Harlan J. Brothers - AbsoluteAstronomy.com

Harlan J. Brothers is an inventor, mathematician

Mathematician

A mathematician is a person whose primary area of study is the field of mathematics. Mathematicians are concerned with quantity, structure, space, and change....

, and musician

Musician

A musician is an artist who plays a musical instrument. It may or may not be the person's profession. Musicians can be classified by their roles in performing music and writing music.Also....* A person who makes music a profession....

based in Branford, Connecticut

Branford, Connecticut

-Landmarks and attractions:Branford has six historic districts that are listed on the U.S. National Register of Historic Places . These include buildings in Federal, Arts and Crafts, and Queen Anne styles of architecture...

Life and work

In 1997, while examining the sequence

Sequence

In mathematics, a sequence is an ordered list of objects . Like a set, it contains members , and the number of terms is called the length of the sequence. Unlike a set, order matters, and exactly the same elements can appear multiple times at different positions in 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
E (mathematical constant)
The mathematical constant ' is the unique real number such that the value of the derivative of the function at the point is equal to 1. The function so defined is called the exponential function, and its inverse is the natural logarithm, or logarithm to base...

, also known as the base of the natural logarithm

Natural logarithm

The natural logarithm is the logarithm to the base e, where e is an irrational and transcendental constant approximately equal to 2.718281828...

. Like its more famous cousin π

' is a mathematical constant that is the ratio of any circle's circumference to its diameter. is approximately equal to 3.14. Many formulae in mathematics, science, and engineering involve , which makes it one of the most important mathematical constants...

, e is a transcendental number

Transcendental number

In mathematics, a transcendental number is a number that is not algebraic—that is, it is not a root of a non-constant polynomial equation with rational coefficients. The most prominent examples of transcendental numbers are π and e...

that appears in a wide range of formulas in mathematics

Mathematics

Mathematics is the study of quantity, space, structure, and change. Mathematicians seek out patterns and formulate new conjectures. Mathematicians resolve the truth or falsity of conjectures by mathematical proofs, which are arguments sufficient to convince other mathematicians of their validity...

and physics

Physics

Physics is a natural science that involves the study of matter and its motion through spacetime, along with related concepts such as energy and force. More broadly, it is the general analysis of nature, conducted in order to understand how the universe behaves.Physics is one of the oldest academic...

.

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
Scientific American
Scientific American is a popular science magazine. It is notable for its long history of presenting science monthly to an educated but not necessarily scientific public, through its careful attention to the clarity of its text as well as the quality of its specially commissioned color graphics...

.

His communication with “Science Friday” led to a fruitful collaboration with meteorologist John Knox

John Knox (meteorologist)

John Knox is a meteorologist who researches clear-air turbulence and who also received media attention for discussing ways of calculating the mathematical constant e, together with inventor Harlan J. Brothers....

. 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

Calculus

Calculus is a branch of mathematics focused on limits, functions, derivatives, integrals, and infinite series. This subject constitutes a major part of modern mathematics education. It has two major branches, differential calculus and integral calculus, which are related by the fundamental theorem...

curriculum by way of a popular textbook on the subject.

Brothers went back to school to study calculus and differential equation

Differential equation

A differential equation is a mathematical equation for an unknown function of one or several variables that relates the values of the function itself and its derivatives of various orders...

s. 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

Benoît Mandelbrot

Benoît B. Mandelbrot was a French American mathematician. Born in Poland, he moved to France with his family when he was a child...

and Michael Frame at Yale University

Yale University

Yale University is a private, Ivy League university located in New Haven, Connecticut, United States. Founded in 1701 in the Colony of Connecticut, the university is the third-oldest institution of higher education in the United States...

. 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 Director of Technology at The Country School, Brothers holds five patents and is a trained and actively performing guitarist and composer.

Publications

2012 "Benoit Mandelbrot: Educator." With N. Neger. In: Benoit Mandelbrot - A Life in Many Dimensions, World Scientific Publishing, edited by Michael Frame (Fall, 2012).
2012 "Pascal's Prism." The Mathematical Gazette, Accepted for publication, July 2012.
2012 "Pascal's Triangle: The Hidden Stor-e." The Mathematical Gazette, Accepted for publication, March 2012.
2011 "Finding e in Pascal’s Triangle." Mathematics Magazine, Accepted for publication, Vol. 17, No. 4, 2011.
2010 "Mandel-Bach Journey: A marriage of musical and visual fractals." Proceedings of Bridges Pecs, 2010; pages 475-478.
2009. "Intervallic scaling in the Bach cello suites." Fractals, Vol. 17, No. 4, 2009; pages 537-545.
2008. "How to design your own pi to e converter." The AMATYC Review, Vol. 30, No. 1, 2008; pages 29–35.
2007. "Structural Scaling in Bach’s Cello Suite No. 3.” Fractals, Vol. 15, No. 1, 2007; pages 89-95.
2004. "Improving the convergence of Newton's series approximation for e.” The College Mathematics Journal, Vol. 35, No. 1, 2004; pages 34-39.
1999. "Novel series-based approximations to e.” With J. A. Knox. In: The College Mathematics Journal, Vol. 30, No. 4, 1999; pages 269-275.
1998. "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.

External links

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Life and work

Publications

Further reading

External links