{"title":"积分平铺五边形","authors":"Alissa S. Crans, Glen T. Whitney","doi":"10.1080/0025570X.2023.2176101","DOIUrl":null,"url":null,"abstract":"Summary For four decades, Mathematics Magazine has chronicled the quest to find all convex pentagons that tile the plane. Illustrating this story physically leads to the question: What integer-sided convex pentagons tile the plane? Using results from classical number theory along with convexity and continuity principles, we provide a complete answer to this question.","PeriodicalId":18344,"journal":{"name":"Mathematics Magazine","volume":null,"pages":null},"PeriodicalIF":0.0000,"publicationDate":"2023-03-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Integral Tiling Pentagons\",\"authors\":\"Alissa S. Crans, Glen T. Whitney\",\"doi\":\"10.1080/0025570X.2023.2176101\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"Summary For four decades, Mathematics Magazine has chronicled the quest to find all convex pentagons that tile the plane. Illustrating this story physically leads to the question: What integer-sided convex pentagons tile the plane? Using results from classical number theory along with convexity and continuity principles, we provide a complete answer to this question.\",\"PeriodicalId\":18344,\"journal\":{\"name\":\"Mathematics Magazine\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2023-03-13\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Mathematics Magazine\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1080/0025570X.2023.2176101\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q4\",\"JCRName\":\"Mathematics\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Mathematics Magazine","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1080/0025570X.2023.2176101","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"Mathematics","Score":null,"Total":0}
Summary For four decades, Mathematics Magazine has chronicled the quest to find all convex pentagons that tile the plane. Illustrating this story physically leads to the question: What integer-sided convex pentagons tile the plane? Using results from classical number theory along with convexity and continuity principles, we provide a complete answer to this question.
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