Although Hippias' quadratrix cannot truely be constructed in the classical Greek sense of construction - i.e. compass and straightedge - we can classically construct 2^*n* points on the curve for arbitrarily large *n*. This construction is giving in the following activity.

- Start by constructing a square
**ABPO**. - Bisect angle
**AOP**. - Construct the perpendicular bisector of segment
**OA**. - The point of intersection of the angle bisector and the perpendicular bisector is a point on the quadratrix.
- To construct two additional points on the quadratrix, bisect the two angles formed in Step 1.
- Construct the perpendicular bisectors of the two segments formed in Step 2 (by bisecting
**OA**). - The intersection of
**corresponding**angle bisectors and perpendicular bisectors are points on the quadratrix. - Continue in this manner by dividing angle
**AOP**into 2^*n*parts and segment**OA**into the same number of parts for arbitrarily large*n*. The intersection of**corresponding**parts are points on the quadratrix.

It is interesting to note that this construction method to find points on Hippias' quadratrix has nothing to do with the concept of uniform motion in the difinition.

Return to Hippias' Quadratrix Page

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http://www.geom.umn.edu/~huberty/math5337/groupe/quadconstruct.html

Created: March 1996 ---- Last Modified: July 6, 1997

Copyright © 1996-1997 Michael D. Huberty, Ko Hayashi & Chia Vang