• Let C be a curve in the plane that
includes the origin and is
twice continuously differentiable at the
origin. Define Cr, P, Q, and R as in the Generalized
Shrinking Circle Problem. If the curvature
at the origin, k, is positive, the osculating circle of C at the origin has radius r=1/k and center (a, b) where a2 + b2 = r2.
•
•Then,
• R à (4r, 0 ) if b=0
• R à ( 0, 0 ) otherwise
•