Abstract
Motivated by a problem posed by David A. Singer in 1999 and by the classical Bernoulli lemniscate and the Norwich spiral, we study the plane curves whose curvature is expressed in terms of the distance from a point. In terms of the geometric angular momentum, we provide new characterizations of some well-known curves, like the mentioned Bernoulli lemniscate, the inverse Norwich spiral, the anti-clothoid, the cardioid, the sinusoidal spirals and the Cassini ovals. We also find out several new families of plane curves whose intrinsic equations are expressed in terms of elementary functions and we are able to get their arc-length parametrizations and they are depicted graphically.
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