Description - For this project, students will research a topic
related to the subject matter of the course. The end result of the
project will be
(1) a written paper four or more pages in length
and
(2) a poster to present during a poster session in class.
Students may work individually or in pairs (no more than two in a group).
Students who work in pairs will submit one paper and one poster and will
receive the same grade for the project.
Due dates -
Wed. Nov. 5 - Submit the topic you will do. If you are working with another person, the two of you should submit one paper with both names.
Wed. Nov. 19 - Submit a list of references and an outline of your paper. You should have at least one reference (preferably more!) which is not a webpage. Visit the Mathematics Library in Altgeld Hall.
Wed. Dec. 3 - Posters due. There will be poster sessions in class on Dec. 3, 5, 8, 10
Wed. Dec. 10 - papers due.
Some possible topics
□
Geometry
before
□
The
history of geometry in the Islamic world
□
Other
axiomatic systems, such as Peano’s axioms for
the natural
□ Russell and Whitehead's Principia Mathematica (history of axiomatic systems)
□ Development of a lesson plan for high school students based on some geometric topic (the subject should go beyond what we’ve covered in class).
□ Godel's Incompleteness Theorem
□ Some portion of the history of non-Euclidean geometry
□ Use of Euclidean or non-Euclidean geometry in computer graphics
□ Euclidean constructions (ruler and compass)
□ Frieze groups, wallpaper groups, tilings
□ Spherical geometry
□ Models of hyperbolic geometry
□ Some topic from projective geometry
□ Use of perspective in drawing
□ Hyperbolic geometry in art (e.g. M.C. Escher)
□ Hilbert's axioms for Euclidean geometry
□ Differential or Riemannian Geometry
□ Applications of Geometry (in some other field of study)
□ Solid geometry (3 dimensions)
□ Classification of Platonic solids
□ Use of geometry in map-making
□ Hilbert's axioms for Euclidean geometry
□ Angle trisection
□ Proofs of the Pythagorean Theorem
□ Affine geometry
□ Napoleon’s Theorem
□ Triangle centers
□ Metric spaces
□ Conformal maps
□ Mappings of the globe
□ Differential or Riemannian Geometry
□ Applications of Geometry (in some other field of study)
□ History of geometry education
□ Some area of non-Euclidean Geometry which we have not covered
□ or you can suggest your own topic – there are hundreds
of possibilities...
Some places to browse for ideas:
Cut-the-knot, http://www.cut-the-knot.com/
Wikipedia,
www.wikipedia.com
Geometry Junkyard, http://www.ics.uci.edu/~eppstein/junkyard/
Geometry in Action (applications of
geometry), http://www.ics.uci.edu/~eppstein/geom.html