ABSTRACT

String art is a well-known and popular activity that uses string, a board, and nails to produce artistic images (although there are variations that use different modalities). This activity is beloved because simple counting rules are used to create beautiful images that can both adorn walls and excite young minds. The downside of this highly tactile activity is that it is quite time-consuming and rigid. By contrast, electronic string art offers much more flexibility to set up or change nail locations and counting rules, and the images created from those changes change instantaneously.

Electronic String Art: Rhythmic Mathematics invites readers to use the author’s digital resources available on the ESA website to play with the parameters inherent in string art models while offering concise, accessible explanations of the underlying mathematical principles regarding how the images were created and how they change. Readers will have the opportunity to create visually beautiful works of art while learning concepts from geometry, number theory, and modular arithmetic from approximately 200 short-interdependent sections.

Features

  • Readers are able to drill-down on images in order to understand why they work using short (1 to 2 page) stand-alone sections
    • Sections are lessons that were created so that they could be digested in a single sitting
    • These sections are stand-alone in the sense that they need not be read sequentially but can be referred to based on images that the reader finds interesting
  • An open-ended, inherently flexible teaching resource for elementary, middle, and high school-level mathematics
    • The most mathematically challenging sections (or portions of a section) are designated MA and may not be accessible to elementary and middle school readers
  • Will be appreciated by anyone interested in recreational mathematics or mathematical artworks even if the users are not interested in the underlying mathematics
  • Includes exercises, solutions, and many online digital resources
  • These QR codes take you to these digital resources. One takes you directly to the web version of the string art model (used as a starting point for teaching the parameters of the model in Section 25.5). The other takes you to the ESA web page with additional links to a variety of resources.

part I|38 pages

Preliminary Issues

chapter Chapter 1|10 pages

Introduction and Overview

chapter Chapter 2|26 pages

Polygons and Stars

part II|156 pages

String Art

chapter Chapter 3|5 pages

String Art Basics

chapter Chapter 4|11 pages

Issues Involving Commonality

chapter Chapter 5|10 pages

Cycles

chapter Chapter 6|8 pages

Alternative ways to Obtain an Image

chapter Chapter 7|7 pages

Levels of Subdivision Points

chapter Chapter 8|10 pages

Shape-Shifting Polygons

chapter Chapter 9|12 pages

An Overarching Question

chapter Chapter 10|17 pages

Functionally Modified String Art Files

chapter Chapter 11|30 pages

A Sampling of Image Archetypes

chapter Chapter 12|24 pages

n = P Images

chapter Chapter 13|7 pages

60-Second Images

chapter Chapter 14|13 pages

Challenge Questions for Part II

part III|82 pages

Variations on the String Art Model

chapter Chapter 15|14 pages

Centered-Point Flowers

chapter Chapter 16|14 pages

Double Jump Models

chapter Chapter 17|9 pages

Four-Color Clock Arithmetic

chapter Chapter 18|14 pages

Larger Jump Set Models

chapter Chapter 19|11 pages

Busting Out of Our Polygonal Constraint

chapter Chapter 20|18 pages

Challenge Questions for Part III

part IV|58 pages

Issues, Mathematical and Otherwise

chapter Chapter 21|9 pages

Basic Properties of Numbers

chapter Chapter 22|5 pages

Angles in Polygons and Stars

chapter Chapter 23|7 pages

Modular Arithmetic

chapter Chapter 24|8 pages

Modular Multiplicative Inverses, MMI

chapter Chapter 25|9 pages

A Guide to the Web Model

chapter Chapter 26|9 pages

Suggestions for Mathematics Teachers

chapter Chapter 27|5 pages

Challenge Question Answers