### Pi is Forever

September 23, 2010 In the past, there was just one type of record involving pi; namely, the number of digits calculated. Of course, such a contest can go on forever, since pi is a transcendental, irrational number with a number sequence that does not repeat. How many decimal places of pi are really needed? I've memorized eleven places, which is definitely overkill for all practical calculations. As I wrote in a previous article, (Another Piece of Pi, July 28, 2010), we only need twenty-seven digits of pi to calculate the circumference of the universe to better than a meter, and thirty-eight digits to get a value of the circumference closer than the size of an atom. The current record for calculating digits of pi is apparently five trillion digits (5,000,000,000,000).[1] This record was accomplished in August, 2010, by Shigeru Kondo, a Japanese systems engineer, on home-built hardware. The calculation took a little more than ninety days. Yukiko Kondo, Shigeru's wife seemed to be more impressed by the $240 monthly electrical bill than the calculation,[1] but I'm sure she's really proud of her husband. There are other pi records, like the recitation of digits of pi from memory. The record for this appears to held by another Japanese, Akira Haraguchi, who recited 100,000 digits of pi from memory in a span of sixteen hours in October, 2006.[2] Because of an interesting discovery by David Bailey, Peter Borwein and Simon Plouffe (BBP), there's another way to set a record for pi calculation. They published a formula for finding any digit of pi without calculation of the preceding digits.[3] That this result is unusual is clearly an understatement, but it gives computer people another shot at the record books; namely, the largest calculated digit of pi. That record now stands at 2,000,000,000,000,000 binary digits.[4] Nicholas Sze of Yahoo used more than a thousand cloud computers to find the 2,000,000,000,000,000th binary digit of pi in 23 days - It's zero.[5] Of course, as one Internet commentator put it, Sze had a fifty-fifty chance of getting it right from the onset. The effort was done on a cluster that varied in size from 1000 to 4000 machines, each machine of which had two quad-core CPUs with clock speeds of 1.8 GHz to 2.5 GHz.[5] If you're computing that many digits of anything, you need to use libraries that allow calculations with large numbers. The one that I use is the GNU Multiple Precision Arithmetic Library. If you're just calculating a few thousand digits of pi, this isn't required. I've written a C program that uses the BBP technique to calculate 20,000 hex digits of pi (source code here). It uses code published by David Bailey,[6] and it calculates these 20,000 hex digits in just 35 seconds on my dual core, 2.66 GHz computer. Here are the first 300 hex digits of pi, as calculated by the program.243F6A8885 | A308D31319 | 8A2E037073 |

44A4093822 | 299F31D008 | 2EFA98EC4E |

6C89452821 | E638D01377 | BE5466CF34 |

E90C6CC0AC | 29B7C97C50 | DD3F84D5B5 |

B547091792 | 16D5D98979 | FB1BD1310B |

A698DFB5AC | 2FFD72DBD0 | 1ADFB7B8E1 |

AFED6A267E | 96BA7C9045 | F12C7F9924 |

A19947B391 | 6CF70801F2 | E2858EFC16 |

636920D871 | 574E69A458 | FEA3F4933D |

7E0D95748F | 728EB65871 | 8BCD588215 |

"Somewhere inside the digits of pi is a representation for all of us -- the atomic coordinates of all our atoms, our genetic code, all our thoughts, all our memories. Given this fact, all of us are alive, and hopefully happy, in pi. Pi makes us live forever. We all lead virtual lives in pi. We are immortal."You can try to find parts of yourself in pi, here.[10]

### References:

- Julian Ryall, "Japanese man calculates Pi to 5 trillion digits on homemade computer," Telegraph (UK), August 31, 2010.
- 100,000 Digits of Pi, This Blog, October 10, 2006.
- David H. Bailey, Peter B. Borwein and Simon Plouffe,"On the Rapid Computation of Various Polylogarithmic Constants". Mathematics of Computation, vol. 66, no. 218 (April 1997), pp. 903-913.
- Jason Palmer, "Pi record smashed as team finds two-quadrillionth digit," BBC News, September 16, 2010.
- Tsz-Wo Sze, "The Two Quadrillionth Bit of Pi is 0! Distributed Computation of Pi with Apache Hadoop," arXiv Preprint Server, August 18, 2010.
- David H. Bailey, "BBP Code Directory" (Updated September 8, 2006)
- David Whitehouse, "How random is pi?," BBC News, July 23, 2002.
- David H. Bailey and Richard E. Crandall, "On the Random Character of Fundamental Constant Expansions," Experimental Mathematics, vol. 10, no. 2 (2001), pp. 175-190.
- Cliff Pickover, "We are in Digits of Pi and Live Forever," May 2003.
- David G. Andersen, The Pi Searcher Web Site

*Permanent Link to this article*

Linked Keywords: pi; transcendental; irrational; universe; size of atom; Japanese; David Bailey; Peter Borwein; Simon Plouffe; formula; binary; cloud computers; quad-core; GNU Multiple Precision Arithmetic Library; pi_hex.c; randomness; proof; experiment; Clifford Pickover.

RSS Feed

### Google Search

Latest Books by Dev Gualtieri

Thanks to Cory Doctorow of BoingBoing for his favorable review of Secret Codes!

Other Books

- Whiskey - January 20, 2020

- An Elastocaloric Calorimeter - January 13, 2020

- Elastocaloric Effect - January 6, 2020

- Christmas 2019 - December 23, 2019

- Our Accelerating Universe - December 16, 2019

- Math is Beautiful - December 9, 2019

- Giovanni Battista Riccioli - December 2, 2019

- Consider a Spherical Turkey - November 25, 2019

- Metamaterial Lenses - November 18, 2019

- Computing Chaos - November 11, 2019

- Ultra-Hyper-Super Black - November 4, 2019

- Interstellar Comets - October 28, 2019

- Magnetic Pole Flip - October 21, 2019

- Calvin Quate (1923-2019) - October 14, 2019

- Transistor Threads - October 7, 2019

- Scientific Broadness - September 30, 2019

- Squaring the Circle - September 23, 2019

- Death by Air Pollution - September 16, 2019

- Lots, and Lots, of Dots - September 9, 2019

- Fiber-Optic Sensors - September 2, 2019

- Is Science Simply Beautiful? - August 26, 2019

- Torqued Light - August 19, 2019

- The Dragonfly of Titan - August 12, 2019

- Optical Ruler - August 5, 2019

- Bolometry - July 29, 2019

- Too Many Commercials - July 22, 2019

- Lost Moons - July 15, 2019

- Go with the Flow - July 8, 2019

- Ion-Gated Transistors - July 1, 2019

### Deep Archive

Deep Archive 2006-2008

**Blog Article Directory on a Single Page**