Friday, April 15, 2016

Curve Stitching and Folding: A Hands on Activity

This weekend, the AMS will be hosting a curve stitching activity at the 2016 USA Science & Engineering Festival held in Washington, DC. The idea is that you can create curves by drawing, folding, or stitching a bunch of straight lines. Below is a quick example I folded (folds are drawn over for visibility), using a Project Origami activity. 


You can prove that the lines I folded are all tangent to a parabola whose focus is the marked point and whose directrix is the bottom edge of the paper. This means that the parabola is the envelope of the family of lines I folded. Yarn also works well to create the lines (hence the name curve stitching), as when you thread yarn through two holes and pull it taut, you get a straight line connecting those points. The AMS website has pictures, pattern sheets with instructions, and further resources to check out. This would make a great math circle activity.  Even elementary school students can do the stitching and marvel at the cool pattern they formed!

2 comments:

  1. Fun stuff! I love using that Project Origami book for math circles activities. Also, I did an REU on origami back in the day, and it's a great way to get undergraduate project ideas!

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    1. Yes, Project Origami is one of my favorite books! I don't work with undergraduates a lot, but I'm currently on the lookout for mini-REU type projects that advanced middle and high school students can work on.

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