Note to instructor: Need picture here. Either spring 98 result, or
Put Kirk's donut picture in top corner. Use columnspan 2
MAT 272 

Calculus and Analytic Geometry III 


Project 1 

Parameterized curves 


Due dates, Tasks, Deliverables,
Evaluation, Advice
Due dates: (subject
to negotiation on Monday Jan 26)
Friday, January 30
postponed to Monday February 2

Time table for team meetings, action plans, teamroles (rotate these),
and responsibilities.
Sketch of word on graph paper with clearly labeled axes, labeled tickmarks,
and marked times at selected points 
Friday, February 6 
All technical work completed (except possibly for curvature and reparameterization).
1 page sample of formulas and MAPLE code
Sketch/outline for 1page poster (handdrawn outline is fine).
Timetable for team meetings, action plans, teamroles and responsibilities.

Friday, February 13
Return to the top. 
Final writeup and poster (or WWWpage) due. 
Tasks:
 1. Fix a word, number or name.
The only restrictions are that it must have at least four characters, and
must include at least one horizontal, vertical, slanted, and curved segment
each. Think of programming a pen plotter, or a weldingrobot (constant
speed !!).
 Consider the word as a curve in the plane and find a single parameterization
for the entire curve:
At any time the "robot/plotter" can be only at one location and
hence different pieces must utilize distinct time intervals.
Note: use equal scales on the coordinate axes (angles are important
in the velocity/acceleration parts of this project).
 Use MAPLE to plot the parameterized curve.
Visit this worksheet
for help for an effective MAPLE syntax.
Use the plot option scaling=constrained.
 By hand mark typical velocity and acceleration vectors at various
points along the curve (on printout).
 Calculate and graph the speed (as a function of time).
 Calculate and graph the perpendicular component of the acceleration
vectors (as a function of time).
 Calculate and graph the curvature (as a function of time).
 Try to reparameterize the curve by arc length (i.e. rescale the parameterization
to achieve constant speed equal to one).
Then repeat the last four steps.
 Prepare a laminated 11"x17" poster that summarizes your work.
As possible audiences think of an accreditation or curriculum committee
as a possible audience, your prospective employer, or other students who
you want to impress with the work performed in this class. See the advice
below.
 For bonus credit:
Pick your favorite parameterized surface in 3space.
Consider your word as written in the parameterplane (e.g. what you called
x and y above, simply think of as theta and phi, or u and v).
Use a computer to plot the word spelled on the surface in 3space.
In this part the artistic and practical components will earn the most credit.
 Prepare a WWWpage similar to the poster described above. See also
the advice below.
Return to the top.
Deliverables:
The final writeup must be signed by all teammembers. It should include
a brief narrative about the project; complete technical work (formulas,
calculations, justifications and explanations), but put long computer printouts
into appendix, the plot (computerprintouts) of the curve with marked vectors
as above; a plot of the surface (optional, color printer available).
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Evaluation:
Incomplete work will be rejected and assigned 0 points. Intermediate
timelines are worth 20 points each. Final writeup: 40 points for technical
correctness. 20 points for presentation including the laminated poster.
The WWW page may earn 10 bonus points but only if final writeup + intermediate
timelines are over 90 pts. The curve on a surface may earn up to 20 bonus
points!
Unless negotiated otherwise each team will get only one grade. However,
if all students in a team agree, they may choose to allocate a small portion
to reward special efforts etc. Guidelines: In each team the average must
agree with the grade assigned to the team. Each team member's credit must
lie between 80% and 120% of the team average. In case the team chooses
not to give every member the same number of points, they must turn in a
separate page together with the final report, that is signed by all team
members, and that specifies what percentage each team member shall earn.
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Advice:
 You are encouraged to visit the
WWWpages of last semester's projects.
Clearly you need to choose your own "words". Take their
writeups as an inspiration, a possible source of help, and avoid mistakes
made last year. In particular, technical content comes first, pretty
typing and neat WWWfeatures are luxury and will not earn any credit unless
the technical part is correct! Since you have last semester's results available,
the expectations for you are clearly higher!
 Practically all parts of the project are either very important for
later parts of the course (line integrals etc), or are likely items that
may be encountered on the next test!
 Be ambitious and pick an exciting surface  this part is much easier
than the others, and can yield really beautiful results!
 Start early, and don't hesitate to ask for help ask for help as soon
as you are stuck.
 This is a mathematics class  compete team against team in the mathematical
work, but please share freely between teams any tricks regarding with the
computer software.
 Before finalizing and laminating your poster bring a draft to the instructors
office to get feedback (avoid embarrassing mistakes on poster).
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