polar curvePolarCurve2005-05-18 17:52:462005-05-20 11:55:44Examplefamous curveslemniscaterhodoneacardioidlimacon\usepackage{amssymb,amscd}
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% define commands herePolar curves are plane curves in $\mathbb{R}^2$ that are expressed in polar coordinates $(r,\theta)$. The two simplest polar curves are obtained when one of the two coordinates is set to be a constant. If the first coordinate is set to a constant $r$, we have a circle with radius $\lvert r \rvert$, or a point when $r=0$. When the second coordinate is the constant instead, say $c$, we have a straight line through the (polar) origin, with slope = $\tan c$.
\begin{center}
\includegraphics{polar_curve_1.eps}
\hspace{1in}
\includegraphics{polar_curve_2.eps}
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Using polar coordinates, one can generate many visually pleasing
curves. Below are some of the most popular ones.
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\includegraphics{polar_curve_3.eps}
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\includegraphics{polar_curve_4.eps}
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\includegraphics{polar_curve_5.eps}
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\includegraphics{polar_curve_6.eps}
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\includegraphics{polar_curve_7.eps}
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\includegraphics{polar_curve_8.eps}
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\includegraphics{polar_curve_9.eps}
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