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Epicycloid Evolute

\begin{figure}\begin{center}\BoxedEPSF{EpicycloidEvolute.epsf scaled 800}\end{center}\end{figure}

The Evolute of the Epicycloid

$\displaystyle x$ $\textstyle =$ $\displaystyle (a+b)\cos t-b\cos\left[{\left({a+b\over b}\right)t}\right]$  
$\displaystyle y$ $\textstyle =$ $\displaystyle (a+b)\sin t-b\sin\left[{\left({a+b\over b}\right)t}\right]$  

is another Epicycloid given by
$\displaystyle x$ $\textstyle =$ $\displaystyle {a\over a+2b}\left\{{(a+b)\cos t+b\cos\left[{\left({a+b\over b}\right)t}\right]}\right\}$  
$\displaystyle y$ $\textstyle =$ $\displaystyle {a\over a+2b}\left\{{(a+b)\sin t+b\cos\left[{\left({a+b\over b}\right)t}\right]}\right\}.$  




© 1996-9 Eric W. Weisstein
1999-05-25