Hyperbolic portion: See me to receive the shapes necessary to create a hyperbolic plane. After cutting/taping the plane together (it will be bumpy!), pull the plane as straight as possible to draw one straight line. The longer the better for this project. Pull the plane as straight as possible to draw two more sides of the triangle. Measure the angles. What do you notice about the triangle angle sum? Conject something here.
Spherical Geometry: Using a sphere (dodgeball, globe, etc.) and three skinny strips of paper, create a triangle with straight paper lines directly on the sphere. Measure the angles of this triangle. What do you notice about the triangle angle sum? Conject something for spherical geometry.
Compare the angle sums for the three types of geometry. Look online (or use your own information) to compare parallel lines in the three geometries. Compare and contrast parallel lines and how those impact the triangle angle measures.
Completing this project requires:
1. A correctly assembled hyperbolic plane with a triangle drawn in.
2. Measure of triangle's angles and conjecture for all triangle angle measures in hyperbolic geometry.
3. Picture or model of a triangle in spherical geometry.
4. Measure of triangle's angles and conjecture for all triangle angle measures in hyperbolic geometry.
5. Summary paragraph (written in standard English) regarding triangle angle measures and parallel lines, comparing hyperbolic, Euclidean, and spherical geometry.
Subscribe to:
Post Comments (Atom)
No comments:
Post a Comment