Skip to main content

The Life of π: From Archimedes to ENIAC and Beyond

  • Chapter
  • First Online:
Book cover From Alexandria, Through Baghdad

Abstract

The desire to understand π, the challenge, and originally the need, to calculate ever more accurate values of π, the ratio of the circumference of a circle to its diameter, has captured mathematicians— great and less great — for many centuries. And, especially recently, π has provided compelling examples of computational mathematics. π, uniquely in mathematics, is pervasive in popular culture and the popular imagination. In this paper, I intersperse a largely chronological account of π’s mathematical and numerical status with examples of its ubiquity.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 84.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 109.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 109.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  • Amoroso, F., Viola, ?, 2008. Irrational and transcendental numbers. In: Bartocci, C, Odifreddi, P. (eds.), Mathematics and Culture, Volume II. La matematica: Problemi e teoremi. Turino: Guilio Einaudi Editori.

    Google Scholar 

  • Arndt, J., Haenel, C, 2001. Pi Unleashed. Springer-Verlag, New York.

    Book  MATH  Google Scholar 

  • Bailey, D.H., Borwein, J.M., 2011. Exploratory experimentation and computation. Notices of the American Mathematical Society 58, 1410–1419.

    MathSciNet  MATH  Google Scholar 

  • Bailey, D., Borwein, J., Calkin, N., Girgensohn, R., Luke, R., Moll, V, 2007. Experimental Mathematics in Action. A.K. Peters, Wellesley, MA.

    Google Scholar 

  • Bailey, D.H., Borwein, J.M., Mattingly, A., Wightwick, G., 2013. The computation of previously inaccessible digits of π2 and Catalan's Constant. Notices of the American Mathematical Society 50, 844–854.

    Article  MathSciNet  Google Scholar 

  • Berggren, L., Borwein, J.M., Borwein, P.B., 2004. Pi: A Source Book, 3rd edition. New York, Springer.

    Google Scholar 

  • Baruah, N.D., Berndt, B.C., Chan, H.H., 2009. Ramanujan's series for l/π: A survey. American Mathematical Monthly 116, 567–587.

    Article  MathSciNet  MATH  Google Scholar 

  • Blatner, D., 1997. The Joy of Pi. Walker and Co., New York.

    Google Scholar 

  • Borwein, J.M., 1998. Brouwer-Heyting sequences converge. Mathematical Intelligencer 20, 14–15.

    Article  MathSciNet  MATH  Google Scholar 

  • Borwein, J.M., 2008. La vita di pi greco: from Archimedes to ENIAC and beyond, in Bartocci, C, Odifreddi, P. (eds.), Mathematics and Culture, Volume II. La matematica: Problemi e teoremi, Guilio Einaudi Editori, Turino, pp. 249–285.

    Google Scholar 

  • Borwein, J.M., Bailey, D.H., 2008. Mathematics by Experiment: Plausible Reasoning in the 21st Century, 2nd expanded edition. A.K. Peters, Wellesley, MA. Ą

    Google Scholar 

  • Borwein, J.M., Borwein, P.B., 1987. Pi and the AGM. Wiley, New York.

    MATH  Google Scholar 

  • ——— 1988. Ramanujan and Pi. Scientific American 256, 112–117. Reprinted in: Berndt, B.C., Rankin, R.A. (eds.), 2001, Ramanujan: Essays and Surveys. American Mathematical Society, Providence, pp. 187–199. (Also in: Berggren, Borwein and Borwein [2004].)

    Google Scholar 

  • Borwein, J.M., Borwein, P.B., Bailey, D.H., 1989. Ramanujan, modular equations and approximations to pi or how to compute one billion digits of pi. American Mathematical Monthly 96, 201–219. Reprinted in: Organic Mathematics Proceedings, http://www.cecm.sfu.ca/organics, 1996. (Also in: Berggren, Borwein and Borwein [2004].)

  • Borwein, J., Nuyens, D., Straub, A., Wan, J., 2011 Some arithmetic properties of short random walk integrals. The Ramanujan Journal 26, 109–132.

    Article  MathSciNet  MATH  Google Scholar 

  • Churchland, P., 2007. Neurophilosophy at Work. Cambridge University Press, Cambridge.

    Book  Google Scholar 

  • Eymard, P., Lafon, J.-R, 2003. The Number π. American Mathematical Society, Providence.

    Google Scholar 

  • Guillera, J., 2008a. Hypergeometric identities for 10 extended Ramanujan-type series. Ramanujan Journal 15, 219–234.

    Article  MathSciNet  MATH  Google Scholar 

  • ——— 2008b. Easy proofs of some Borwein algorithms for π. American Mathematical Monthly 115, 850–854.

    MathSciNet  MATH  Google Scholar 

  • Heath, T.L., 1912. The Works of Archimedes, Cambridge University Press, Cambridge.

    Google Scholar 

  • Lucas, S.K., 2009. Integral approximations to pi with nonnegative integrands. American Mathematical Monthly 116, 166–172.

    Article  MathSciNet  MATH  Google Scholar 

  • McCartney, S., 1999. ENIAC: The Triumphs and Tragedies of the World's First Computer. Walker and Co., New York.

    Google Scholar 

  • Schioper, H.C., The chronology of pi. Mathematics Magazine 23, 165–170, 216–228, 279–283. (Also in: Berggren, Borwein and Borwein [2004].)

    Google Scholar 

  • Singmaster, D., 1985. The legal values of Pi. Mathematical Intelligencer 7, 69–72. (Also in: Berggren, Borwein and Borwein [2004].)

    Article  MathSciNet  MATH  Google Scholar 

  • Tsumura, H., 2004. An elementary proof of Euler's formula for ζ(2η). American Mathematical Monthly, 430–431.

    Google Scholar 

  • von Baeyer, H.C., 2003. Information: The New Language of Science. Harvard University Press, Cambridge, MA.

    Google Scholar 

  • Zudilin, W., 2008. Ramanujan-type formulae for Ι/π: A second wind. ArXiv:0712.1332v2.

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2014 Springer-Verlag Berlin Heidelberg

About this chapter

Cite this chapter

Borwein, J.M. (2014). The Life of π: From Archimedes to ENIAC and Beyond. In: Sidoli, N., Van Brummelen, G. (eds) From Alexandria, Through Baghdad. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-36736-6_24

Download citation

Publish with us

Policies and ethics