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<record version="1" id="659">
 <title>dihedral angle</title>
 <name>DihedralAngle</name>
 <created>2009-04-18 08:59:20</created>
 <modified>2009-04-18 08:59:20</modified>
 <type>Definition</type>
 <creator id="21" name="pahio"/>
 <modifier id="1" name="bloftin"/>
 <comment>The PNG render is failing because the article uses:

\usepackage{pstricks}
\usepackage{pst-plot}

and in your environment that pulls in pstricks-add, which then dies on:

I can't find file `pst-arrow'

So this is another PSTricks-chain failure, not a math-content failure.

Recommended fix
remove pstricks and pst-plot
add graphicx
replace the inline PSTricks sketch with a static PNG
optionally keep a TikZ source file for the figure</comment>
 <author id="21" name="pahio"/>
 <classification>
	<category scheme="pacs" code="02.40.Dr"/>
 </classification>
 <preamble>% 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}
\usepackage{pstricks}
\usepackage{pst-plot}

% there are many more packages, add them here as you need them

% define commands here

\theoremstyle{definition}
\newtheorem*{thmplain}{Theorem}</preamble>
 <content>Two distinct half-planes, emanating from a same line $l$, \PMlinkescapetext{divide} the space ($\mathbb{R}^3$) into two regions called {\em dihedral angles}.\, The line $l$ is the {\em edge} of the dihedral angle and the bounding half-planes are its {\em sides}.

\begin{center}
\begin{pspicture}(-3,-1)(3,3)
\psline[linewidth=0.05](-2.5,-1)(1.5,-1)(2.5,0)(2,2)(-2,2)
\psline(-2,2)(-1.5,0)(-2.5,-1)
\psline(-2.1,0)(3,0)
\rput(0,0.2){$l$}
\end{pspicture}
\end{center}


The angle, which the sides of a dihedral planes separate from a normal plane of the edge, is the {\em normal section} of the dihedral angle.\, Apparently, all normal sections are equal.\, According to the \PMlinkescapetext{size} of the normal section, the dihedral angle may be called acute, right, obtuse, straight, \PMlinkname{skew}{ConvexAngle}, convex and concave.\, Unlike the angle between two planes, a dihedral angle may be over 90 \PMlinkescapetext{degrees}.

If two planes intersect each other and if one of the four dihedral angles formed is right, then also the others are right.\, Then we say that the planes are {\em perpendicular} to each other.</content>
</record>
