Appendix A

Creating a Hyperbolic Surface

  1. Print out the page of curvilinear triangles.
  2. Make as many copies of the triangle sheets as necessary. Each group of students will need at least 35 triangles to make their sheets.
  3. Cut out each triangle.
  4. Tape 7 of these triangles together around one vertex. Note this model will NOT lay flat. At this stage, it should look like this:
  5. Seven triangles taped together all with a common center

  6. Continue taping more triangles together until you have seven triangles around each of the seven triangles from step 4. At this stage , it should look like this:
  7. many triangles taped together

  8. As you will notice, the triangles have curved sides. When they are taped together seven to each vertex they form a model of hyperbolic geometry.
  9. You may also choose to make this surface out of a more durable material such a cloth or clay. Use the curvilinear triangle found above to make a template to cut your material. Then sew or mold as appropriate. Some art supply companies make products that you can mold wet and which then harden to form a dry foam rubber like substance. These products work particularly well for this activity.
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