Harlan J. Brothers

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"_"n"}="n"^"n" ), Brothers discovered some simple algebraic formulas that yielded the number 2.71828..., the universal constant "e", also known as the base of the natural logarithm. Like its more famous cousin 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. 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 equations. He went on to publish methods for deriving infinite series that include the fastest known formulas for approximating "e". ["Improving the convergence of Newton's series approximation for "e".” "The College Mathematics Journal", Vol. 35, No. 1, 2004; pages 34-39.]

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.

ee 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

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]