Supplementary Investigation 3

Tangents and Curves of Constant Width

Tool(s) Geometers Sketchpad

Data File(s) si3

Focus A curve of constant width is a convex oval in which the distance between parallel tangents is constant.

Tasks

1. Double click the Animate button. A single click stops the animation. The curve may be resized by moving points A and B. Discuss your observations.

2. Imagine that the parallel lines were fixed and the curve turned between them. What shape would the turning curve trace out between the lines? If you had a drill that behaved in this manner, what shape holes would it drill?

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