Line Design (a.k.a. String Art)

In general, one of my goals in designing the Hands-On Math apps was to create ways to simulate learning experiences that students would have if using actual manipulatives.  Simulated manipulatives can offer additional learning opportunities.

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Special features, in the Line Design app, take the learning opportunities beyond what can be down with physical manipulates.  For example, a grid with the x and y axes labelled can be added to the image.

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Line Design can be used for exploring the relationship between geometry and art.  In addition to calling line designs, string art, sometimes it is referred to as aesthenometry, Using the term, aesthenometry, refers more to the aesthetic beauty of the designs.

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It is always fun for students to use boards, nails and various colors of embroidery thread to make string artworks to hang on their wall.  The process involves lots of careful planning, measuring and some materials (boards, nails and string).  The Line Design app can be used to plan the project and to provide help in choosing the colors and design patterns to be used.

Personally my favorite pattern to use for instructional purposes is the circle.  When the circle design is selected a slider appears.  Using the slider the number of points on the circle can be set to any number between 3 and 36.

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There are lots of mathematically interesting explorations that are available in this mode.  Here are a couple of suggestions:

  1. With the number of points set to 12, what shape will result if lines are draw to connect every other point?
  2. What shape results when the number of points is set to 10 and every other point is connected.  What about connecting every fourth point.
  3. What’s the difference between setting the number of points to a prime number versus a composite number?
  4. Set the number of points to 24.  Explore connecting every 4, 6, or 8 point.

The learning environment gets even richer if the circular protractor is added to the iPad display.  In this mode students can measure angles. Here we have the number of points set to 36.  The screen shows a 30° angle.  Two legs of the triangle are radii of the same circle and therefore congruent.  What is the measure of the other two angles?

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