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Intrinsically Defined Curves and Special Functions

Antonín Slavík
Mathematics Magazine
Vol. 86, No. 3 (June 2013), pp. 211-219
DOI: 10.4169/math.mag.86.3.211
Stable URL: http://www.jstor.org/stable/10.4169/math.mag.86.3.211
Page Count: 9
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Abstract

Summary We study two classes of plane curves with prescribed curvature. First, we investigate spirals whose curvature is a power function, and express coordinates of the spirals’ centers in terms of the gamma function. For curves in the second family, the curvature is a multiple of the sine function. We show that this family contains infinitely many closed curves and provide their characterization in terms of the zeroth-order Bessel function.

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