Why Pi Fact Sheet

“This value, represented by the symbol π (pi), has puzzled mathematicians for nearly four thousand years, generating more interest, consuming more brainpower, and filling more waste baskets with discarded theories than any other single number…you will never find an exact value for π.” **David Blatner** The Joy of π...

π Humankind’s fascination with pi vastly transcends practical need. “Ten decimals are sufficient to give the circumference of the earth to the fraction of an inch [if earth were a perfect circle which it is not], and thirty decimals would give the circumference of the whole visible universe to a quantity imperceptible with the most powerful telescope.” Simon Newcomb quoted in *Mathematics and the Imagination* by Edward Kasner and James Newman.

π Pi’s symbol is the 16th letter of the Greek alphabet (π).

π The first time the symbol π (16th letter of the Greek alphabet) was used to denote pi was in William Jone’s *Symopsis Palmariorum Matheseos* published in 1706.

π Egyptian scribe Ahmes’ “Rhind Papyrus” implies a pi ratio of 3.16049 over 3,650 years ago – within one percent of the true value – and it is the first know reference to pi.

π A number of ancient Greeks, including Archimedes of Syracuse, offered values for pi starting about 2,500 years ago.

π China’s Ch’ang Hong implied a pi ratio of 3.162 about 1,800 years ago.

π 1,500 years ago Chinese astronomer Tsu Ch’ungchih and his son, Tsu Keng-chih deduced that pi is approximately 3.1415929 – astoundingly they were within 8-millionths of 1 percent difference from the now-accepted value for pi.

π Also around 1,500 years ago in India, mathematician Aryabhata approximated pi at 3.1416.

π In 1579 French lawyer and mathematician Francois Viète for the first time described pi using an infinite product, one of the first steps in the evolution of mathematics toward trigonometry and calculus.

π German mathematician Ludolf van Ceulen spent most of his adult life calculating pi to 35 decimals by the time of his death in 1610 – legend says his pi value was engraved on his tombstone in St. Peter’s church in Leyden, Germany. The tombstone has since been lost and there is no report if it was round or rectangular in shape.

π Leonardo da Vinci (1452-1519) developed a novel way to measure the area of a circle using the rotation of wheel half the thickness of its radius.

π By 1699, Englishman Abraham Sharp found 72 decimals of pi.

π By 1873, Englishman William Shanks calculated pi to 707 digits. “The accomplishment was hailed throughout the civilized world 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, making all subsequent numbers wrong -- an error that was not discovered until 72 years later!)

π In 1947 English mathematician D.F. Ferguson was believed to be first to use a mechanical calculator to compute pi. He computed pi to 808 digits. In 1948, Levi Smith and John Wrench found the 1,000th digit of pi. Crude calculators of the era could only compute one or two additional digits per day.

π In 1948 in Aberdeen, Maryland, George Reitwiesner, John von Neumann and N.C. Metropolis used one of the earliest computers, ENIAC, to compute pi to 2,037 digits. The ENIAC had 19,000 vacuum tubes and hundreds of thousands of transistors and capacitors. It could compute an additional pi digit every two minutes.

π In 1958, an IBM 704 computer calculated the first 707 digits of pi in 40 seconds – a feat that had taken a year on the ENIAC computer a decade earlier, and had taken mathematician William Shanks a major portion of his adult lifetime to do by hand. In 1973, Jean Guilloud and M. Bouyer found the one millionth digit of pi (which happens to be 1). In 1982, pi was calculated past the eight millionth digit in Japan. By 1995, David and Gregory Chudnovsky had computed pi to the one billionth digit.

π “Computing pi is the ultimate stress test for a computer – a kind of digital cardiogram.” Islands of Truth by Ivars Peterson.

π On October 4, 2006, Akria Haraguchi, a 60 year old Japanese mental health counselor who lives near Tokyo, recited pi to 100,000 decimal places from memory. It took him fourteen and a half hours. Haraguchi is seeking to be listed in the *Guinness Book of Records *which at the time, listed Hiroyuki Goto also of Japan, as the record holder having recited 42,195 pi decimal places from memory in February of 1995.

π In April, 1995, the Reuters wire service reported that a twelve-year-old Chinese boy, Zhang Zhuo, recited the value of pi to 4,000 decimal places from memory. It took him twenty-five minutes. This is probably a world record for a pre-teen.

π Many believe that the North American record is held by Gaurav Raja. In 2006 he recited 10,980 digits of pi. At the time, he was a junior in high school in Roanoke, Virginia, and among other recognition, he appeared on the *Today Show*.

π “Since there are 360 degrees in a circle and pi is intimately connected with the circle, we eagerly look at the 360th digit. Again we are rewarded with a most remarkable fact. At [the 359th digit] we find 360. Thus 360 is ‘centered’ over [the 360th digit].” *The Magic of Pi*, Monte Zerger.

π “You can determine your hat size by measuring the circumference of your head, then divide by pi, and round off to the nearest one-eighth inch.” *The Joy of Pi*, David Blatner.

“The history of π is a quaint little mirror in the history of man.” **Petr Beckman** A History of π