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\course \hfill Russell Brown \\
Project 1  \hfill  8 September 1998.

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For our first project, your assignment is to do parts 1 to 5 of the
Laboratory project on families of hypocycloids on p. 55 of
Stewart. You will begin in recitation. You will probably need
additional time outside of recitation to complete this project. the
project is due on Friday, 9/18 at 10am.


You are to work in groups of 2 to 4.
 If you wish to work with
someone in a different section, please see Brown to make arrangements.
Each group should hand in a 2-7 page report describing what you have
done and answering each of the questions in Stewart's text.
Your answers to  2,  3 and 4  should be illustrated by sketches which
you have copied from your calculator screen. Please label these
sketches and give the values of the parameters $a$ and $b$ so that I
 can check your work, if
necessary.  In 1 and 5 you will want to include a sketch to illustrate
 the quantities which arise in your derivation. All answers should be
 written out in complete sentences. Use the explanations from the text
 as models for your answers.




{\bf Plotting hypocycloid curves efficiently. } You will find the entering
the Bezier curve into your calculator is very time consuming. Since
the project involves a bit of experimentation, you will want to be
able to do this as efficiently as possible. One way to do this is to
enter the functions on p. 55 into your calculator with letters for the
parameters $a$ and $b$.  (On the TI-82, letters are obtained by
touching the grey {\tt ALPHA } key and then touching the key with the
desired letter in grey at the upper right hand corner of the key.
Then you may store numerical values to the letters $A$ and $B$ and
plot the graph. This is done entering the number, touching the {\tt
STO } key, entering the letter and then touching the {\tt ENTER } key.
For example, if you touch {\tt 5, STO, ALPHA, A, ENTER } then
$$
5\rightarrow A
$$
appears on your screen.  Now, if you touch {\tt ALPHA, A, ENTER } the
calculator evaluates {\tt A } to the numerical value 5.
Now you may change the values of A and B in the formulas for the
hypocycloid without having to reenter the entire expression.

{\bf Policy on group work. }  Each member of the group must make a
substantial contribution to the project.  To make sure that each of
you abide by this policy, write on  the cover page: ``Each member
of the group made  substantial contribution to the completion of this
project''. Then each group member must sign. By signing, you are
indicating that you agree with this statement. 

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