Cartesian coordinates CartesianCoordinates 2004-07-23 05:18:40 2007-05-28 03:54:34 Definition frame abscissa ordinate applicate coordinate % 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} % used for TeXing text within eps files %\usepackage{psfrag} % need this for including graphics (\includegraphics) %\usepackage{graphicx} % for neatly defining theorems and propositions %\usepackage{amsthm} % making logically defined graphics %\usepackage{xypic} % there are many more packages, add them here as you need them % define commands here The {\em Cartesian coordinates} of a point in $\mathbb{R}^3$ for determining its \PMlinkescapetext{place} in three-dimensional space are the three real numbers $x$, $y$ and $z$, which are called \begin{itemize} \item $x$-coordinate or {\em abscissa}, \item $y$-coordinate or {\em ordinate}, \item $z$-coordinate or {\em applicate}. \end{itemize} The last name ``applicate'' is rare in English, but its \PMlinkescapetext{equivalents} in continental European \PMlinkescapetext{languages}, as ``die Applikate'' in German and ``aplikaat'' in Estonian, are more known. Similarly, in $\mathbb{R}^n$ for all\, $n = 1,\,2,\,3,\,\ldots$\, one needs $n$ coordinates for specifying the location of a point.