Skip to main content
Log in

e: The Master of All

  • Article
  • Published:
The Mathematical Intelligencer Aims and scope Submit manuscript

An Erratum to this article was published on 01 June 2006

Conclusion

The time has come to end our stroll through the Garden ofe-den, even though we have yet to taste many of its most succulent fruits, such as exponential splines [62]. However, I would like to conclude my p-e-an toe in a lighter vein.

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

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  1. C. C. Gillispie,Biographical Dictionary of Mathematics, Charles Scribner’s Sons, New York, 1991.

    Google Scholar 

  2. W. Dunham,Euler: The Master of Us All, Mathematical Association of America, Washington, DC, 1999.

    MATH  Google Scholar 

  3. U. G. Mitchell and M. Strain, The Numbere, Osiris 1 (1936), 476–496.

    Article  Google Scholar 

  4. J. L. Coolidge, The Numbere, American Mathematical Monthly 57(1950), 591–602.

    Article  MATH  MathSciNet  Google Scholar 

  5. E. Maor,e: The Story of a Number, Princeton University Press, Princeton, NJ, 1994.

    MATH  Google Scholar 

  6. A. H. Bell,The Exponential and Hyperbolic Functions and Their Applications, Pitman&Sons, London, 1932.

    MATH  Google Scholar 

  7. M. E. J. Gheury de Bray,Exponentials Made Easy, Macmillan & Co., London, 1921.

    MATH  Google Scholar 

  8. P. Beckmann,A History of π, Barnes&Noble, New York, 1993.

    Google Scholar 

  9. J. H. Conway and R. H. Guy,The Book of Numbers, Springer Verlag, New York, 1996.

    Book  MATH  Google Scholar 

  10. M. Brede, On the Convergence of the Sequence Defining Euler’s Number,Mathematical Intelligencer 27 (2005), 6–7.

    Article  MATH  Google Scholar 

  11. H. J. Brothers and J. A. Knox, New Closed-Form Approximations to the Logarithmic Constante, Mathematical Intelligencer 20 (1998), 25–29.

    Article  MATH  MathSciNet  Google Scholar 

  12. D. Wells,The Penguin Dictionary of Curious and Interesting Numbers, Penguin Books Ltd., Middlesex, England, 1986.

    Google Scholar 

  13. M. Gardner,The Unexpected Hanging and Other Mathematical Diversions, Simon and Schuster, New York, 1969.

    Google Scholar 

  14. H. J. Brothers, Improving the Convergence of Newton’s Series Approximation for e,College Mathematics Journal 35(1) (2004), 34–39.

    Article  Google Scholar 

  15. J. A. Knox and H. J. Brothers, Novel Series-Based Approximations toe, College Mathematics Journal 30(4) (1999), 269–275.

    Article  MATH  MathSciNet  Google Scholar 

  16. C. D. Olds, The Simple Continued Fraction Expression fore, American Mathematical Monthly 77 (1970), 968–974.

    Article  MATH  MathSciNet  Google Scholar 

  17. N. Pippenger, An Infinite Product fore, American Mathematical Monthly 87(5) (1980), 391.

    Article  MathSciNet  Google Scholar 

  18. X. Gourdon and P. Sebah,The Constant e and Its Computation, http://numbers.computation.free.fr/Constants/E/e.html.

  19. A. Baker,Transcendental Number Theory, Cambridge University Press, Cambridge, 1975.

    Book  MATH  Google Scholar 

  20. I. Niven, Which is Larger,e π or πe? in πA Century of Calculus, Part II: 1969–1991, Mathematical Association of America, Washington, DC, 1992, 445–447.

    Google Scholar 

  21. J. M. Borwein and P. B. Borwein,Pi and the AGM, Wiley-Interscience, New York, 1987.

    MATH  Google Scholar 

  22. S. R. Finch,Mathematical Constants, Cambridge University Press, Cambridge, 2003.

    MATH  Google Scholar 

  23. R. Courant and H. Robbins,What Is Mathematics?, Oxford University Press, New York, 1941.

    Google Scholar 

  24. G. H. Hardy and E. M. Wright,An Introduction to the Theory of Numbers, Third Edition, Oxford University Press, London, 1954.

    MATH  Google Scholar 

  25. P. Ribenboim,The New Book of Prime Number Records, Springer, New York, 1996.

    Book  MATH  Google Scholar 

  26. S. M. Ruiz, A Result on Prime Numbers,Mathematical Gazette 81 (1997), 269–270.

    Article  Google Scholar 

  27. E.T. Bell,Men of Mathematics, Simon and Schuster, New York, 1965.

    Google Scholar 

  28. H. V. Baravalle, The Number e—The Base of the Natural Logarithms,The Mathematics Teacher 38 (1945), 350–355.

    Google Scholar 

  29. B. Friedman,Lectures on Applications-Oriented Mathematics, Holden-Day, San Francisco, 1969.

    MATH  Google Scholar 

  30. G. H. Hardy,Ramanujan, AMS Chelsea, Providence, Rl, 1999.

    Google Scholar 

  31. J. Aczél,On Applications and Theory of Functional Equations, Academic Press, New York, 1969.

    MATH  Google Scholar 

  32. H. Bateman,Differential Equations, Chelsea, New York, 1966.

    MATH  Google Scholar 

  33. R. E. O’Malley,Thinking About Ordinary Differential Equations, Cambridge University Press, New York, 1997.

    Book  MATH  Google Scholar 

  34. G. Boole,Calculus of Finite Differences, Chelsea, New York, 1970.

    Google Scholar 

  35. S. lyanaga and Y. Kawada,Encyclopedic Dictionary of Mathematics, MIT Press, Cambridge, MA, 1980.

    Google Scholar 

  36. J. Spanier and K. B. Oldham,An Atlas of Functions, Hemisphere, New York, 1987.

    MATH  Google Scholar 

  37. K. W. Morton,Numerical Solution of Convection-Diffusion Problems, Chapman&Hall, London, 1996.

    MATH  Google Scholar 

  38. E. P. Doolan, J. J. H. Miller, and W. H. A. Schilders,Uniform Numerical Methods for Problems with Initial and Boundary Layers, Boole Press, Dublin, 1980.

