This paper presents global differential invariants of curves and paths in the 2-dimensional Euclidean geometry for the groups of Euclidean transformations M(2) and special Euclidean transformations $M^{+}(2)$. For these groups, analogues of the fundamental theorem for Euclidean curves are obtained in terms of global differential invariants of a path and a curve. Moreover, for given two paths(or curves) with the common differential G-invariants, evident forms of all Euclidean transformations that maps one of the paths (or curves) to the other are found. .
Primary Language | English |
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Subjects | Mathematical Sciences |
Journal Section | Research Article |
Authors | |
Publication Date | October 15, 2020 |
Acceptance Date | September 15, 2020 |
Published in Issue | Year 2020 Volume: 13 Issue: 2 |