{"title":"Die Infizierung des mathbb{Z}^2","authors":"K. Altmann","doi":"10.4171/em/488","DOIUrl":"https://doi.org/10.4171/em/488","url":null,"abstract":"","PeriodicalId":41994,"journal":{"name":"Elemente der Mathematik","volume":" ","pages":""},"PeriodicalIF":0.1,"publicationDate":"2022-10-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47377605","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":"Unlikely leading digits of powers of 2","authors":"Sungkon Chang","doi":"10.4171/em/487","DOIUrl":"https://doi.org/10.4171/em/487","url":null,"abstract":"","PeriodicalId":41994,"journal":{"name":"Elemente der Mathematik","volume":" ","pages":""},"PeriodicalIF":0.1,"publicationDate":"2022-10-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48172058","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":"Two proofs of Bondy’s theorem on induced subsets and two related questions","authors":"H. A. ShahAli","doi":"10.4171/em/486","DOIUrl":"https://doi.org/10.4171/em/486","url":null,"abstract":"","PeriodicalId":41994,"journal":{"name":"Elemente der Mathematik","volume":" ","pages":""},"PeriodicalIF":0.1,"publicationDate":"2022-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45392438","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}
Many proofs of the Fundamental Theorem of Algebra, including various proofs based on the theory of analytic functions of a complex variable, are known. To the best of our knowledge, this proof is different from the existing ones.
{"title":"A simple proof of the Fundamental Theorem of Algebra","authors":"B. Chakraborty","doi":"10.4171/em/484","DOIUrl":"https://doi.org/10.4171/em/484","url":null,"abstract":"Many proofs of the Fundamental Theorem of Algebra, including various proofs based on the theory of analytic functions of a complex variable, are known. To the best of our knowledge, this proof is different from the existing ones.","PeriodicalId":41994,"journal":{"name":"Elemente der Mathematik","volume":" ","pages":""},"PeriodicalIF":0.1,"publicationDate":"2022-07-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42551501","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":"Regression ellipses via hyperbolic geometry","authors":"Lilija Naiwert, K. Spindler","doi":"10.4171/em/480","DOIUrl":"https://doi.org/10.4171/em/480","url":null,"abstract":"","PeriodicalId":41994,"journal":{"name":"Elemente der Mathematik","volume":" ","pages":""},"PeriodicalIF":0.1,"publicationDate":"2022-06-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46747038","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":"Approximation of polynomials by Hermite interpolation","authors":"R. Kantrowitz, Mike Neumann","doi":"10.4171/em/481","DOIUrl":"https://doi.org/10.4171/em/481","url":null,"abstract":"","PeriodicalId":41994,"journal":{"name":"Elemente der Mathematik","volume":" ","pages":""},"PeriodicalIF":0.1,"publicationDate":"2022-06-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43880548","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}
We give a short proof of the quadratic reciprocity law using Gauss's Lemma and Hermite's identity.
利用高斯引理和埃尔米特恒等式给出二次互易律的简短证明。
{"title":"Hermite’s identity and the quadratic reciprocity law","authors":"F. Lemmermeyer","doi":"10.4171/em/485","DOIUrl":"https://doi.org/10.4171/em/485","url":null,"abstract":"We give a short proof of the quadratic reciprocity law using Gauss's Lemma and Hermite's identity.","PeriodicalId":41994,"journal":{"name":"Elemente der Mathematik","volume":"1 1","pages":""},"PeriodicalIF":0.1,"publicationDate":"2022-05-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41940229","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":"Unit squares with unit line segments","authors":"Manije Shahali, H. A. ShahAli","doi":"10.4171/em/479","DOIUrl":"https://doi.org/10.4171/em/479","url":null,"abstract":"","PeriodicalId":41994,"journal":{"name":"Elemente der Mathematik","volume":" ","pages":""},"PeriodicalIF":0.1,"publicationDate":"2022-05-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43143873","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":"Isogonal cevians and inequalities for quotients of cevians","authors":"Martin Lukarevski, D. Marinescu","doi":"10.4171/em/477","DOIUrl":"https://doi.org/10.4171/em/477","url":null,"abstract":"","PeriodicalId":41994,"journal":{"name":"Elemente der Mathematik","volume":" ","pages":""},"PeriodicalIF":0.1,"publicationDate":"2022-04-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47495743","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}