PlanetMath (more info)
 Math for the people, by the people. Sponsor PlanetMath
Encyclopedia | Requests | Forums | Docs | Wiki | Random | RSS  
Login
create new user
name:
pass:
forget your password?
Main Menu
Revision difference : explementary
Version current Version 4
The {\em explementary arc} of an arc $a$ of a circle is the arc forming together with $a$ the full circle. The {\em explementary arc} of an arc $a$ of a circle is the arc forming together with $a$ the full circle.
Two angles are called {\em explementary angles} of each other, if their sum is the {\em full angle} $2\pi$, i.e. $360^\circ$. In the below picture, the \PMlinkescapetext{interior angle} \,$\alpha = 60^\circ$\, of an equilateral triangle and its explementary angle\, $\beta = 300^\circ$\, (which is an \PMlinkescapetext{exterior angle} of the triangle) are seen. Two angles are called {\em explementary angles} of each other, if their sum is the {\em full angle} $2\pi$, i.e. $360^\circ$. In the below picture, the \PMlinkescapetext{interior angle} \,$\alpha = 60^\circ$\, of an equilateral triangle and its explementary angle\, $\beta = 300^\circ$\, (which is an \PMlinkescapetext{exterior angle} of the triangle) are seen.
\begin{center} \begin{center}
\begin{pspicture}(-2,-1)(2,3) \begin{pspicture}(-1,-3)(2,3)
\pspolygon(-1.5,0)(1.5,0)(0,2.6) \pspolygon(-1.5,0)(1.5,0)(0,2.6)
\psarc(0,2.6){0.2}{-60}{240} \psarc(0,2.6){0.2}{-60}{240}
\rput[a](0,2.2){$\alpha$} \rput[a](0,2.2){$\alpha$}
\rput[a](-0.2,2.9){$\beta$} \rput[a](-0.2,2.9){$\beta$}
\rput(-2,-0.5){.}
\rput(2,3){.}
\end{pspicture} \end{pspicture}
\end{center} \end{center}