Iza Danielewska, Dawid Poławski, Dominika Sterczewska, Michał Zwierzyński
{"title":"Artistic Aspects of the Wigner Caustic and the Centre Symmetry Set","authors":"Iza Danielewska, Dawid Poławski, Dominika Sterczewska, Michał Zwierzyński","doi":"arxiv-2409.04443","DOIUrl":null,"url":null,"abstract":"The Wigner caustic and the Centre Symmetry Set of a closed smooth planar\ncurve are known singular sets which generically admit only cusp singularities.\nApplications of these objects in semi-classical quantum physics, in chaos\ntheory, in singularity theory, in convex geometry, have been studied since the\n1970s until today. These sets can be viewed as envelopes of special families of\nlines and thanks to that they have many geometric artistic values.","PeriodicalId":501502,"journal":{"name":"arXiv - MATH - General Mathematics","volume":"15 1","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2024-08-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"arXiv - MATH - General Mathematics","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/arxiv-2409.04443","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 0
Abstract
The Wigner caustic and the Centre Symmetry Set of a closed smooth planar
curve are known singular sets which generically admit only cusp singularities.
Applications of these objects in semi-classical quantum physics, in chaos
theory, in singularity theory, in convex geometry, have been studied since the
1970s until today. These sets can be viewed as envelopes of special families of
lines and thanks to that they have many geometric artistic values.
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