coordinate systemsCoordinateSystems2005-04-28 03:57:142008-09-21 01:04:01Definition% this is the default PlanetMath preamble. as your knowledge
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\newcommand{\sR}[0]{\mathbb{R}}
\newcommand{\sC}[0]{\mathbb{C}}
\newcommand{\sN}[0]{\mathbb{N}}
\newcommand{\sZ}[0]{\mathbb{Z}}
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\newcommand{\Z}{\mathbbmss{Z}}
\newcommand{\C}{\mathbbmss{C}}
\newcommand{\F}{\mathbbmss{F}}
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\newcommand*{\norm}[1]{\lVert #1 \rVert}
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\newtheorem{thm}{Theorem}
\newtheorem{defn}{Definition}
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\newtheorem{cor}{Corollary}\subsubsection*{Plane}
\begin{enumerate}
\item Cartesian coordinates
\item Polar coordinates
\end{enumerate}
\subsubsection*{$\R^3$}
\begin{enumerate}
\item \PMlinkname{Cartesian coordinates}{CartesianCoordinates}
\item Spherical coordinates
\item Cylindrical coordinates
\end{enumerate}
\subsubsection*{Sphere $S^2$}
\begin{enumerate}
\item Stereographic projection
\item Mercator projection
\item ..
\end{enumerate}
\subsubsection*{Miscellaneous}
\begin{enumerate}
\item Barycentric coordinates
\item Homogeneous coordinates $(x,\,y,\,t)$ in plane, $(x,\,y,\,z,\,t)$ in $\R^3$
\end{enumerate}
\subsubsection*{Differential geometry}
\begin{enumerate}
\item \PMlinkname{Normal coordinates}{RiemannNormalCoordinates} in Riemann geometry
\item \PMlinkname{Darboux coordinates}{DarbouxsTheoremSymplecticGeometry} in symplectic geometry
\item Gaussian coordinates
\item Fermi coordinates for a submanifold
\item Boundary coordinates
\end{enumerate}
\subsubsection*{Coordinate transformations}
\begin{enumerate}
\item \PMlinkname{affine transformations}{AffineTransformation}
\item \PMlinkname{continuous transformations}{HomotopyOfPaths} in algebraic topology (homotopy theory)
\item Lorentz group transformations
\item Cartesian-to-polar coordinate transformations
\item Cartesian-to-spherical coordinate transformations
\item A.
\item B.
\end{enumerate}