octant Octant 2009-03-22 13:40:01 2009-03-23 07:41:48 Definition solid angle first octant % 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 \theoremstyle{definition} \newtheorem*{thmplain}{Theorem} The coordinate planes ($yz$-plane, $zx$-plane, $xy$-plane) \PMlinkescapetext{divide} the space $\mathbb{R}^3$ into eight trihedral angles, which are called the \emph{octants} of the space.\, The magnitude of each octant as a solid angle is $\frac{\pi}{2}$.\, Any coordinate of a point moving in a certain octant preserves its \PMlinkname{sign}{SignumFunction}.\, One calls the octant, where all three coordinates are nonnegative, \emph{the first octant}.\, The other octants have no agreed numbering; see still \PMlinkexternal{Wikipedia}{http://de.wikipedia.org/wiki/Oktant_(Geometrie)}.