hbrothers Brothers Technology, LLC   Harlan J. BrothersMathematics




  • Name:

     Harlan J. Brothers

  • Institution:

    Brothers Technology, LLC

  • Position:

  • Location:

     United States

  • Field of Science:

    Mathematics

  • Website / Blog:

    www.brotherstechnology.com

  • Online Status: status







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    • About my Work: 


      For six years I worked with Michael Frame and Benoit Mandelbrot at Yale University to explore the use of fractals in mathematics education. Projects at Yale included a lecture and workshop on the subject of fractal music composition and analysis.

      During an informal discussion in 2003 regarding the apparent lack of clarity associated with the subject, Benoit Mandelbrot suggested to me that I undertake a mathematically rigorous treatment of fractal music. The first result was a lecture and lab I presented at the 2004 Fractal Geometry Summer Workshop at Yale. More recently, I published a paper entitled "Structural Scaling in Bach’s Cello Suite No. 3," which appeared in the journal Fractals (Vol. 15, No. 1, 2007; pages 89-95). The article reveals musical structure related to the Cantor set and helps to establish a mathematical foundation for the classification of fractal music. A new article, entitled "Intervallic Scaling in the Bach Cello Suites," appears in the current issue of Fractals. The paper describes a novel and robust approach to establishing the existence of power-laws in music.

    • Projects: 


      * Commercial encryption system
      * iPhone application
      * Two journal articles

      I am currently appearing in Michael Lawrence's new documentary, "Bach & Friends" where I discuss Bach, mathematics, and fractal geometry. The film includes my production of a zoom animation into the Mandelbrot set:

      http://www.youtube.com/watch?v=d6PBFa3VozE

    • Vita / Publications: 


      H. J. Brothers, "Intervallic scaling in the Bach cello suites." Fractals, Vol. 17, No. 4, 2009; pages 537-545.

      H. J. Brothers, "How to design your own pi to e converter." The AMATYC Review, Vol. 30, No. 1, 2008; pages 29–35.

      H. J. Brothers, "Structural scaling in Bach’s cello suite no. 3." Fractals, Vol. 15, No. 1, 2007; pages 89-95.

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

      J. A. Knox and H. J. Brothers, Novel series-based approximations to e. College Mathematics Journal, Vol. 30, No. 4, 1999; pages 269-275. [126KB]

      (NOTE: The above paper was selected by mathematicians Ron Larson, Robert P. Hostetler, and Bruce H. Edwards as one of the fifty best articles on calculus from MAA periodicals. It is now a supplement to their textbook, Calculus with Analytic Geometry, Seventh Edition.)

      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.

    • Grants and Awards: 


    • About my Institution: 


      We create a broad range of intellectual property for license and sale. Current projects range from novel consumer devices to commercial encryption techniques and educational tools.

    • Additional Information: 


      I've had a long-standing interest in number theory and its applications and have discovered formulas and relationships relating to the constants e, pi, and Euler's gamma. My paper entitled "Improving the Convergence of Newton's Series Approximation for e" includes the fastest known methods for computing this fundamental constant of nature.
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    The Mandelbrot zoom I produced for Bach and Friends - www.youtube.com/watch?v=d6PBFa3VozE

     































     

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