Part I. Preliminary Issues. 1. Introduction and Overview. 2. How Polygons are Drawn. 3. String Art Basics. 4. Issues involving Commonality. 5. Cycles. 6. Alternative ways to Obtain an Image. 7. Levels of Subdivision Points. 8. Shape-Shifting Polygons. 9. An Overarching Question. 10. Functionally Modified String Art files. 11. A sampling of Image Archetypes. 12. n = P images. 13. 60-Second Images. 14. Challenge Questions for Part II. 15. Centered-Point Flowers. 16. Double Jump Models. 17. Four Color Clock Arithmetic. 18. Larger Jump Set Models. 19. Busting out of our Polygonal Constraint. 20. Challenge Questions for Part III. 21. Basic Properties of Numbers. 22. Angles in Polygons and Stars. 23. Modular Arithmetic. 24. Modular Multiplicative Inverses, MMI. 25. A Guide to the Web Model. 26. Suggestions for Mathematics Teachers.
Biography
Stephen Erfle is a professor at Dickinson College. Although he was trained as a microeconomic theorist specializing in industrial organization and regulation, he has spent much of his academic life working at the borders of traditional economics. He has used his economist’s toolkit to examine topics in a wide variety of fields including public health, exercise psychology, political geography, mathematics education, and communications theory in addition to economics.
He has consulted for a variety of organizations including the Seagram Classics Wine Company, the Forum on Education Abroad, and the Pennsylvania Department of Health. His Seagram Classics sabbatical reoriented the direction of his teaching and research as it turned his former analytical focus (theorem and proof) into a more empirical focus (what does the data tell us). It also led him to cofound the international business and management major at Dickinson College. One of the core courses in that major, Managerial Decision Making, teaches students to analyze the kinds of decisions he was asked to answer during his time working for Seagram Classics.
He has spent much of his time in the past couple of decades devoted to pedagogical issues revolving around providing geometric interpretations and explanations for a variety of topics. The books and papers in these topic areas seek to explain economic and mathematical concepts in intuitive terms, often to students with limited mathematical backgrounds.
He received his BS in Mathematics and BA in Economics from University of California, Davis, and Ph.D. in Economics from Harvard University.
“This large format paperback edition of Stephen Erfle's "Electronic String Art: Rhythmic Mathematics" from CRC Press is especially and unreservedly recommended for personal, professional, and college/university library digital art collections.”
-Midwest Book Review
"String art involves winding string around nails on a board (hence is unrelated to string figures, in which string is strung using fingers of one or more people). Author Erfle provides parameterized spreadsheet and web-based tools to produce images with varying characteristics (although all are centrally symmetric). The book contains lessons on how the images change with the parameters, suitable for middle school students. Little mathematics beyond counting is assumed, but later explanations involve modular arithmetic and theorems about angles in a circle."
-MAA Mathematics Magazine
