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Topic: Geometry Center Summer Course for Teachers
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Gene Klotz

Posts: 30
Registered: 12/3/04
Geometry Center Summer Course for Teachers
Posted: Jan 23, 1993 4:19 PM
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Geometry and the Imagination:

Computation, Visualization
and Graphics
1993 Summer Course for Teachers

The Geometry Center

The National Science & Technology Research
Center for Computation & Visualization of
Geometric Structures

Geometry and the Imagination: Computation, Visualization and
Graphics is the title of The Geometry CenterUs 1993 summer course.
Computer generated images have become central to our lives.
Advertising images, rock videos, and first run movies all use the
computer to generate important images. Here you will learn some of
the mathematical ideas and computational principles behind the
computer generated image.

Course content:
Computer generated images are created by combining
algorithms for doing a variety of geometric tasks. These algorithms
give the computer the ability to do geometry as a human would. We
will develop the ideas behind a few geometric algorithms. Ideas will
be Rvertically integrated.S That is, we will consider the geometry
necessary to model the problem, the data structures used to develop
the algorithm, the programs written to implement the algorithm and
the images produced by the algorithm. The ideas we develop will
build from basic principles, starting from the geometry and computer
representation of points, lines and polygons. We will assume that
students are conversant with the details of courses in high school
geometry and are not averse to computers.
Problems involving creating and decomposing complex objects
will be presented. The Voronoi diagram data structure, an important
modelling structure, will be presented. Ray tracing, the method used
to create the images you see on television, will be developed from
basic geometric primitives. Artistic considerations that arise in
creating satisfying images will be described. All of these ideas will
be developed from concepts used in the high school geometry

% to understand the nature of geometric
% to use and modify software for creating graphical
% to examine accessible and interesting examples
% to prepare to communicate your understanding to

Dates and Times:
June 21-July 2, 1993, weekdays 9:00 a.m. -
5:00 p.m.
Evening and weekend activities will be

The course enrollment is limited to 50 students. Up to 30
senior high school teachers will be invited into the program based on
application procedures. Applications from middle school teachers
with a strong math background and interest are also welcome. The
remaining places will be filled by the college students accepted into
the ten week research and training program of the Center. Women
and underrepresented minorities are especially encouraged to apply.
Applications should be received by Feburary 1, 1993 to guarantee

Tuition for the course has been waived.
6 credits for Math 5025 and 5025X through the Extension
Division of the University of Minnesota for satisfactory completion of
the course. Pass/fail basis only. A $35 registration fee will be due
the first day of class if you wish to have credits officially recorded on
a transcript. Cost of the transcript is additional.

It will be assumed that students have some familiarity with
computation. A tutorial will be given Sunday, June 20, 1993, to
provide students with the appropriate background.

Course materials:
There are no assigned texts. Materials will be distributed
during class.

It is highly recommended that all participants stay in the
dorms on campus. Past experience and evaluations from former
participants show that this is invaluable, even if the participant is a
Twin Citian.
From Sunday, June 20, through Friday, July 2, air-conditioned
housing in double rooms with full meal service will be provided at no
charge for all participants who request it at Middlebrook Hall on the
West Bank of the University of Minnesota

Travel allowances of up to $100 for out-of-state teachers will
be provided.

Course Faculty:

David Dobkin is a Professor of Computer Science at Princeton
University. His research interests concern the theoretical and
practical issues related to doing geometry by computer. David is also
deeply involved in the development of curricula at Princeton for
computer science education, but his secret fantasy is to be a great
basketball player.

Pat Hanrahan is an Associate Professor of Computer Science at
Princeton University. His research interests center on the rendering
problem, the problem of creating photorealistic images by computer.
For a number of years, Pat was Chief Scientist at Pixar (formerly
Lucas Films) and has given hundreds of talks presenting graphics to
general audiences.

Vibeke Sorenson is director of the Computer Animation
Laboratory at the California Institute of the Arts. She is an active
computer artist who has shown her work internationally. Vibeke has
also worked closely with David in developing curricula.

Diane Souvaine is an Associate Professor of Computer Science at
Rutgers University and Associate Director of DIMACS. Her research
interests are in computational geometry and practical applications of
geometric algorithms. Diane has also been actively involved in
developing the DIMACS education program in discrete math for high

For further information, please contact:

The Geometry Center
1300 South Second Street
Minneapolis, MN 55454
Phone: (612) 626-0888
Fax: (612) 626-7131

The University of Minnesota is committed to the policy that all
persons shall have access to its programs, facilities and employment
without regard to race, color, creed, religion, national origin, sex,
marital status or sexual orientation.

Applications should be submitted by February 1, 1993

Return application for the summer course to:
The Geometry Center
Summer Course '93
1300 South Second Street
Minneapolis, MN 55454



Home phone:

School where teaching:

School address:

School phone:

Teaching assignment:

Ethnicity (circle one): Black Asian Hispanic White
Native American Other

Sex (please circle): M F

Yes No I plan to attend the Sunday, June 20, 1992,
computer session.

Yes No I plan to stay in the dorm. Please reserve a room for me.

Yes No I will need parking at the dorm.

Attach a short statement concerning your interest in the course
and your anticipated classroom use of the materials created.

Attach a statement of support from an appropriate administrator which
indicates that you would be able to incorporate these materials into at
least one class that you will teach in 1993-94.

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