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Subject:   RE: pantograph
Author: stek
Date: Feb 16 2009

If you have Sketchpad, Cabri, etc. available, you can construct one very easily.
The simple solution is to use a transformation: Dilate point A relative to fixed
point B, creating dilated point C. Then drag point A and trace point C. The
scale factor for the dilation determines the amount of stretching or shrinking
that occurs. Use a negative scale factor to put the image on the opposite side
of B.

Modeling an actual physical pantograph rules out dilation, and so requires a
Euclidean construction. This is a bit more complex; the basic idea is to use a
construction, based on similar triangles, that fixes the lengths of the bars.
(These fixed-length bars are constructed using a
circle-by-center-and-radius construction so that they are free to pivot
while remaining fixed in length.)

Let me know if you want the details of the construction. (If you have either
Exploring Geometry with The Geometer's Sketchpad or a Sketchpad LessonLink
subscription, you already have it. Look for the "Modeling a Pantograph"

Best Regards,

Scott Steketee
Sketchpad Projects

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