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Harlan J. Brothers
'''Harlan J. Brothers''' (19?? &ndash; present) is a teacher, musician, and inventor living in Branford, CT.  

In 1997, while examining the [[sequence]] of counting numbers raised to their own power ( {a<sub>n</sub>}=n<sup>n</sup> ), Brothers discovered some simple algebraic formulas that yielded the number 2.71828..., the universal constant <i>e</i>, also known as the base of the [[natural logarithm]].  Like its more famous cousin [[&#960pi|&pi;]], <i>e</i> is a [[transcendental number]] that appears in a wide range of formulas in math and physics.

Having no formal college-level mathematics education, he sent brief descriptions of his findings to the host of the [[National Public Radio]] show “&#8220;Science Friday”&#8221; and also to a well-known mathematician at <i>[[Scientific American]]</i>.

His communication with “&#8220;Science Friday”&#8221; led to a fruitful collaboration with [[meteorologist]] John Knox.  Together they discovered over two dozen new formulas and published two papers on their methods.  These methods subsequently found their way into the standard college [[calculus]] curriculum by way of a popular textbook on the subject.

(contracted; show full)
*[http://classes.yale.edu/fractals/labs/fractalmusiclab/FractalMusicLab.html/  Fractal Music pages at Yale]
*[http://www.thecountryschool.org/zfac_hbrothers.htm/ The Country School: Harlan Brothers]

==Literature==
*Clifford A. Pickover. "Wonders of Numbers," page 4.  Oxford University Press, New York, 2001.

*H. J. Brothers, [http://www.brotherstechnology.com/docs/icnsae_(cmj0104-300dpi).pdf  "Improving the convergence of Newton's series approximation for <i>e</i>.
”&#8221;] <i>The College Mathematics Journal</i>, volume 35, number 1, 2004; pages 34-39.

*J. A. Knox and H. J. Brothers, [http://www.brotherstechnology.com/docs/cmj_paper1.pdf  "Novel series-based approximations to <i>e</i>.”&#8221;] <i>The College Mathematics Journal</i>, volume 30, number 4, 1999; pages 269-275.

*H. J. Brothers and J. A. Knox, [http://www.brotherstechnology.com/docs/mi_paper1.pdf  "New closed-form approximations to the Logarithmic Constant <i>e</i>.”&#8221;] <i>The Mathematical Intelligencer</i>, volume 20, number 4, 1998; pages 25-29.

[[Category:American mathematicians|Brothers, Harlan]]