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The Curvature of a Surface

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

Abstract

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
  2. 2.
    M. Beeson, Notes on Minimal Surfaces, preprint, 2007, http://michaelbeeson.com/research/papers/IntroMinimal.pdf 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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