Centre Symmetry Sets of Families of Plane Curves

Centre Symmetry Sets of Families of Plane Curves

We study centre symmetry sets and equidistants for a I-parameter family of plane curves where, for a special member of the family, there exist two inflexions with parallel tangents. Some results can be obtained by reducing a generating family to normal forms, but others require direct calculation fr...

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Bibliographic Details
Main Authors: Giblin Peter, Reeve Graham
Format: Article
Language:English
Published: De Gruyter 2015-06-01
Series:Demonstratio Mathematica
Subjects:
central symmetry
plane curves
caustic
wavefront
Online Access:http://www.degruyter.com/view/j/dema.2015.48.issue-2/dema-2015-0016/dema-2015-0016.xml?format=INT
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spelling doaj-a4ee34cd4e04411b9d731593d944af392020-11-24T21:21:04ZengDe GruyterDemonstratio Mathematica0420-12132391-46612015-06-0148216719210.1515/dema-2015-0016dema-2015-0016Centre Symmetry Sets of Families of Plane CurvesGiblin Peter0Reeve Graham1DEPARTMENT OF MATHEMATICAL SCIENCES THE UNIVERSITY OF LIVERPOOL L69 7ZL, UKICMC, UNIVERSIDADE DE SÃO PAULO SÃO CARLOS SP, BRAZILWe study centre symmetry sets and equidistants for a I-parameter family of plane curves where, for a special member of the family, there exist two inflexions with parallel tangents. Some results can be obtained by reducing a generating family to normal forms, but others require direct calculation from the generating family.http://www.degruyter.com/view/j/dema.2015.48.issue-2/dema-2015-0016/dema-2015-0016.xml?format=INTcentral symmetryplane curvescausticwavefront
collection DOAJ
language English
format Article
sources DOAJ
author Giblin Peter
Reeve Graham
spellingShingle Giblin Peter
Reeve Graham
Centre Symmetry Sets of Families of Plane Curves
Demonstratio Mathematica
central symmetry
plane curves
caustic
wavefront
author_facet Giblin Peter
Reeve Graham
author_sort Giblin Peter
title Centre Symmetry Sets of Families of Plane Curves
title_short Centre Symmetry Sets of Families of Plane Curves
title_full Centre Symmetry Sets of Families of Plane Curves
title_fullStr Centre Symmetry Sets of Families of Plane Curves
title_full_unstemmed Centre Symmetry Sets of Families of Plane Curves
title_sort centre symmetry sets of families of plane curves
publisher De Gruyter
series Demonstratio Mathematica
issn 0420-1213
2391-4661
publishDate 2015-06-01
description We study centre symmetry sets and equidistants for a I-parameter family of plane curves where, for a special member of the family, there exist two inflexions with parallel tangents. Some results can be obtained by reducing a generating family to normal forms, but others require direct calculation from the generating family.
topic central symmetry
plane curves
caustic
wavefront
url http://www.degruyter.com/view/j/dema.2015.48.issue-2/dema-2015-0016/dema-2015-0016.xml?format=INT
work_keys_str_mv AT giblinpeter centresymmetrysetsoffamiliesofplanecurves
AT reevegraham centresymmetrysetsoffamiliesofplanecurves
_version_ 1726001341015261184

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