{"title":"将正方形平行打包成菱形","authors":"M. Liu, Z. Su","doi":"10.1007/s10474-024-01446-7","DOIUrl":null,"url":null,"abstract":"<div><p> Suppose that <span>\\(R_{\\alpha}\\)</span> is a rhombus with side length <span>\\(1\\)</span> and with acute angle <span>\\(\\alpha\\)</span>. Let <span>\\(\\{S_{n}\\}\\)</span> be any collection of squares. In this note a tight upper bound of the sum of the areas of squares from <span>\\(\\{S_{n}\\}\\)</span> that can be parallel packed into <span>\\(R_{\\alpha}\\)</span> is given.</p></div>","PeriodicalId":50894,"journal":{"name":"Acta Mathematica Hungarica","volume":"173 2","pages":"471 - 499"},"PeriodicalIF":0.6000,"publicationDate":"2024-08-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Parallel packing squares into a rhombus\",\"authors\":\"M. Liu, Z. Su\",\"doi\":\"10.1007/s10474-024-01446-7\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><p> Suppose that <span>\\\\(R_{\\\\alpha}\\\\)</span> is a rhombus with side length <span>\\\\(1\\\\)</span> and with acute angle <span>\\\\(\\\\alpha\\\\)</span>. Let <span>\\\\(\\\\{S_{n}\\\\}\\\\)</span> be any collection of squares. In this note a tight upper bound of the sum of the areas of squares from <span>\\\\(\\\\{S_{n}\\\\}\\\\)</span> that can be parallel packed into <span>\\\\(R_{\\\\alpha}\\\\)</span> is given.</p></div>\",\"PeriodicalId\":50894,\"journal\":{\"name\":\"Acta Mathematica Hungarica\",\"volume\":\"173 2\",\"pages\":\"471 - 499\"},\"PeriodicalIF\":0.6000,\"publicationDate\":\"2024-08-16\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Acta Mathematica Hungarica\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://link.springer.com/article/10.1007/s10474-024-01446-7\",\"RegionNum\":3,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q3\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Acta Mathematica Hungarica","FirstCategoryId":"100","ListUrlMain":"https://link.springer.com/article/10.1007/s10474-024-01446-7","RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"MATHEMATICS","Score":null,"Total":0}
Suppose that \(R_{\alpha}\) is a rhombus with side length \(1\) and with acute angle \(\alpha\). Let \(\{S_{n}\}\) be any collection of squares. In this note a tight upper bound of the sum of the areas of squares from \(\{S_{n}\}\) that can be parallel packed into \(R_{\alpha}\) 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.
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