Below is a list of topics from which you may choose projects for Explorations in Geometry. Each item on the list is really an umbrella topic that allows for lots of choices under the umbrella. You aren't restricted to using topics from the list, but you need to consult with me prior to doing the project. If nothing on the list so far looks interesting, please think about alternatives! I'm working on a resource list to go along with the project list.

1. Tilings of the plane (Tessellations)
See Tessellations: The Secrets of Interlocking Patterns, Ginny Byer, Contemporary Books, 1999 and this web site, Science U:See also: and	Click above for an interactive example.

2. Tilings of 3-space

Try http://spacebrick.com/geometry/index.html

3. Proofs of the Pythagorean Theorem: Thomas Jefferson did one - how about you?

4. Symmetry	Below is a black and white photo of an origami quilt (interlocking folded squares of paper - no glue, no tape) made by Char Morrow. What are its symmetries?
See Visions of Symmetry, Doris Schattschneider, Freeman, 1990; Symmetry in Chaos, Michael Field and Solomon Golubitsky, Oxford University Press, 1992

5. Origami
See Unit Origami, Tomoku Fuse, Japan Publications, Inc. ISBN 0 87040 852 6 and Tom Hull's origami pages. Also, a great index page that builds on our classroom exercises and has directions for modular and tesselating origami and other mathematical origami is HERE.	Click above to go to the Playground section, which has links to several Sketchpad versions of origami 'quilts.' See MASU for folding applets. See Kim's Crane for origami paper purchases.

6. "Modern" applications of geometry
Click here for the description of a source book, Geometry at Work, that describes many applications you might investigate.

7. Folding geometry

Click HERE to go to the geometry seminar link to folding geometry. (Later in the course)

8. Projective geometry and Perspective.	Desargues' Theorem
See chapters 3 and 4 of Geometry by Brannan, et. al., Cambridge University Press. ISBN 0 521 59787 0 See also nifty multiple point perspective drawings HERE. Try also * and my interactive **.	Click above for a start on projective geometry, with an illustration, created by Char Morrow, of Desargues' Theorem . Is it 2-dimensional or 3-dimensional?

9. Description of art through the lens of geometry	CLICK on Carlo Seguin's web page for leads on connections between geometry and sculpture.
Science News article on Marcel Duchamp. (No longer directly available)

10. Connections to philosophy

Please see JMorrow if interested. Try Experimental Geometry; Such a direction for the project is related to Project #23 below. Click HERE for a short list of readings and other resources.

11. The flight of moths, chase trajectories

Click HERE for an interactive example. Try these experiments: Change the angle parameter and the flight check distance parameter (both at the bottom of the sketch); Drag the light source away from the moth's initial position. Try to figure out, from the example, what assumptions are being made about how a moth navigates. Click here for more discussion of the flight of moths. (The discussion is Under Construction)

12. Visual foolery
Check out the  Exploratorium  on-line illusions.

13. Coordinate geometry
	Why is it so hard to make the fold for an equilateral triangle? Coordinate geometry gives both a visual and quantitative explanation.

14. Robotic Arms	Click below for a two-dimensional interactive example.

15. Pin-jointed frames
Click on the diagram to see a simulation, using Geometer's Sketchpad, of a typical pin-jointed frame.	As point D is driven around a circle, where do the points P and P' in the above pin-jointed contraption go?

16. Descartes' mechanisms
After clicking on the diagram above for an interactive sketch, drag point L to rotate the ruler about G and watch the curve traced by point C.

17. Solving "calculus-type" optimization problems using Sketchpad	The sides of the rectangle are made from the line segment at the top. The division point is used to determine the length and width of the rectangle.
Click HERE for a set of "calculus"  problems that can be solved by using dynamic geometry software.	Click on the image above, which shows a sketch used to solve an optimization problem, to get an interactive sketch that illustrates the use of dynamic geometry software.

18. Traditional Islamic designs
Click on the design to the right for directions to construct designs like the one shown and variations of it.

19. Use of geometric terminology in natural language

What's the point? I draw the line at doing any more projects! Don't fall under a mathematician's sphere of influence!

20. Use of geometric concepts in literature

See, e.g., Borges' The Death of a Compass and Stoppard's Arcadia.

21. "Higher" and "Lower" Dimensions

Explore 2 and 4 dimensional geometries. See, e.g., the classic Flatland, (review from Science News) the modern Flatterland, and Geometry, Relativity and the Fourth Dimension. Check out the hypercube.

22. Algebraic Geometry	Learn how algebraic geometry is used in computer-aided geometric design. See, Computers take algebraic geometry back to its roots in What's happening in the mathematical sciences, 1998-1999.
23. Spatial Curvature	See Penrose for some speculation on the curvature of the universe and related work of Jeff Weeks. (Neither of these two links are now available.)
24. Fractals and Chaos	Start HERE for inspiration and all-around great fun.
25. Dynamic Geometry of Toys	Some of Alexander Caldwell's toys, on exhibit at the Berkshire Museum, are displayed below. Explore the geometry of such toys. (You might start with some physics or some ideas about wire toys.)