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Chapter6Elliptic Geometry

Elliptic geometry is the second type of non-Euclidean geometry that might describe the geometry of the universe. In this chapter we focus our attention on two-dimensional elliptic geometry, and the sphere will be our guide. The chapter begins with a review of stereographic projection, and how this map is used to transfer information about the sphere onto the extended plane, focusing on antipodal points. We develop elliptic geometry in Sections 6.2 and 6.3, and then pause our story in Section 6.4 to reflect on what we have established, geometry-wise, before we continue on toward geometry on surfaces in Chapter 7.