\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}