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Journal of Mathematical Sciences

, Volume 149, Issue 1, pp 971–995 | Cite as

A method for solving the problem of isometric realization of developments

  • S. N. Mikhalev
Article

Abstract

We suggest a new algorithmic solution for the problem of isometric realization of developments. For any development, a system of polynomial equations is composed such that its solutions are, in some sense, in bijective correspondence with all possible isometric realizations of the development. An important advantage of this method is the fact that it can be used in practical computations.

Keywords

Dihedral Angle Polynomial Equation Simplicial Complex Hamiltonian Cycle Boundary Edge 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. 1.
    D. Cox, J. Little, and D. O’Shea, Ideals, Varieties, and Algorithms, Springer, New York (1996).MATHGoogle Scholar
  2. 2.
    A. Legendre, Elements de Geometrie (1806).Google Scholar
  3. 3.
    I. Kh. Sabitov, “The local theory of bendings of surfaces,” in: Encyclopedia of Mathematical Sciences, Vol. 48, Springer, Berlin (1992), pp. 179–250.Google Scholar
  4. 4.
    I. Kh. Sabitov, “The generalized Heron-Tartaglia formula and some of its consequences,” Mat. Sb., 189, No. 10, 105–134 (1998).MathSciNetGoogle Scholar
  5. 5.
    I. Kh. Sabitov, “Algorithmic solution of the problem of isometric realization for two-dimensional polyhedral metrics,” Russ. Acad. Sci. Izv. Math., 66, No. 2, 377–391 (2002).MATHMathSciNetGoogle Scholar
  6. 6.
    H. Whitney, “A theorem on graphs,” Ann. Math., 32, 378–390 (1931).CrossRefMathSciNetGoogle Scholar

Copyright information

© Springer Science+Business Media, Inc. 2008

Authors and Affiliations

  1. 1.Moscow State UniversityRussia

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