MATH 1511 – Final Project
Instructions: You must type all answers to the following questions into a Maple worksheet (which should also
contain your name). You must send me that Maple worksheet as an attachment to an email message to me
(wachsmut@shu.edu) on or before May 6, 2005. You are required to complete this assignment on your own, but
you may use Maple, and/or any type of calculator, and/or any Calc book you like.
It is perfectly okay to use Maple to help you with any calculation, but if you rather do the calculations manually, that
would be fine as well as long as you type up sufficient explanations in your Maple worksheet.
To answer the various “conjectures”, type as much as you feel is necessary to convey your ideas. Support your
conjectures with Maple plots or computations, if appropriate.
I know it is exceedingly easy to “copy” assignments like this – any plagiarism or cheating I detect it will result in 0
points for every project involved and any further action that seems appropriate. Note that all projects differ slightly.
If you have any questions, please send me electronic mail as soon as possible.
Question 1: Below are four parametric curves, and four named parametric equations. Which
curve belongs to which equation?
Lissajous curve:
)cos(4)( ttx
)2sin(2)( tty
Evolute of ellipse:
)(cos)(
3
ttx
)(sin2)(
3
tty
Involute of circle:
)sin()cos()( ttttx
)cos()sin()( tttty
Serpentine curve:
)cot()( ttx
)cos()sin(4)( ttty
Conjecture: Describe how the Lissajous curves
)cos(4)( ttx
,
)sin(2)( ntty
will look for
different values of n, where n is a positive integer.
Question 2: In Greek, the word cycloid means “wheel”, the word hypocycloid means “under the
wheel”, and the word epicycloid means “upon the wheel”. You can obtain an epicycloids, for
example, by tracing a point on a small circle as it rolls around the outside circumference of a
larger circle.
A Hypocycloid H(A, B) has the following parametric equation:
