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Circular and Countercircular Images of Plane Curves

by Thomas F. Banchoff and E. F. Beckenbach

We extend Gauss's notion of the circular image of a plane curve,
and we introduce the notion of a countercircular image of a plane
curve from a point on the plane. The relationship between these
two images are discussed, and we demonstrate examples of its
application in global differential geometry of plane curves.