{"title":"Apparent paradoxical partitions in countable sets","authors":"M. Ayad, O. Kihel","doi":"10.4171/em/456","DOIUrl":"https://doi.org/10.4171/em/456","url":null,"abstract":"","PeriodicalId":41994,"journal":{"name":"Elemente der Mathematik","volume":" ","pages":""},"PeriodicalIF":0.1,"publicationDate":"2021-06-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47863162","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Short Note Teildreiecke und Kreise","authors":"Peter Thurnheer","doi":"10.4171/EM/454","DOIUrl":"https://doi.org/10.4171/EM/454","url":null,"abstract":"","PeriodicalId":41994,"journal":{"name":"Elemente der Mathematik","volume":" ","pages":""},"PeriodicalIF":0.1,"publicationDate":"2021-06-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43886875","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
In 2017 [1] a definition of spiral tilings was given, thereby answering a question posed by Grünbaum and Shephard in the late 1970s. The author had the pleasure to discuss the topic via e-mail with Branko Grünbaum in his 87th year. During this correspondence the question arose whether a spiral structure (given a certain definition of it) could be recognized automatically or whether “to some extent, at least, the spiral effect is psychological”, as Grünbaum and Shephard had conjectured in 1987 (see exercise section of chapter 9.5 in [4]). In this paper, an algorithm for automatic detection of such a tiling’s spiral structure and its first implementation results will be discussed. Finally, the definitions for several types of spiral tilings will be refined based on this investigation.
{"title":"Is the spiral effect psychological?","authors":"B. Klaassen","doi":"10.4171/EM/465","DOIUrl":"https://doi.org/10.4171/EM/465","url":null,"abstract":"In 2017 [1] a definition of spiral tilings was given, thereby answering a question posed by Grünbaum and Shephard in the late 1970s. The author had the pleasure to discuss the topic via e-mail with Branko Grünbaum in his 87th year. During this correspondence the question arose whether a spiral structure (given a certain definition of it) could be recognized automatically or whether “to some extent, at least, the spiral effect is psychological”, as Grünbaum and Shephard had conjectured in 1987 (see exercise section of chapter 9.5 in [4]). In this paper, an algorithm for automatic detection of such a tiling’s spiral structure and its first implementation results will be discussed. Finally, the definitions for several types of spiral tilings will be refined based on this investigation.","PeriodicalId":41994,"journal":{"name":"Elemente der Mathematik","volume":" ","pages":""},"PeriodicalIF":0.1,"publicationDate":"2021-06-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41551684","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"A note on the Diophantine equation $(x+1)^3+(x+2)^3+cdots+(2x)^3=y^n$","authors":"N. X. Tho","doi":"10.4171/EM/450","DOIUrl":"https://doi.org/10.4171/EM/450","url":null,"abstract":"","PeriodicalId":41994,"journal":{"name":"Elemente der Mathematik","volume":" ","pages":""},"PeriodicalIF":0.1,"publicationDate":"2021-05-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49601857","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
The paper introduces cycles cross ratio, which extends the classic cross ratio of four points to various settings: conformal geometry, Lie spheres geometry, etc. Just like its classic counterpart cycles cross ratio is a measure of anharmonicity between spheres with respect to inversion. It also provides a M"obius invariant distance between spheres. Many further properties of cycles cross ratio awaiting their exploration. In abstract framework the new invariant can be considered in any projective space with a bilinear pairing.
{"title":"Cycles cross ratio: An invitation","authors":"V. Kisil","doi":"10.4171/EM/471","DOIUrl":"https://doi.org/10.4171/EM/471","url":null,"abstract":"The paper introduces cycles cross ratio, which extends the classic cross ratio of four points to various settings: conformal geometry, Lie spheres geometry, etc. Just like its classic counterpart cycles cross ratio is a measure of anharmonicity between spheres with respect to inversion. It also provides a M\"obius invariant distance between spheres. Many further properties of cycles cross ratio awaiting their exploration. In abstract framework the new invariant can be considered in any projective space with a bilinear pairing.","PeriodicalId":41994,"journal":{"name":"Elemente der Mathematik","volume":" ","pages":""},"PeriodicalIF":0.1,"publicationDate":"2021-05-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45897797","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Eulers Lösung eines difficiliorum Problematum","authors":"G. Wanner","doi":"10.4171/EM/447","DOIUrl":"https://doi.org/10.4171/EM/447","url":null,"abstract":"","PeriodicalId":41994,"journal":{"name":"Elemente der Mathematik","volume":" ","pages":""},"PeriodicalIF":0.1,"publicationDate":"2021-05-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48181437","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Factorization of Delannoy matrices","authors":"Roberta Brawer","doi":"10.4171/EM/440","DOIUrl":"https://doi.org/10.4171/EM/440","url":null,"abstract":"","PeriodicalId":41994,"journal":{"name":"Elemente der Mathematik","volume":" ","pages":""},"PeriodicalIF":0.1,"publicationDate":"2021-04-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49345821","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
京公网安备 11010802042870号
京ICP备2023020795号-1
扫码关注我们
求助内容：
应助结果提醒方式：