Suggested Readings

BELCASTRO, SARAH-MARIE, and THOMAS C. HULL. Classifying frieze patterns without using groups, College Mathematics Journal, 33 (March 2002): 93–98. Elementary analysis of why there are only seven ways to repeat a pattern along a strip.

CARSON, JUDITHLYNNE. Fibonacci numbers and pineapple phyllotaxy, Two-Year College Mathematics Journal, 9 (3) (June 1978): 132–136.

CROWE, DONALD W. Symmetry, Rigid Motions and Patterns, High School Mathematics and Its Applications (HiMAP) Module 4, COMAP, Lexington, MA, 1987. Reprinted in smaller format in The UMAP Journal, 8 (3) (1987): 207–236. Instructional module on rigid motions of the plane, strip patterns, and wallpaper patterns, with worksheets.

HAYES, BRIAN. Group theory in the bedroom, American Scientist, 93 (5) (September-October 2005): 393ff, at www.americanscientist.org/issues/id.3465,y.2005,no.9,content.true,page.1,css.print/issue.aspx. Reprinted, with afterthoughts, in Group Theory in the Bedroom, and Other Mathematical Diversions, Hill and Wang, New York, 2008, pp. 219–237, 252–253.

LEE, KEVIN D. KaleidoMania!: Interactive Symmetry, Windows/Macintosh program, Key Curriculum Press, Emeryville, California, 1999. Lets the user construct rosette, strip, and wallpaper patterns.

LIVIO, MARIO. The Golden Ratio: The Story of Phi, the World’s Most Astonishing Number, Broadway Books, New York, 2002. Reviewed in Notices of the American Mathematical Society, 52 (3) (March 2005): 344–347, at www.ams.org/notices/200503/rev-markowsky.pdf.

MANDELBROT, BENOIT B., and RICHARD L. HUDSON. The (mis)Behavior of Markets: A Fractal View of Risk, Ruin, and Reward, Basic Books, New York, 2004.

MARKOWSKY, GEORGE. Misconceptions about the golden ratio, College Mathematics Journal, 23 (1) (January 1992): 2–19.

POLSTER, BURKARD, and MARTY ROSS. Fibonacci or fairy tale? Math Horizons (February 2015): 16–17.

POSAMENTIER, ALFRED S., and INGMAR LEHMANN. The (Fabulous) Fibonacci Numbers, Prometheus Books, Amherst, NY, 2007.

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POSAMENTIER, ALFRED S., and INGMAR LEHMANN. The Glorious Golden Ratio, Prometheus Books, Amherst, NY, 2011.

WALSER, HANS. The Golden Section, Mathematical Association of America, Washington, DC, 2001.

WASHBURN, DOROTHY K., and DONALD W. CROWE. Symmetries of Culture: Theory and Practice of Plane Pattern Analysis, University of Washington Press, Seattle, 1988. An introduction to the mathematics of symmetry, splendidly illustrated with photographs of patterns from cultures all over the world. Includes a complete analysis of patterns with two colors and proofs that there are only four rigid motions in the plane and exactly seven strip patterns.