Some Project Ideas:

Straight-Forward Projects:

• Create a saddle surface in polar form and rotate it to view it from different views. Recall that a saddle has the form z = r^2 sin(2 theta).

• Create a higher order saddle in polar form (the standard saddle has two "ups" and two "downs" due to the factor of 2 in the equation above). Make a saddle with 3 ups and downs, and view it from various angles.

• Create the graph of the function z = x^3 + ax - y^2 for x in [-1.5,1.5] and y in [-1.2,1.2]. Choose an interesting value for a. Using the standard file square.quad that comes with Geomview, slice the graph of the surface by horizontal planes. Make a movie of the plane slicing the surface as it moves from z = -1 to z = 1.

• Make a helicoid (it is parameterized by (u cos(v), u sin(v), a v)) and animate it so that it translates along its axis while rotating. Try to make the rotation rate such that the helicoid appears to "screw" through space.

More Challenging:

• For the cubit surface in the third example anove, animate the surface as the parameter a changes from -1 to 1.

• Create a surface in space (for example, you could use one of the surfaces from the previous examples) and animate a point moving along a path on the surface. You might use a very small sphere to represent the point on the surface.

• Make a movie of a ball bouncing off a wall. Can you make the ball deform when it hits?

• Make a movie of a ball bouncing several times on the ground under the influence of gravity.

• Make a movie of a collision between two unequal spherical masses. Make sure that momentum is conserved. (You might try having one mass be at rest for your first attempt).

• Make a movie of two balloons connected by a rigid pipe: have one balloon shrink and the other expand. Can you make the changes in volume between the two spheres match?

The Geometry Center Home Page

Comments to: webmaster@www.geom.uiuc.edu
Created: Jun 01 1996 --- Last modified: Jun 01 1996