Napier's Logarithms

This paper discusses the historical development of Napier's logarithms and their lack of a base with current logarithms, which employ a base 10.

2,090 words () | 5 sources | MLA | 2008 United States

Paper Summary:

This paper explains that John Napier, in 1614, took an algebraic approach by defining logarithms as a ratio of two distances within a geometric pattern, base 1/e, which substituted for his lack of a base as in the currently used common logarithmic base 10. The author points out that the real benefit of these logarithms was that they simplified mathematical calculations by providing a shortcut for exponential factors just as exponents are a shortcut for multiplication. The paper relates that, since Napier's original logarithms lacked a common base, they were more consistently accurate but not as easy to manipulate as the common logarithms employed today. The author states that the common logarithms are much easier to calculate but only sufficiently accurate as compared to Napier's original logarithms. The paper includes graphs.

Table of Contents:
Introduction
Historical Background
Napier's Logarithms
Base 10 Logarithms
Conclusion

From the Paper:

"While initially Napier's logarithms did not employ a base in the traditional sense he eventually adjusted his logarithms to account for a consistent base in much the same way they are currently employed today. Napier worked with another mathematician, a man by the name of Henry Briggs, to change his logarithmic forms to the form now currently common which is the L/e equation. Thus, Naperian logarithms now are described as points that are moving along a straight trajectory and indicated by units prescribed in length."

Sample of Sources Used:

Cropper, William H. Great Physicists: The Life and Times of Leading Physicists from Galileo to Hawking. New York: Oxford University Press, 2001.
Gossin, Pamela, et al., eds. Encyclopedia of Literature and Science. Westport, CT: Greenwood Press, 2002.
Kaplan, Robert, and Ellen Kaplan. The Art of the Infinite: The Pleasures of Mathematics. New York: Oxford University Press, 2003.
Medio, Alfredo, and Marji Lines. Nonlinear Dynamics: A Primer. Cambridge, England: Cambridge University Press, 2001.
Windelspecht, Michael. Groundbreaking Scientific Experiments, Inventions, and Discoveries of the 17Th Century. Westport, CT: Greenwood Press, 2002.