HARLAN J. BROTHERS

'Harlan J. Brothers' is an inventor, mathematician, and musician, living in Branford, Connecticut.
In 1997, while examining the sequence of counting numbers raised to their own power ( {a_n}=nⁿ ), 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 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 “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''.
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 musician.

Contents

See also

External links

Literature

See also

★ List of amateur mathematicians

External links

★ Mathematics page of Harlan Brothers

★ NASA Goddard Institute for Space Studies – "Serendipit–e"

★ ''Science News'' – Ivars Peterson

★ Introduction to Fractals

★ Fractals in Mathematics Education

★ Yale Workshop on Fractal Music (mirror)

★ Harlan Brothers: Research on Fractal Music

★ Article in The Citizen Scientist

★ The Country School: Harlan Brothers

Literature

★ 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.

★ H. J. Brothers, "Structural Scaling in Bach’s Cello Suite No. 3.” ''Fractals'', Vol. 15, No. 1, 2007; pages 1-7.

★ H. J. Brothers, "Improving the convergence of Newton's series approximation for ''e''.” ''The College Mathematics Journal'', Vol. 35, No. 1, 2004; pages 34-39.

★ J. A. Knox and H. J. Brothers, "Novel series-based approximations to ''e''.” ''The College Mathematics Journal'', Vol. 30, No. 4, 1999; pages 269-275.

★ H. J. Brothers and J. A. Knox, "New closed-form approximations to the Logarithmic Constant ''e''.” ''The Mathematical Intelligencer'', Vol. 20, No. 4, 1998; pages 25-29.