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\begin{document}
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$\displaystyle \varepsilon$%
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\begin{displaymath}\begin{split}   \frac{S}{2N} &= (R-w+w_x)(\frac{\pi}{N} - \varepsilon) +                   (r_1+w_x)a+(R-w-r_1)\frac{\sin{\varepsilon}}{\sin{\eta}}\\                  & \quad - (r_1+w_x)\tan{(\frac{\pi}{2}-\eta)}                + (r_2-w_x)(\frac{\pi}{2}-\eta) \\                 & \quad - (r_2-wx)\tan{(\frac{\pi}{2}-\eta)}\\                 &= (R-w+w_x)(\frac{\pi}{N} - \varepsilon) +                   (r_1+w_x)a+(R-w-r_1)\frac{\sin{\varepsilon}}{\sin{\eta}}\\                  & \quad - (r_1+r_2)\tan{(\frac{\pi}{2}-\eta)}                + (r_2-w_x)(\frac{\pi}{2}-\eta)\\    \end{split}\end{displaymath}%
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\begin{displaymath}\begin{split}   \frac{S}{2N} &= (R-w+w_x)(\frac{\pi}{N} - \varepsilon) +                  (r_1+w_x)a+(R-w-r_1)\frac{\sin{\varepsilon}}{\sin{\eta}}\\                  & \quad - (r_1+w_x)\tan{(\frac{\pi}{2}-\eta)}\\   \end{split}\end{displaymath}%
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\begin{displaymath}\begin{split}    \frac{\delta S}{\delta w_x} &= 2N\left[ \frac{\pi}{N} -\varepsilon +                                   a - \tan{(\frac{\pi}{2} - \eta)} \right]\\                                 &= 2N\left[ \frac{\pi}{2} - \eta +                                   \frac{\pi}{N} - \tan{(\frac{\pi}{2}                                   - \eta)} \right]\\    \end{split}\end{displaymath}%
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$\displaystyle \frac{S}{2N} = (R-w+w_x)(\frac{\pi}{N}-\varepsilon) +                 (r_1+w_x)\left[ \varepsilon +                \arcsin{(\frac{R-w-r_1}{r_1+w_x}\sin{\varepsilon}}) \right]$%
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{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline998}%
$ r_1 = 1/16 in$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay1004}%
$\displaystyle w = 0.500$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlpictureA{tex2html_wrap617}%
\includegraphics[]{img/res.ps}%
\lthtmlpictureZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlpictureA{tex2html_wrap625}%
\includegraphics[height=4in]{img/perimeter.ps}%
\lthtmlpictureZ
\lthtmlcheckvsize\clearpage}

\stepcounter{section}

\end{document}