String Art: An Adventure in Line Designs

Sometimes what starts out as a doodle can become an exploration in math and appreciated as art.  In my last post, Vi Hart  demonstrated the power of dots and lines and their connections to the conic sections – parabolas, hyperbolas, and more!  Watch that video for the first time and/or watch it again!  Every year I watched my students create their string art designs and every year I saw new designs,  Students beamed with pride when they brought in the finished project. I know that my own children’s projects are still hanging in our house!

Who says you can’t create curves with line segments? It’s fascinating to discover a curve formed from a series of straight line segments. Line designs utilize basic geometric forms, making curves out of segments. Order and symmetry are the basis of string art’s appeal. Elaborate designs can be created with geometric shapes, points, and colored string.

Line designs form a basis for mathematical understanding of geometric shapes and relationships of points, segments, and angles. Each of the line segments is really a tangent for each of the curves being formed. But because of what we focus on, we often see the curves. For example, some of the curves that can be created are circles, parabolas, ellipses, hyperbolas, spirals, and some less known curves called cardioids, limacons, and deltoids. Yet in each case they were created with angles of different sizes, regular and irregular polygons, and a lot of segments and points.

Attractive and sophisticated line designs can be produced and created using only a ruler, compass, protractor, pencil, and paper. Computers and dynamic geometry software such as Geometer’s Sketchpad can be used to help students explore these shapes and Symmetry – line symmetry, rotational symmetry, and point symmetry while bringing interest and charm to their string art.

Start with something like the drawing on the right and end up with string art like the ones on the right.

Watch a video to learn how to set up ANGLES for string art String art with circles

Students can use nails and wood, foam core or cork with strong pins, or a stiff piece of cardboard or thin wood with holes in it to provide your working surface. They can paint or cover the working surface. String, embroidery thread or thin yarn can be used to stitch a piece of mathematical art. The original placement of the nails/holes help to determine the shape of the final project. For instance, if the diagonals of a regular 24-gon (an icosikaitetragon) are constructed in different patterns, you might see many concentric circles. By adding different layers, different colors, and/or varying the way you connect the nails/holes, the design gets more interesting. Sometimes the empty spaces in the design are as important as the placement of the string. Notice how a curve was formed by connecting points along the sides of an angle in the illustration below. Students can use a compass (and straightedge and colored pencils) or dynamic geometry software to create an original and interesting pattern to stitch.

Here are some good websites to find directions, examples and more!!!

Don’t want to pound nails or push pins? Take a look at these sites for ideas!

What did the string art look like?  See examples of student work

Other available documents to download

  • major parts and materials
  • teacher notes
  • grading rubric

About napmath

I recently retired from full-time teaching. I taught students in High School math classes from Basic Math through AP Calculus. I have been into integrating technology into my classes since 1981. I am Nationally Board Certified, am the proud recipient of a Presidential Award of Excellence in Math Teaching, text book author, Golden Apple Scholar, Certified SMART Board Trainer, Regional Technology Teacher of the Year, and give workshops across the country - geometry, Common Core, mathematics, Interactive Whiteboards, and technology. I am currently working as an adjunct faculty member at Illinois Wesleyan University and authoring books for SMART Boards and Promethean Boards with Vision Technology.
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One Response to String Art: An Adventure in Line Designs

  1. David Press says:

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