String Art and Envelopes, Family of Curves

cults3d

####String Art and Envelopes This is a classic math activity appropriate for children and adults at all levels, easy entry with advanced potentials. There is a lot of existing literature about the string art and the mathematical appeal of the envelopes (or family of curves). #####Among the designs: 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 (with the help of perhaps some super glue?) An equilateral triangle A square. Bars can connected end to end to make various shapes. #####Notes 1. A drop of super glue may be helpful to prevent the angles from changing when tension builds up. Because of the printing material and the tension, it is not practical to make connectors that allow accurate angles, which, in fact, does not matter mathematically. 2. Thin rubber bands or colorful sewing threads or even dental floss can be used to make the envelopes. I just used a spool of rope, as you can see in the pictures. 3. The models can be used for many other mathematical activities such as multiplication or fractions or geometric explorations. Each bar is 12 cm long; the square is 12 x 12. ####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