 TOPICS  # Inverse Curve

Given a circle with center and radius , then two points and are inverse with respect to if . If describes a curve , then describes a curve called the inverse of with respect to the circle (with inversion center ). The Peaucellier inversor can be used to construct an inverse curve from a given curve.

If the polar equation of is , then the inverse curve has polar equation (1)

If and , then the inverse has equations   (2)   (3)

Inversion, Inversion Center, Inversion Circle, Peaucellier Inversor, Reciprocal, Reciprocal Curve, Reciprocation

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## References

Lawrence, J. D. "Inversion." §2.3 in A Catalog of Special Plane Curves. New York: Dover, pp. 43-46 and 203, 1972.Welke, S. "Inversion of Elementary Algebraic Curves with Respect to a Circle." Mathematica Educ. Res. 4, 16-22, 1995.Wells, D. The Penguin Dictionary of Curious and Interesting Geometry. London: Penguin, p. 120, 1991.Yates, R. C. "Inversion." A Handbook on Curves and Their Properties. Ann Arbor, MI: J. W. Edwards, pp. 127-134, 1952.

Inverse Curve

## Cite this as:

Weisstein, Eric W. "Inverse Curve." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/InverseCurve.html