Parabolas can be obtained from straight segments that connect two moving points. As one of the points changes its position along a line, the other changes position along another line. The succession of segments joining the moving points are traced. This family of line segments will form a parabola. Each segment is tangent to the parabola.

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The interactive figures generated with a dynamic geometry program (Jackiw, 1995; 1998) can be used by middle and high school students to enjoy the beauty of string parabolas and to develop familiarity with them. We give some ideas on how to connect string parabolas to the mathematics class. Some activities are for middle school and early high school students to make connections to mathematical representations such as equations and graphs. Students can stitch, draw, or use a graphing calculator to generate a parabola with straight segments. They can learn some properties of tangent lines to a parabola. More advanced students can use calculus ideas to obtain the equation of the curve that is tangent to a family of straight lines.

Press Animate. Figure 1. Parabola

Content

How a parabola is formed from straight lines

Mathematical analysis of string parabolas

• Activities for middle school and early high school

• Activities for calculus students

Interactive figures

Further explorations

• A gallery of parabola string designs

• Paper folding method

Conclusion

References