{"title":"Packing Spheres in High Dimensions","authors":"Charles Day","doi":"10.1103/physics.16.s131","DOIUrl":null,"url":null,"abstract":"V eit Elser of Cornell University has just described a new way to elucidate a problem that has baffled mathematicians for over a century: How densely can identical spheres be packed as the dimension of the spheres and of the space they occupy grow ever larger [1]? Schemes for densely packing spheres have been worked out in low dimensions and for two special cases: 8 and 24 dimensions. (A sphere in n-dimensional space is a set of points that are the same fixed distance away from a given center point.) Surprisingly, some schemes in high dimensions are little better than a random approach. What’s more, a century of research has failed to improve on the result from Hermann Minkowski, a Germanmathematician who came up with the concept of four-dimensional spacetime, that with each additional dimension, the highest fraction of space that can be occupied by spheres falls by a factor of 2. Intuitively, the rate of decrease should be slower.","PeriodicalId":20136,"journal":{"name":"Physics","volume":"74 1","pages":"0"},"PeriodicalIF":1.5000,"publicationDate":"2023-09-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Physics","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1103/physics.16.s131","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"PHYSICS, MULTIDISCIPLINARY","Score":null,"Total":0}
引用次数: 0
Abstract
V eit Elser of Cornell University has just described a new way to elucidate a problem that has baffled mathematicians for over a century: How densely can identical spheres be packed as the dimension of the spheres and of the space they occupy grow ever larger [1]? Schemes for densely packing spheres have been worked out in low dimensions and for two special cases: 8 and 24 dimensions. (A sphere in n-dimensional space is a set of points that are the same fixed distance away from a given center point.) Surprisingly, some schemes in high dimensions are little better than a random approach. What’s more, a century of research has failed to improve on the result from Hermann Minkowski, a Germanmathematician who came up with the concept of four-dimensional spacetime, that with each additional dimension, the highest fraction of space that can be occupied by spheres falls by a factor of 2. Intuitively, the rate of decrease should be slower.