Everyone knows that the value of pi is 3.14… er, something, but how many people know where the ratio comes from?
Actually, the proportion came from nature: it is the ratio between the circumference of a circle and its diameter, and it was always there, waiting to be discovered. But who discovered it? In honor of Pi Day, here’s a semi-short history of how pi came to be known as 3.14 (1592653589793238462643383279502884197169… and so on).
Editor’s Note: This article was originally published in 2010. We are republishing it today in honor of Pi Day, 3/14.
the history lesson
It is difficult to pinpoint who, exactly, was the first to be aware of the constant ratio between the circumference of a circle and its diameter, although human civilizations seem to have been aware of it as early as 2550 BC.
The Great Pyramid of Giza, which was built between 2550 and 2500 BC, has a perimeter of 1,760 cubits and a height of 280 cubits, giving it a ratio of 1760/280, or roughly 2 times pi. (A cubit is about 18 inches, although it was measured by the length of a person’s forearm and therefore varied from person to person.) Egyptologists believe these proportions were chosen for symbolic reasons, but of course we can never be too sure.
The oldest textual evidence for pi dates back to 1900 BC; both the Babylonians and the Egyptians had a rough idea of value. The Babylonians estimated pi to be about 25/8 (3.125), while the Egyptians estimated it to be about 256/81 (about 3.16). Archimedes did not calculate the exact value of pi, but instead found a very close approximation. He — he used 96-sided polygons to arrive at a value that was between 3.1408 and 3.14285. The ancient Greek mathematician Archimedes of Syracuse (287-212 BC) is considered to have been the first to compute an accurate estimate of the value of pi. He accomplished this by finding the areas of two polygons: the polygon that was inscribed within a circle and the polygon in which a circle was circumscribed (see the figure above, right).
The Chinese mathematician Zhu Chongzhi (AD 429-500) used a similar method to approximate the value of pi, using a 12,288-sided polygon. His best guess was 355/113.
The approximate ratio of pi also appears in the Bible in 1 Kings 7:23:
“And he made a molten sea, ten cubits from one edge to the other: it was round, and its height was five cubits; and a cord of thirty cubits encircled it round about.”
(I should point out that the Biblical ratio for pi might be more accurate than one might think, since cubits change depending on the length of a person’s forearm. So, assuming the Bible doesn’t quote cubits from the same person every time. ..)
In the 15th century, the Indian mathematician Madhavan of Sangamagramam discovered what is now known as the Madhava-Leibniz series (named after the German mathematician Gottfried Leibniz, who rediscovered the series in the 17th century), an infinite series that converges on four . Later, Madhavan calculated pi to 11 decimal places.
Later, in 1707, the Welsh mathematician William Jones was the first to use the Greek letter pi (π) to denote the constant proportion, although it was not until 1737 that the Swiss mathematician and physicist Leonhard Euler popularized the use of the symbol. The symbol π is taken from the Greek word for “perimeter”.
The most accurate calculation of pi before the advent of the computer was made by DF Ferguson, who calculated pi to 620 digits in 1945 (previously William Shanks had calculated pi to 707 digits in 1874, but only 527 of those digits were correct). .
Of course, then computers came on the scene and the calculation of pi knew no bounds, starting with DF Ferguson’s calculation of pi to 710 digits in 1947 with a desktop calculator to Takahashi Kanada’s calculation of pi to 206,158,430,000 digits in 1999 with a Hitachi SR8000.
Shigeru Kondo carried out the longest calculation of pi to date on October 19, 2011. Kondo used Alexander Yee’s y-cruncher program to calculate pi to 10 trillion digits, which is a record calculation for both supercomputers and computers. home computers.
So there you have it: the Egyptians calculated pi using pyramids (or did they calculate pyramids using pi?), Archimedes pulled out the 96-gon, Zhu Chongzhi bested it with a 12,288-gon (or did 12,192 best it?), Ferguson he calculated 620 digits by hand, and Kondo used a supercomputer to capture the current world record of 10 trillion digits.
Pi in pop culture
But wait, the obsession with pi isn’t just limited to mathematicians and scientists. Pi has a special place in popular culture, thanks to its prevalence in mathematical formulas and its mysterious nature. Even completely non-cerebral shows, books, and movies can’t help but mention the popular constant.
For example, pi is mentioned in a scene from Twilightin which vampire boy Robert Pattinson recites the square root of pi (and the energetic Kristin Stewart quickly shuts him up).
The Simpsons he also likes pi (and math references in general). In one scene, two girls at a school for the gifted play tag and say “Cross my heart and I hope to die, here are the digits that make up pi, 3. 1415926535897932384…” In another scene, a sign in the cemetery of Springfield says “Come for the funeral, stay for the π.”
Yes, like it or not, pi is everywhere. Here are a few more places she’s appeared:
- The main character in the award-winning novel (and 2012 film) Life of Pi nicknames himself after the constant.
- A circular room in the Palais de la Découverte science museum in Paris is called the pi room. The room has 707 digits of pi inscribed on its wall (although there is an error starting at the digit 528, thanks to William Shanks’ miscalculations).
- in an episode of Star Trek: The Original SeriesSpock instructs an evil computer to calculate pi to the last digit, which of course it can’t do because, as Spock explains, “the value of pi is a transcendental number with no resolution.”
- Givenchy’s PI cologne for men is advertised as a fragrance that “embodies the confidence of genius.”
- Both MIT and the Georgia Institute of Technology have cheers that include “3.14159.”
- Several other films make reference to pi, including the 1966 Alfred Hitchcock film Torn Curtain, the 1995 Sandra Bullock thriller The Net, the 1998 independent thriller Pi.
Finally, pi is perhaps most rampant in pop culture on March 14: Pi Day! On Pi Day, nerds, geeks, and mildly interested geometry students get together and wear pi-themed clothing, read pi-themed books, and watch pi-themed movies, all while playing games on our Raspberry Pi PCs.
Correction, March 14, 2013: An earlier version of this story erroneously claimed that Archimedean’s estimate for pi was 3.1485. His actual estimate calculated that pi was between 3.1408 and 3.14285. (If he averages these two numbers, he’ll get an intermediate point of 3.141851.) We are sorry for the mistake.
Article originally published on March 13, 2010; updated on March 13, 2013 and March 14, 2023.