Introducing Spherical Geometry
From Prep08Wiki
It helps if students develop an intuitive understanding of geometry before they tackle any serious questions. Hands on activities with balls or software give students different viewpoints and a more concrete understanding of the concepts. First questions should include:
- What do lines, line segments and polygons look like on the sphere?
- What are the differences between Euclidean and spherical geometry?
- What do isometries look like on the sphere?
Read over (and experiment with Spherical Easel):
- escherwiki:Spherical Geometry Exploration This exploration gets to the basics of spherical geometry. The goals are to have a clear understanding of geodesics, and to explore the differences between spherical and Euclidean geometry.
- escherwiki:Spherical Easel Exploration We use Spherical Easel in the classroom for the simple reason that many students have a hard time drawing accurate diagrams by hand. Furthermore this java applet allows us to have the students experiment, do measurements and discover some facts about spherical geometry on their own.
Some discussion questions:
- What material would you cover in pre- and post- activity lectures?
- What would you expect students to struggle with?
- Some of the questions are open ended or ambiguous. How would you deal with that in class?
- How could you test this material?
- Where can you get a bunch of big, cheap balls?
Additional challenge question:
- How many triangles are in the outer shell of Escher's Concentric Rinds.
