{"title":"Parallel covering a parallelogram with squares","authors":"Z.-J. Su, J. Zhang","doi":"10.1007/s10474-024-01407-0","DOIUrl":null,"url":null,"abstract":"<p>Suppose that <span>\\(R(h, \\alpha)\\)</span> is a parallelogram with the longer side 1, with acute angle <span>\\(\\alpha\\)</span> and with height <i>h</i>. Let <i>S</i> be a square with a side parallel to the longer side of <span>\\(R(h, \\alpha)\\)</span> and let <span>\\(\\{S_{n}\\}\\)</span> be a\ncollection of the homothetic copies of <i>S</i>. In this note a tight lower bound\nof the sum of the areas of squares from <span>\\(\\{S_{n}\\}\\)</span> that can parallel cover\n<span>\\(R(h, \\alpha)\\)</span> is given.</p>","PeriodicalId":50894,"journal":{"name":"Acta Mathematica Hungarica","volume":null,"pages":null},"PeriodicalIF":0.6000,"publicationDate":"2024-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Acta Mathematica Hungarica","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1007/s10474-024-01407-0","RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 0
Abstract
Suppose that \(R(h, \alpha)\) is a parallelogram with the longer side 1, with acute angle \(\alpha\) and with height h. Let S be a square with a side parallel to the longer side of \(R(h, \alpha)\) and let \(\{S_{n}\}\) be a
collection of the homothetic copies of S. In this note a tight lower bound
of the sum of the areas of squares from \(\{S_{n}\}\) that can parallel cover
\(R(h, \alpha)\) is given.
期刊介绍:
Acta Mathematica Hungarica is devoted to publishing research articles of top quality in all areas of pure and applied mathematics as well as in theoretical computer science. The journal is published yearly in three volumes (two issues per volume, in total 6 issues) in both print and electronic formats. Acta Mathematica Hungarica (formerly Acta Mathematica Academiae Scientiarum Hungaricae) was founded in 1950 by the Hungarian Academy of Sciences.