    MATH  Google Scholar 

  39. F. B. Hildebrand,Introduction to Numerical Analysis, McGraw-Hill, New York, 1956.

    MATH  Google Scholar 

  40. B. J. McCartin, Exponential Fitting of the Delayed Recruitment/Renewal Equation,Journal of Computational and Applied Mathematics 136 (2001), 343–356.

    Article  MATH  MathSciNet  Google Scholar 

  41. G. A. Baker and P. Graves-Morris,Padé Approximants, 2nd Edition, Cambridge University Press, Cambridge, 1996.

    Book  MATH  Google Scholar 

  42. D. Mortimer,Research on Asymptotics, http://www.maths.ox.ac. uk/~mortimer/research/davidresearch.shtml.

  43. A. C. Fowler,Mathematical Models in the Applied Sciences, Cambridge University Press, Cambridge, 1997.

    Google Scholar 

  44. J. Riordan,An Introduction to Combinatorial Analysis, Princeton University Press, Princeton, NJ, 1980.

    MATH  Google Scholar 

  45. F. Harary and E. M. Palmer,Graphical Enumeration, Academic Press, New York, 1973.

    MATH  Google Scholar 

  46. E. M. Weisstein,Exponential Transform, http.V/mathworld.wolfram. com/ExponentialTransform. html.

  47. F. Harary,Graph Theory, Addison-Wesley, Reading, MA, 1969.

    Google Scholar 

  48. N. J. A. Sloane and S. Plouffe,The Encyclopedia of Integer Sequences, Academic, San Diego, 1995.

    MATH  Google Scholar 

  49. R. J. RiddellContributions to the Theory of Condensation, Ph.D. Dissertation, University of Michigan, UMI Dissertation Services, Ann Arbor, Ml, 1951.

    Google Scholar 

  50. A. S. Householder,The Numerical Treatment of a Single Nonlinear Equation, McGraw-Hill, New York, 1970.

    MATH  Google Scholar 

  51. K. Holmström, A. Ahnesjö, and J. Petersson, Algorithms for Exponential Sum Fitting in Radiotherapy Planning,Technical Report IMa-TOM-2001-02, Department of Mathematics and Physics, Malarden University, Sweden (2001).

    Google Scholar 

  52. G. R. de Prony, Essai éxperimental et analytique,Journal de I ’ École Polytechnique, 1(22) (1795), 24–76.

    Google Scholar 

  53. J. J. O’Connor and E. F. Robertson, Gaspard Clair Frangois Marie Riche de Prony, http://www.groups.dcs.st-and.ac.uk/history/Mathematicians/De_Prony.html.

  54. H. S. Schultz and B. Leonard, Unexpected Occurrences of the Numbere, Mathematics Magazine 62(4) (1989), 269–271.

    Article  Google Scholar 

  55. N. MacKinnon, Another Surprising Appearance ofe, Mathematical Gazette 74(468) (1990), 167–169.

    Article  Google Scholar 

  56. D. J. Colwell, J. R. Gillett and B. C. Jones, That Numbere Again,Mathematical Gazette 75(473) (1991), 329–330.

    Article  Google Scholar 

  57. J. Hornberger and J-H. Ahn, Deciding eligibility for transplantation when a kidney donor is available,Medical Decision Making 17 (1997), 160–170.

    Article  Google Scholar 

  58. H. Cramér,Mathematical Methods of Statistics, Princeton University Press, Princeton, NJ, 1946.

    MATH  Google Scholar 

  59. S. M. Stigler,The History of Statistics, Harvard University Belknap Press, Cambridge, MA, 1986.

    MATH  Google Scholar 

  60. A. Papoulis,Probability, Random Variables, and Stochastic Processes, Second Edition, McGraw-Hill, New York, 1984.

    MATH  Google Scholar 

  61. H. Bateman,Higher Transcendental Functions, Krieger, Malabar, FL, 1981.

    Google Scholar 

  62. B. J. McCartin, Theory of Exponential Splines,Journal of Approximation Theory 66(1) (1991), 1–23.

    Article  MATH  MathSciNet  Google Scholar 

  63. M. Gardner,The Scientific American Book of Mathematical Puzzles and Diversions, Simon and Schuster, New York, 1959.

    Google Scholar 

  64. Z. Barel, A Mnemonic fore, Mathematics Magazine 68 (1995), 253.

    Article  MathSciNet  Google Scholar 

  65. E. Kasner and J. Newman,Mathematics and the Imagination, Simon and Schuster, New York, 1967.

    Google Scholar 

  66. D. Sapp,The e Home Page, http://www.mu.org/~doug/exp/ etop10.html.

Download references

Author information

Authors and Affiliations

Authors

Additional information

An erratum to this article is available at http://dx.doi.org/10.1007/BF02986875.

Rights and permissions

Reprints and permissions

About this article

Cite this article

McCartin, B.J. e: The Master of All. The Mathematical Intelligencer 28, 10–21 (2006). https://doi.org/10.1007/BF02987150

Download citation

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02987150

Keywords

Navigation