Harlan J. Brothers 1301905 224448700 2008-07-08T21:55:17Z SmackBot 433328 Date the maintenance tags or general fixes '''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 &ndash; "Serendipit&ndash;e"] *[http://www.sciencenews.org/articles/20040214/mathtrek.asp/ ''Science News'' &ndash; 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] {{DEFAULTSORT:Brothers, Harlan}} [[Category:American mathematicians]] [[Category:Year of birth missing (living people)]] [[Category:Living people]]