Curve stitching is the craft of creating the illusion of curves by stitching a
sequence of strategically placed straight stitches.  Invented in the mid 1800s
by Mary Boole and utilized by several sculptors over the past century, this
craft allows artistic expression and mathematical activity at several different
levels.  My own experience with curve stitching began with an art project I did
in elementary school, and in recent years, I have used curve stitching in
designing needlepoint Christmas ornaments.  As an instructor I have started
using curve stitching in my mathematics-for-elementary-school-teachers courses.
This presentation will include a summary of a learning activity developed
around curve stitching the envelope of a parabola.  During this activity,
students develop connections between linear and quadratic functions, solve
systems of linear equations, and produce equations of parabolas by the method
of finite differences.  Graphing calculators are used throughout the analysis.
Problems and extensions for higher level math courses will be presented.  A
bibliography of resources will available as a handout.