反射群与pizza定理

IF 0.7 4区数学 Q2 MATHEMATICS

St Petersburg Mathematical Journal Pub Date : 2022-10-31 DOI:10.1090/spmj/1732

Yu. Brailov

{"title":"反射群与pizza定理","authors":"Yu. Brailov","doi":"10.1090/spmj/1732","DOIUrl":null,"url":null,"abstract":"The classical theorem about cutting a round pizza into 8 pieces with straight cuts passing through an arbitrary internal point and forming angles of 45 degrees says that the total areas of odd and even pieces are equal if those pieces are ordered around the center of cutting. The current paper proposes a generalization of the Pizza theorem to any dimension and discovers a relationship with the finite reflection group of the series \n\n \n \n B\n n\n \n B_n\n \n\n.","PeriodicalId":51162,"journal":{"name":"St Petersburg Mathematical Journal","volume":null,"pages":null},"PeriodicalIF":0.7000,"publicationDate":"2022-10-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"1","resultStr":"{\"title\":\"Reflection groups and the pizza theorem\",\"authors\":\"Yu. Brailov\",\"doi\":\"10.1090/spmj/1732\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"The classical theorem about cutting a round pizza into 8 pieces with straight cuts passing through an arbitrary internal point and forming angles of 45 degrees says that the total areas of odd and even pieces are equal if those pieces are ordered around the center of cutting. The current paper proposes a generalization of the Pizza theorem to any dimension and discovers a relationship with the finite reflection group of the series \\n\\n \\n \\n B\\n n\\n \\n B_n\\n \\n\\n.\",\"PeriodicalId\":51162,\"journal\":{\"name\":\"St Petersburg Mathematical Journal\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.7000,\"publicationDate\":\"2022-10-31\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"1\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"St Petersburg Mathematical Journal\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.1090/spmj/1732\",\"RegionNum\":4,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q2\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"St Petersburg Mathematical Journal","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1090/spmj/1732","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATHEMATICS","Score":null,"Total":0}

引用次数: 1

摘要

关于用穿过任意内部点并形成45度角的直切口将圆形披萨切成8块的经典定理表明，如果奇数块和偶数块围绕切割中心排列，则这些块的总面积相等。本文将Pizza定理推广到任意维，并发现了它与BnB_n级数的有限反射群之间的关系。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

查看原文本刊更多论文

Reflection groups and the pizza theorem

The classical theorem about cutting a round pizza into 8 pieces with straight cuts passing through an arbitrary internal point and forming angles of 45 degrees says that the total areas of odd and even pieces are equal if those pieces are ordered around the center of cutting. The current paper proposes a generalization of the Pizza theorem to any dimension and discovers a relationship with the finite reflection group of the series B n B_n .

求助全文

通过发布文献求助，成功后即可免费获取论文全文。去求助

来源期刊

St Petersburg Mathematical Journal MATHEMATICS-

CiteScore

1.00

自引率

12.50%

发文量

审稿时长

>12 weeks

期刊介绍： This journal is a cover-to-cover translation into English of Algebra i Analiz, published six times a year by the mathematics section of the Russian Academy of Sciences.