• Kristopher Tapp
Part of the Undergraduate Texts in Mathematics book series (UTM)


The most fundamental concept for studying the geometry of \(\mathbb{R}^{2}\) is a straight line. The goal of this chapter is to generalize this fundamental notion from \(\mathbb{R}^{2}\) to arbitrary regular surfaces. Although most surfaces curve in such a way that they don’t contain any straight lines, they do contain curves called geodesics, which will turn out to share many important characterizing properties of straight lines.

Copyright information

© Springer International Publishing Switzerland 2016

Authors and Affiliations

  • Kristopher Tapp
    • 1
  1. 1.Department of MathematicsSaint Joseph’s UniversityPhiladelphiaUSA

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