{"title":"108.16 Golden triangles founded on Kepler’s triangle","authors":"Aldo Scimone","doi":"10.1017/mag.2024.33","DOIUrl":"https://doi.org/10.1017/mag.2024.33","url":null,"abstract":"","PeriodicalId":22812,"journal":{"name":"The Mathematical Gazette","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-02-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139834379","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 2 × 2 identity matrix, $${I_2} = left( begin{gathered}{rm{1 ,,,0}} hfill {rm{0 ,,,1}} hfill end{gathered} right)$$, has an infinite number of square roots. The purpose of this paper is to show some interesting patterns that appear among these square roots. In the process, we will take a brief tour of some topics in number theory, including Pythagorean triples, Eisenstein triples, Fibonacci numbers, Pell numbers and Diophantine triples.
{"title":"Patterns among square roots of the 2 × 2 identity matrix","authors":"H. Sporn","doi":"10.1017/mag.2024.14","DOIUrl":"https://doi.org/10.1017/mag.2024.14","url":null,"abstract":"The 2 × 2 identity matrix, $${I_2} = left( begin{gathered}{rm{1 ,,,0}} hfill {rm{0 ,,,1}} hfill end{gathered} right)$$, has an infinite number of square roots. The purpose of this paper is to show some interesting patterns that appear among these square roots. In the process, we will take a brief tour of some topics in number theory, including Pythagorean triples, Eisenstein triples, Fibonacci numbers, Pell numbers and Diophantine triples.","PeriodicalId":22812,"journal":{"name":"The Mathematical Gazette","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-02-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139834865","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":"Theory of infinite sequences and series by Ludmila Bourchtein and Andrei Bourchtein , pp. 377, £54.99, (paper), ISBN 978-3-03079-430-9, Springer Verlag (2022)","authors":"Martin Lukarevski","doi":"10.1017/mag.2024.48","DOIUrl":"https://doi.org/10.1017/mag.2024.48","url":null,"abstract":"","PeriodicalId":22812,"journal":{"name":"The Mathematical Gazette","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-02-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139835336","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":"Can fish count? by Brian Butterworth , pp. 373, £20, (hard), ISBN 978-1-52941-125-6, Quercus Books (2022)","authors":"Anne Haworth","doi":"10.1017/mag.2024.46","DOIUrl":"https://doi.org/10.1017/mag.2024.46","url":null,"abstract":"","PeriodicalId":22812,"journal":{"name":"The Mathematical Gazette","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-02-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139835361","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":"Change and variations, a history of differential equations to 1900 by Jeremy Gray , pp. 261, £29.99, (hard), ISBN 978-3-03070-574-9, Springer Verlag (2021)","authors":"P. MacGregor","doi":"10.1017/mag.2024.44","DOIUrl":"https://doi.org/10.1017/mag.2024.44","url":null,"abstract":"","PeriodicalId":22812,"journal":{"name":"The Mathematical Gazette","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-02-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139835629","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}
There is a very interesting mathematical puzzle involving the geometrical configuration in the book Mathematical Curiosities [1, 2] by Alfred Posamentier and Ingmar Lehmann. It is shown in Figure 1.
{"title":"Some generalisations and extensions of a remarkable geometry puzzle","authors":"Quang Hung Tran","doi":"10.1017/mag.2024.6","DOIUrl":"https://doi.org/10.1017/mag.2024.6","url":null,"abstract":"There is a very interesting mathematical puzzle involving the geometrical configuration in the book Mathematical Curiosities [1, 2] by Alfred Posamentier and Ingmar Lehmann. It is shown in Figure 1.","PeriodicalId":22812,"journal":{"name":"The Mathematical Gazette","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-02-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139774100","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":"Another appearance of the golden ratio","authors":"Nick Lord","doi":"10.1017/mag.2024.38","DOIUrl":"https://doi.org/10.1017/mag.2024.38","url":null,"abstract":"","PeriodicalId":22812,"journal":{"name":"The Mathematical Gazette","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-02-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139776608","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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