{"title":"Formulations: architecture, mathematics, culture by Andrew Witt , pp. 428, £23.15, (paper), ISBN 978-0-262-54300-2, Massachusetts Institute of Technology Press (2021)","authors":"T. Crilly","doi":"10.1017/mag.2024.45","DOIUrl":"https://doi.org/10.1017/mag.2024.45","url":null,"abstract":"","PeriodicalId":22812,"journal":{"name":"The Mathematical Gazette","volume":"158 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-02-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139834893","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":"108.06 Simple bounds on a sum pertinent to primes","authors":"Hazar Aydin","doi":"10.1017/mag.2024.23","DOIUrl":"https://doi.org/10.1017/mag.2024.23","url":null,"abstract":"","PeriodicalId":22812,"journal":{"name":"The Mathematical Gazette","volume":"665 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-02-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139835779","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":"108.18 A one-line proof of the Finsler-Hadwiger inequality","authors":"Nick Lord","doi":"10.1017/mag.2024.35","DOIUrl":"https://doi.org/10.1017/mag.2024.35","url":null,"abstract":"","PeriodicalId":22812,"journal":{"name":"The Mathematical Gazette","volume":"260 ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-02-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139836128","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}
On 10th July 1796, when he was still a teenager, Gauss famously wrote EYPHKA! in his diary when recording the completion of a proof that every positive integer is the sum of at most three triangular numbers.
{"title":"The Eureka theorem of Gauss","authors":"Stan Dolan","doi":"10.1017/mag.2024.15","DOIUrl":"https://doi.org/10.1017/mag.2024.15","url":null,"abstract":"On 10th July 1796, when he was still a teenager, Gauss famously wrote EYPHKA! in his diary when recording the completion of a proof that every positive integer is the sum of at most three triangular numbers.","PeriodicalId":22812,"journal":{"name":"The Mathematical Gazette","volume":"59 2","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-02-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139836217","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":"108.18 A one-line proof of the Finsler-Hadwiger inequality","authors":"Nick Lord","doi":"10.1017/mag.2024.35","DOIUrl":"https://doi.org/10.1017/mag.2024.35","url":null,"abstract":"","PeriodicalId":22812,"journal":{"name":"The Mathematical Gazette","volume":"24 12","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-02-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139776301","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":"108.04 Digital root analysis of Smith numbers","authors":"Shyam Sunder Gupta","doi":"10.1017/mag.2024.21","DOIUrl":"https://doi.org/10.1017/mag.2024.21","url":null,"abstract":"","PeriodicalId":22812,"journal":{"name":"The Mathematical Gazette","volume":"6 3","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-02-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139776450","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 idea of using the generalised inverse of a singular matrix A to solve the matrix equation Ax = b has been discussed in the earlier papers [1, 2, 3, 4] in the Gazette. Here we discuss three simple geometric questions which are of interest in their own right, and which illustrate the use of the generalised inverse of a matrix. The three questions are about polygons and circles in the Euclidean plane. We need not assume that a polygon is a simple closed curve, nor that it is convex: indeed, abstractly, a polygon is just a finite sequence (v1, …, vn) of its distinct, consecutive, vertices. It is convenient to let vn + 1 = v1 and (later) Cn + 1 = C1.
{"title":"Singular matrices and pairwise-tangent circles","authors":"A. Beardon","doi":"10.1017/mag.2024.3","DOIUrl":"https://doi.org/10.1017/mag.2024.3","url":null,"abstract":"The idea of using the generalised inverse of a singular matrix A to solve the matrix equation Ax = b has been discussed in the earlier papers [1, 2, 3, 4] in the Gazette. Here we discuss three simple geometric questions which are of interest in their own right, and which illustrate the use of the generalised inverse of a matrix. The three questions are about polygons and circles in the Euclidean plane. We need not assume that a polygon is a simple closed curve, nor that it is convex: indeed, abstractly, a polygon is just a finite sequence (v1, …, vn) of its distinct, consecutive, vertices. It is convenient to let vn + 1 = v1 and (later) Cn + 1 = C1.","PeriodicalId":22812,"journal":{"name":"The Mathematical Gazette","volume":"12 9","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-02-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139776518","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}
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