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Evolutes of dual spherical curves for ruled surfaces
Author(s) -
Li Yanlin,
Pei Donghe
Publication year - 2016
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.3748
Subject(s) - dual (grammatical number) , mathematics , unit sphere , euclidean geometry , gravitational singularity , ruled surface , space (punctuation) , euclidean space , unit (ring theory) , surface (topology) , geometry , pure mathematics , mathematical analysis , computer science , art , literature , mathematics education , operating system
E. Study found that there is a one‐to‐one correspondence between the oriented lines in Euclidean three space and the dual points of the dual unit sphere in dual three space, and it has wide applications in Engineering. In this paper, we investigate a ruled surface as a curve on the dual unit sphere by using E. Study's theory. Then we define the notion of evolutes of dual spherical curves for ruled surfaces and establish the relationships between singularities of these subjects and geometric invariants of dual spherical curves. Finally, we give an example to illustrate our findings. Copyright © 2015 John Wiley & Sons, Ltd.