Discrete differential geometry of triangle tiles and algebra of closed trajectories

Details Discrete differential geometry of triangle tiles and algebra of closed trajectories Discrete differential geometry of triangle tiles and algebra of closed trajectories

2006-07-03

arxiv.org/abs/math/0607051v1

Mathematics

Combinatorics

15 pages, 6 figures

Scientific paper

This paper proposes a new mathematical framework that can be applied to biological problems such as analysis of the structures of proteins and protein complexes. In particular, it gives a new method for encoding the three-dimensional structure of a protein into a binary sequence, where proteins are approximated by a folded tetrahedron sequence. It also gives a new algebraic framework for describing molecular complexes and their interactions. For simplicity, we shall explain the framework in the case of two-dimensional objects. Then, the binary code of a plane curve is obtained as the ``second derivative'' of the curve and ``fusion and fission'' of closed trajectories is described algebraically.

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