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Applied Physics and Mathematics Annotation << Back
THE GROUP OF SYMMETRY OF PLANE CURVES |
M.I. GORFINKEL
Under changes and transforming of objects some of their
characteristics vanish while other properties reserve but
the third ones appear. The greatest stability to changes have
statutes according to which equations of plane curves are
analyses. Analyses as laws plane curves equations remain
unchanged under admissible transformations. Plane
curves (coordinates x, y) are transformed to the surfaces
(coordinates x, y, z) .equations of curves are preserved,
but their parameters are changed which the value that is
proportional to z. The plane curves invariant relative to the
transformation of the system of coordinates and creates
the group of symmetry. The group of symmetry – the unity
of oppositions: this is the unity of preserving equations on
the surface and in the space, from one side, and changing
of difference of parameters of these equations, from the
other side. The limited turn z0 surfaces into initial plane
curves.
Key words: invariant, transformation of coordinates, surface,
unity of oppositions.
Contacts: E-mail: cancel@baa.by
Pp. 57-58. |
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