Publications

• H. J. Brothers, Pascal's Triangle, Sidi Polynomials, and Powers of e. Missouri Journal of Mathematical Sciences, Accepted, 2024.

• H. J. Brothers, Using Iterated Function Systems to Reveal Biases in the Distribution of Prime Numbers. In Submission, 2024. (2016 draft can be found at: arXiv e-prints, arXiv:1701.00698).

• H. J. Brothers, Giants Steps: The Fractal Structure of John Coltrane’s Iconic Solo. Towards Data Science,

 September 2022.

• H. J. Brothers, Fractal Music from Randomness. Towards Data Science, July 2022.

• H. J. Brothers, The Nature of Fractal Music, in Benoit Mandelbrot - A Life in Many Dimensions, edited by Michael Frame, World Scientific Publishing (May, 2015). (Supplementary material)

• N. Neger and H. J. Brothers, Benoit Mandelbrot: Educator, in Benoit Mandelbrot - A Life in Many Dimensions, edited by Michael Frame, World Scientific Publishing (May, 2015).

• M. F. Barnsley, M. Berry, M. Frame, I. Stewart, D. Mumford, K. Falconer, R. Eglash, H. J. Brothers, N. Lesmoir-Gordon, J. Barrallo, Glimpses of Benoit Mandelbrot (1924-2010). Notices of the American Mathematical Society, Vol. 8, No. 59, 2012; pages 1056-1063.

• H. J. Brothers, Pascal's prism. The Mathematical Gazette, Vol. 96, No. 536, 2012; pages 213-220. (Supplementary material)

• H. J. Brothers, Pascal's triangle: The hidden stor-e. The Mathematical Gazette, Vol. 96, No. 535, 2012; pages 145-148.

• H. J. Brothers, Finding e in Pascal’s triangle. Mathematics Magazine, Vol. 85, No. 1, 2012; page 51.

• H. J. Brothers, Mandel-Bach Journey: A marriage of musical and visual fractals. Proceedings of Bridges Pecs, 2010; pages 475-478.

• H. J. Brothers, Intervallic scaling in the Bach cello suites. Fractals, Vol. 17, No. 4, 2009; pages 537-545. (Supplementary material)

• 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. (Supplementary material)

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

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

(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 appears as a supplement to their textbook, Calculus with Analytic Geometry)

• 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.