Kempe's Multiplicator

To accompany Folding and Unfolding in Computational Geometry: Part I: Ch.4: Kempe's Universality Theorem:Fig.19
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The first construction multiplies the given angle by two.(Also known as Kempe's reversor).

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The second construction extends the first, and shows how to multiply a given angle by 3. He calls it a "multiplicator." It can clearly be extended to multiply any given angle by a positive integer r.

Multiplicator (Proc. London Math Soc.) Multiplicator (How to Draw a Straight Line)

Click on and drag the green point. The three angles incident to A are always equal to each other. (Again, the scale of the linkage can be adjusted by dragging point B.)

Please enable Java for an interactive construction (with Cinderella).

Created with Cinderella
Applets created by Dessislava Michaylova, modified by Michiko Charley