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Parallel curves at infinity. (English)
Pi Mu Epsilon J. 10, No. 1, 39-41 (1994).
Let $β$(t) = (x(t), y(t)) denote a smooth curve in $R^2$. We will say that a curve $β_r$ is r-parallel to $β$ if $β_r(t)=β(t)+rN(t)$ where $N(t)=(-y\rq(t),x\rq(t))/\sqrt{(x\rq(t))^2+(y\rq(t))^2}$. In this note we will show that at infinity all r-parallel curves are circles. (orig.)
Classification: I65
Keywords: r-parallel curves