%Space Curves
%If you modify this file, please indicate here and in the footnote.
%Math263C 

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\begin{document}

\begin{center}
\Large
Space Curves\footnote{Copyright \copyright 2006 Todd Young.
All rights reserved. Please address comments to young@math.ohiou.edu.}
\end{center}

\begin{enumerate}

\item Try the following commands:\\
      \verb& t = 0:pi/60:8*pi; & \\
      \verb& x = cos(t); & \\
      \verb& y = sin(t); & \\
      \verb& z = t;& \\
      \verb& plot3(x,y,z)&\\
What is the geometric object? Click on the \verb&Tools& icon
and select \verb&Rotate 3D&. You can then use the mouse to
rotate the plot. Repeat the above command but change the 60 
in the first command to 6. That is the effect? What is the
effect of changing the 8 to 4?

      
\item Try the following commands:\\
      \verb& t = -2:.1:2; & \\
      \verb& x = t; & \\
      \verb& y = t.^2; & \\
      \verb& z = t.^3; & \\
      \verb& plot3(x,y,z) & \\
Click on the \verb&Tools& icon, select \verb&Rotate 3D& and use the mouse to
rotate the plot. What do the projections on the $x$-$y$ and $x$-$z$ planes
look like? What about the $y$-$z$ plane? Write the equations of
these projections in cartesian coordinates, i.e. $x$ and $y$ for the first one,
$x$ and $z$ for the second, etc..

\item Try the following commands and describe the graph (rotate if needed):\\
      \verb& t = 0:.01*pi:2*pi; & \\
      \verb& x = (4+sin(20*t))*cos(t); & \\
      \verb& y = (4+sin(20*t))*sin(t); & \\
      \verb& z = cos(20*t); & \\
      \verb& plot3(x,y,z) &


\item Try the following commands and describe the graph (rotate if needed):\\
      \verb& t = 0:.01*pi:4*pi; & \\
      \verb& x = (2+cos(1.5*t)).*cos(t); & \\
      \verb& y = (2+cos(1.5*t)).*sin(t); & \\
      \verb& z = sin(1.5*t); & \\
      \verb& plot3(x,y,z) & \\




\item Using complete sentences and standard mathematical notation, 
prepare a brief written report.  Do {\bf not} get a printout.

\end{enumerate}

\vfill

\textsf{\noindent
The user plots (parametric) curves in 3 dimensions. }


\end{document}
