famous curvesFamousCurvesInThePlane2005-05-18 13:58:542009-09-21 19:08:26Topic% this is the default PlanetMath preamble. as your knowledge
% of TeX increases, you will probably want to edit this, but
% it should be fine as is for beginners.
% almost certainly you want these
\usepackage{amssymb}
\usepackage{amsmath}
\usepackage{amsfonts}
\usepackage{amsthm}
\usepackage{mathrsfs}
% used for TeXing text within eps files
%\usepackage{psfrag}
% need this for including graphics (\includegraphics)
%\usepackage{graphicx}
% for neatly defining theorems and propositions
%
% making logically defined graphics
%\usepackage{xypic}
% there are many more packages, add them here as you need them
% define commands here
\newcommand{\sR}[0]{\mathbb{R}}
\newcommand{\sC}[0]{\mathbb{C}}
\newcommand{\sN}[0]{\mathbb{N}}
\newcommand{\sZ}[0]{\mathbb{Z}}
\usepackage{bbm}
\newcommand{\Z}{\mathbbmss{Z}}
\newcommand{\C}{\mathbbmss{C}}
\newcommand{\F}{\mathbbmss{F}}
\newcommand{\R}{\mathbbmss{R}}
\newcommand{\Q}{\mathbbmss{Q}}
\newcommand*{\norm}[1]{\lVert #1 \rVert}
\newcommand*{\abs}[1]{| #1 |}
\newtheorem{thm}{Theorem}
\newtheorem{defn}{Definition}
\newtheorem{prop}{Proposition}
\newtheorem{lemma}{Lemma}
\newtheorem{cor}{Corollary}\subsection*{Closed curves}
\begin{itemize}
\item Circle
\item Ellipse
\item Astroid
\item Cardioid
\item Cassini oval
\item Lemniscate
\item graphs of spherical functions
\item Lissajous curves
\end{itemize}
\subsection*{Periodic curves}
\begin{itemize}
\item Sinusoid
\item Cycloid
\item \PMlinkname{Triangular-wave curve}{SawBladeFunction}
\item Helix
\end{itemize}
\subsection*{Unbounded}
\begin{itemize}
\item \PMlinkname{Line}{LineInThePlane}
\item Hyperbola
\item Parabola
\item Semicubical parabola
\item Logarithmic spiral
\item Archimedean spiral
\item Nielsen's spiral
\item \PMlinkname{Gaussian}{GaussianIntegral} and Lorentzian curves
\item graphs of Bessel functions
\item graphs of Legendre polynomials
\item Catenary
\item Tractrix
\item Clothoid
\item Lam\'e's cubic
\item Witch of Agnesi
\item Cissoid of Diocles
\item Conchoid of Nicomedes
\item Quadratrix of Hippias
\item graphs of damped sine and cosine functions
\item graphs of sinc function, sine integral, gamma function, \PMlinkname{function $x^x$}{FunctionXx}
\end{itemize}
\PMlinkexternal{ENCYCLOP\'EDIE DES FORMES MATH\'EMATIQUES REMARQUABLES}{http://www.mathcurve.com/courbes2d/courbes2d.shtml}