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Journal for Geometry and Graphics 19 (2015), No. 2, 219--226
Copyright Heldermann Verlag 2015

Rose Curves with Chebyshev Polynomials

Lászlo Németh
Institute of Mathematics, University of West Hungary, Ady E. u. 5, 9400 Sopron, Hungary

We present a class of curves derived from a geometrical construction. We take points on two half-lines (or lines). The first point is on one of the half-lines and the second one is on the other half-line, while the next is again on the first half-line, and so on. The distance of two consecutive points is the unit. The orbits of these points when the angle of the lines goes from zero to 2π are similar to lemniscates and rose curves. For determining the parametric equation systems of the curves we use Chebyshev polynomials.

Keywords: Lemniscate, rose curve, Chebyshev polynomials.

MSC: 51N20

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