The Curvature of a Surface

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


A regular surface looks like a plane if one zooms sufficiently in near any point, but if one zooms back out, it might curve and bend through the ambient \(\mathbb{R}^{3}\). That’s what makes differential geometry so much richer than Euclidean geometry.

Recommended Excursions

  1. 1.
    C. Adams, The Knot Book, American Mathematical Society, 2004.zbMATHGoogle Scholar
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    M. Beeson, Notes on Minimal Surfaces, preprint, 2007, Google Scholar
  3. 3.
    V. Blåsjö, The Isoperimetric Problem, American Mathematical Monthly. 112, No. 6 (2005), 526–566.MathSciNetCrossRefGoogle Scholar
  4. 4.
    D. DeTurck, H. Gluck, D. Pomerleano, and D. Shea Vick, The Four Vertex Theorem and Its Converse, Notices of the AMS. 54, No. 2 (2007), 192–206.MathSciNetzbMATHGoogle Scholar
  5. 5.
    R. Osserman, A Survey of Minimal Surfaces, Dover (1986).Google Scholar
  6. 6.
    S. Sawin, South Point Chariot: An Invitation to Differential Geometry, preprint, 2015.Google Scholar
  7. 7.
    D. Sobel, Longitude: The True Story of a Lone Genius Who Solved the Greatest Scientific Problem of His Time, Walker Books, 2007.Google Scholar

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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