Rectification

Quadratrix Synchronization

The quadratrix curve is described as follows: ABCD is a square and BED is a quadrantπ of a circle with centre A and radius AB. As the radius AB rotates about A to move to the position AD then the line BC translates at the same rate parallel to itself (for instance, B′C′) to terminate at AD. Then. the locus of the point of intersection F of the rotating radius AB (for instance, AE=AB) and the parallel translating line BC is the quadratrix.




The quadratrix curve derives its name from the fact that its characteristic property, called its symptoma, encodes a specific relation that decodes into the rectification of the circle. This simply means that the quadratrix curve serves as a bidirectional bridge to square the circle. Originally, it was designed to construct angle division in any given ratio. The rectification property appears to have been discovered afterwards. The curve is generated via synchronized motions, and the ratio of the speeds involved implies π, essentially (the ratio of the circumference of a quadrant and the radius of a circle).

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