String Art and Envelopes, Family of Curves

cults3d

String Art and Envelopes This classic math activity is a great way to get kids and adults alike involved in some serious problem-solving, with an easy entry point that quickly escalates into more complex challenges. There's a wealth of existing literature out there exploring the string art and mathematical appeal of these envelopes, or family of curves. Among the designs you can create: A bar with hexagonal connectors for 60-degree or 120 degree angles. A bar with hexagonal connectors for a 90-degree angle. A bar with octagonal connectors that allow 45-degree, 90-degree, 135 degree angles. A bar with circular connectors for flexible angles - just be sure to use some super glue to keep things in place! An equilateral triangle A square. Bars can be connected end to end to make all sorts of shapes and designs. Notes: 1. A little super glue can go a long way in keeping those angles from shifting as the tension builds up. 2. You can use thin rubber bands, colorful sewing threads, or even dental floss to create your envelopes - I just happened to have some rope on hand. 3. These models are perfect for exploring all sorts of mathematical concepts, like multiplication and fractions, or just for getting a feel for geometric shapes. References: 1. Quenell, Gregory. (2009). Envelopes and String Art. Mathematics Magazine. Vol. 82, No. 3, pp. 174-185. Mathematical Association of America. Available at https://www.jstor.org/stable/27765898 2. http://www.ams.org/publicoutreach/curve-stitching 3. http://users.bestweb.net/~quenell/slides/stringart.pdf 4. https://geometryexpressions.com/downloads/StringArt.pdf 5. https://en.wikipedia.org/wiki/String_art