Spherical Geometry

Spherical Geometry is one of the more well know types of non-Euclidean geometry. Spherical is an excellent place to dive into non-Euclidean systems that differ from the flatness of the usual plane. Some highlihgts to dazzle students include triangles whose angles can add up to 270^o , a new shape called a lune (2-gon), and the very intriguing fact that parallel lines do not exist in spherical geometry!

Note: There are no parallel lines in spherical geometry. There is only one orientation of a line that results in parallel lines in Euclidean. What happens if one looks at a system with infinite parallel lines? (You'll find the answers in Hyperbolic geometry)

Lessons:

Is it a Triangle?

1, 2, and 3-gons on a Sphere

Spherical 2-gons

Spherical 3-gons

Area of a Spherical Triangle

Ribbon around a Box

Triangle Inequality on a Sphere