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\input preamble.tex
\Defnum(\n,2)
\newdimen\x
\newdimen\y
\def\ds{\displaystyle}
% -------------------------------------------------------------------------
% 1. Epicycloid:
% x(t)=r/(n+1)*[n*cos(t)-cos(n*t)]
% y(t)=r/(n+1)*[n*sin(t)-sin(n*t)]
% -------------------------------------------------------------------------
\def\Epicycloid(#1,#2){\Dset(\y,#2) \Dset(\x,#1) \Dadd(\x,1) \Ddiv(\y,\x)
\def\Tx(##1,##2){\Cos(##1,##2) ##2=#1##2 \Dset(\x,##1) \x=#1\x
\Cos(\Np\x,\x) \Sub(##2,\x) \Dmul(##2,\y)}
\def\Ty(##1,##2){\Sin(##1,##2) ##2=#1##2 \Dset(\x,##1) \x=#1\x
\Sin(\Np\x,\x) \Sub(##2,\x) \Dmul(##2,\y)}
\Tplot(200)(0,6.2832)}
% -------------------------------------------------------------------------
% 2. Hypocycloid:
% x(t)=r/(n+1)*[n*cos(t)+cos(n*t)]
% y(t)=r/(n+1)*[n*sin(t)-sin(n*t)]
% -------------------------------------------------------------------------
\def\Hypocycloid(#1,#2){\Dset(\y,#2) \Dset(\x,#1) \Dadd(\x,1) \Ddiv(\y,\x)
\def\Tx(##1,##2){\Cos(##1,##2) ##2=#1##2 \Dset(\x,##1) \x=#1\x
\Cos(\Np\x,\x) \Add(##2,\x) \Dmul(##2,\y)}
\def\Ty(##1,##2){\Sin(##1,##2) ##2=#1##2 \Dset(\x,##1) \x=#1\x
\Sin(\Np\x,\x) \Sub(##2,\x) \Dmul(##2,\y)}
\Tplot(200)(0,6.2832)}
% -------------------------------------------------------------------------
\begin{document}
\unitlength1.5cm
\begin{center}
{\Huge\bf{I. Epicycloids}}
\bigskip
\begin{lapdf}(12,12)(-6,-6)
\Polgrid(1,2)(6)
\Whilenum{\n<7}{\Stepcol(0,23,4) \Epicycloid(\n,6) \Stroke \Add(\n,1)}
\end{lapdf}
$x(t)=\frac{\ds r}{\ds{n+1}}[n\cos(t)-\cos(nt)]$ \qquad
$y(t)=\frac{\ds r}{\ds{n+1}}[n\sin(t)-\sin(nt)]$
\newpage
{\Huge\bf{II. Hypocycloids}}
\bigskip
\begin{lapdf}(12,12)(-6,-6)
\Resetcol
\Polgrid(1,2)(6)
\Whilenum{\n<7}{\Stepcol(0,23,4) \Hypocycloid(\n,6) \Stroke \Add(\n,1)}
\end{lapdf}
$x(t)=\frac{\ds r}{\ds{n+1}}[n\cos(t)+\cos(nt)]$ \qquad
$y(t)=\frac{\ds r}{\ds{n+1}}[n\sin(t)-\sin(nt)]$
\end{center}
\end{document}
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