Harlan J. Brothers
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2008-07-08T21:55:17Z
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'''Harlan J. Brothers''' is an inventor, mathematician, and musician, living in [[Branford, Connecticut]].
== Life and work ==
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 ''[[E (mathematical constant)|e]]'', also known as the base of the [[natural logarithm]]. Like its more famous cousin [[pi|π]], ''e'' is a [[transcendental number]] that appears in a wide range of formulas in [[mathematics]] 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 “Science Friday” and also to a well-known mathematician at ''[[Scientific American]]''.
His communication with “Science Friday” led to a fruitful collaboration with [[meteorologist]] [[John Knox (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.
Brothers went back to school to study calculus and [[differential equation]]s. He went on to publish methods for deriving [[infinite series]] that include the fastest known formulas for approximating ''e''{{Fact|date=March 2008}}.
In the summer of 2001, his professor, Miguel Garcia, introduced him to [[Benoît Mandelbrot]] and Michael Frame at Yale University. Brothers soon began working with them to incorporate the study of [[fractals]] into core mathematics curricula. His current research, begun in collaboration with Frame, is in the field of fractals and music.
In addition to working as a teacher, Brothers holds five patents and is a trained and actively performing guitarist and composer.
==See also==
*[[List of amateur mathematicians]]
== Publications ==
* 1998. [http://www.brotherstechnology.com/docs/mi_paper1.pdf "New closed-form approximations to the Logarithmic Constant ''e''.”] With J. A. Knox. In: ''The Mathematical Intelligencer'', Vol. 20, No. 4, 1998; pages 25-29
* 1999. [http://www.brotherstechnology.com/docs/cmj_paper1.pdf "Novel series-based approximations to ''e''.”] With J. A. Knox. In; ''The College Mathematics Journal'', Vol. 30, No. 4, 1999; pages 269-275.
* 2004. [http://www.brotherstechnology.com/docs/icnsae_(cmj0104-300dpi).pdf "Improving the convergence of Newton's series approximation for ''e''.”] ''The College Mathematics Journal'', Vol. 35, No. 1, 2004; pages 34-39.
* 2007. "Structural Scaling in Bach’s Cello Suite No. 3.” ''Fractals'', Vol. 15, No. 1, 2007; pages 89-95.
== References ==
{{Unreferenced|date=July 2008}}
==Further reading ==
* [[Clifford A. Pickover]]. "The Möbius Strip," page 195. Thunder's Mouth Press, New York, 2006.
* Clifford A. Pickover. "Wonders of Numbers," page 4. Oxford University Press, New York, 2001.
==External links==
*[http://www.brotherstechnology.com/math/index.html Mathematics page of Harlan Brothers]
*[http://www.giss.nasa.gov/research/briefs/knox_03/ NASA Goddard Institute for Space Studies – "Serendipit–e"]
*[http://www.sciencenews.org/articles/20040214/mathtrek.asp/ ''Science News'' – Ivars Peterson]
*[http://www.brotherstechnology.com/docs/fractals.pdf Introduction to Fractals]
*[http://www.brotherstechnology.com/math/fractals-edu.html Fractals in Mathematics Education]
*[http://www.brotherstechnology.com/yale/FractalMusic/FractalMusicLab.html Yale Workshop on Fractal Music (mirror)]
*[http://www.brotherstechnology.com/math/fractal-music.html Harlan Brothers: Research on Fractal Music]
*[http://www.sas.org/tcs/weeklyIssues_2007/2007-03-03/feature1/ Article in ''The Citizen Scientist'']
*[http://www.thecountryschool.org/zfac_hbrothers.html The Country School: Harlan Brothers]
*[http://www.brotherstechnology.com/fractal-music/fractal-music-ws.html Fractal Music Workshops]
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[[Category:American mathematicians]]
[[Category:Year of birth missing (living people)]]
[[Category:Living people]]