correct.
By 1873, Englishman William Shanks calculated π to 707 digits. While it was hailed as the "unveiling of a great mathematical truth,” according to Joy of Pi by David Blatner, Shanks had made a mistake after the 527th place. All subsequent numbers were wrong, but the error wasn't discovered for 72 years.
In 1948, Levi Smith and John Wrench found the 1,000th digit of π. In the same year, one of the earliest computers, ENIAC (which used 19,000 vacuum tubes and hundreds of thousands of transistors and capacitors), was used to compute π to 2,037 digits. In 1958, an IBM 704 computer calculated the first 707 digits of π in 40 seconds. It had taken a year on the ENIAC computer and had taken William Shanks' adult lifetime to do it by hand. In 1973, Jean Guilloud and M. Bouyer found the one millionth digit of π (which happens to be 1). In 1982, π was calculated past the eight millionth digit and in 1995, David and Gregory Chudnovsky computed π to the one billionth digit.
But why pi?
"The beauty of pi, in part, is that it puts infinity within reach. Even young children get this. The digits of pi never end and never show a pattern. They go on forever, seemingly at random—except that they can’t possibly be random, because they embody the order inherent in a perfect circle. This tension between order and randomness is one of the most tantalizing aspects of pi.
"What distinguishes pi from all other numbers is its connection to cycles. For those of us interested in the applications of mathematics to the real world, this makes pi indispensable. Whenever we think about rhythms—processes that repeat periodically, with a fixed tempo, like a pulsing heart or a planet orbiting the sun—we inevitably encounter pi.
"...[P]i appears in the math that describes the gentle breathing of a baby and the circadian rhythms of sleep and wakefulness that govern our bodies. When structural engineers need to design buildings to withstand earthquakes, pi always shows up in their calculations. Pi is inescapable because cycles are the temporal cousins of circles; they are to time as circles are to space. Pi is at the heart of both.
"For this reason, pi is intimately associated with waves, from the ebb and flow of the ocean’s tides to the electromagnetic waves that let us communicate wirelessly. At a deeper level, pi appears in both the statement of Heisenberg’s uncertainty principle and the Schrödinger wave equation, which capture the fundamental behavior of atoms and subatomic particles. In short, pi is woven into our descriptions of the innermost workings of the universe."
– Steven Strogatz “Why Pi Matters,” The New Yorker, March 13, 2015