Construction Project
Due on or before the last day of class
-
Make one or more geometric objects that illustrate a significant mathematical
idea. You may use a computer for
parts of your project, but the construction should include some hand work.
- Write a paper of at least 2 pages explaining the mathematics of your
project. (More than 2 pages if handwritten).
- Do a "show and tell" presentating your project to the class. This can be very short.
Your project may extend one of the topics covered in class, or some other
geometric concept. Here are some suggestions. I have a personal library
that you may borrow from, or find books in the library or at a bookstore.
You may also find some suggestions in math teaching journals.
You are strongly encouraged to consult me about your
project before you start, to make sure it meets my
standards of a "significant mathematical idea".
- Tessellations
- Tessellations with wallpaper symmetry.
Make at least two tessellations of the plane by hand (as opposed to by computer).
Each tessellation must have a wallpaper pattern symmetry; one of them must
have reflections; one of them must have rotations. Suggested techniques/materials:
- Cut out cardboard and trace
- Stencils
- Rubber stamps
- Potato prints
- Tessellations without wallpaper symmetry (for example, Penrose tilings)
- Make a symmetric tessellation of the sphere and a hyperbolic tessellation.
(The hyperbolic ones work better made from cloth.) Suggested materials:
- poster board
- cloth (make a quilt!)
- wood?
- Polyhedra
- dual polyhedra
- stellated polyhedra
- Make two different polyhedra using origami
- Kaleidoscopes
- Kaleidocycles
- Paper pop-ups
- Make a pinhole camera and take pictures with it
- Make two differently shaped camera obscuras