Investigation of Non-Euclidean Geometry
Mathematical Goals:
- Students will develop an understanding for the need for non-Euclidean Geometry.
- Explore and work with the ideas of Spherical Geometry.
- Understand the concepts and ideas of geodesics, the great circle, the sum of the interior angles of a triangle on a sphere.
- Be able to calculate the area of a lune and a triangle on a sphere.
Introduction:
This lesson is developed as an enrichment for the use with small groups. Students will work collaboratively to investigate and discuss the ideas and concepts of Spherical Geometry.
The lesson begins by having students research, which could be assigned for homework the prior class meeting, or students are provided an article explaining the ideas of General Relativity and then students should engage in small group discussion which would then move to a class discussion. Students will then work and discuss hands on activities to develop an understanding of spherical geometry. In the final part of the lesson students will be able to calculate the area of a lune and triangle on a sphere.
