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Extensions of Vittas’ Theorem 维塔斯定理的扩展
The Mathematical Gazette Pub Date : 2024-02-15 DOI: 10.1017/mag.2024.9
N. Dergiades, Quang Hung Tran
{"title":"Extensions of Vittas’ Theorem","authors":"N. Dergiades, Quang Hung Tran","doi":"10.1017/mag.2024.9","DOIUrl":"https://doi.org/10.1017/mag.2024.9","url":null,"abstract":"The Greek architect Kostas Vittas published in 2006 a beautiful theorem ([1]) on the cyclic quadrilateral as follows:Theorem 1 (Kostas Vittas, 2006): If ABCD is a cyclic quadrilateral with P being the intersection of two diagonals AC and BD, then the four Euler lines of the triangles PAB, PBC, PCD and PDA are concurrent.","PeriodicalId":22812,"journal":{"name":"The Mathematical Gazette","volume":"2 11","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-02-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139774346","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}
引用次数: 0
Patterns among square roots of the 2 × 2 identity matrix 2 × 2 同位矩阵平方根之间的模式
The Mathematical Gazette Pub Date : 2024-02-15 DOI: 10.1017/mag.2024.14
H. Sporn
{"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":"58 24","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-02-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139775414","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}
引用次数: 0
A cautionary tale about the pole of polar coordinates 极坐标极点的警示故事
The Mathematical Gazette Pub Date : 2024-02-15 DOI: 10.1017/mag.2024.37
Nick Lord
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引用次数: 0
108.02 Fermat-like equations for fractional parts 108.02 分数部分的费马方程
The Mathematical Gazette Pub Date : 2024-02-15 DOI: 10.1017/mag.2024.19
N. X. Tho, Nguyen Quynh Tram
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引用次数: 0
The polyhedrists: art and geometry in the long sixteenth century by Noam Andrews , pp. 300, $44.95, ISBN 978-0-26204-664-0, MIT Press (2022) 多面体主义者：16 世纪漫长岁月中的艺术与几何》，Noam Andrews 著，第 300 页，44.95 美元，ISBN 978-0-26204-664-0，麻省理工学院出版社 (2022)
The Mathematical Gazette Pub Date : 2024-02-15 DOI: 10.1017/mag.2024.43
G. Leversha
{"title":"The polyhedrists: art and geometry in the long sixteenth century by Noam Andrews , pp. 300, $44.95, ISBN 978-0-26204-664-0, MIT Press (2022)","authors":"G. Leversha","doi":"10.1017/mag.2024.43","DOIUrl":"https://doi.org/10.1017/mag.2024.43","url":null,"abstract":"","PeriodicalId":22812,"journal":{"name":"The Mathematical Gazette","volume":"553 ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-02-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139835009","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}
引用次数: 0
Euler’s prime-producing polynomial revisited 欧拉质点生成多项式再探讨
The Mathematical Gazette Pub Date : 2024-02-15 DOI: 10.1017/mag.2024.11
R. Heffernan, Nick Lord, Des MacHale
{"title":"Euler’s prime-producing polynomial revisited","authors":"R. Heffernan, Nick Lord, Des MacHale","doi":"10.1017/mag.2024.11","DOIUrl":"https://doi.org/10.1017/mag.2024.11","url":null,"abstract":"Euler’s polynomial f (n) = n2 + n + 41 is famous for producing 40 different prime numbers when the consecutive values 0, 1, …, 39 are substituted: see Table 1. Some authors, including Euler, prefer the polynomial f (n − 1) = n2 − n + 41 with prime values for n = 1, …, 40. Since f (−n) = f (n − 1), f (n) actually takes prime values (with each value repeated once) for n = −40, −39, …, 39; equivalently the polynomial f (n − 40) = n2 − 79n + 1601 takes (repeated) prime values for n = 0, 1, …, 79.","PeriodicalId":22812,"journal":{"name":"The Mathematical Gazette","volume":"39 5","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-02-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139775806","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}
引用次数: 0
A student's guide to Laplace transforms by Daniel Fleisch , pp. 218, £17.99, (paper), ISBN 978-1-00909-629-4, Cambridge University Press (2022) 拉普拉斯变换学生指南》，丹尼尔-弗莱施著，第 218 页，17.99 英镑（纸质），ISBN 978-1-00909-629-4，剑桥大学出版社（2022 年）。
The Mathematical Gazette Pub Date : 2024-02-15 DOI: 10.1017/mag.2024.49
Sue Colwell
{"title":"A student's guide to Laplace transforms by Daniel Fleisch , pp. 218, £17.99, (paper), ISBN 978-1-00909-629-4, Cambridge University Press (2022)","authors":"Sue Colwell","doi":"10.1017/mag.2024.49","DOIUrl":"https://doi.org/10.1017/mag.2024.49","url":null,"abstract":"","PeriodicalId":22812,"journal":{"name":"The Mathematical Gazette","volume":"13 11","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-02-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139776585","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}
引用次数: 0
Lost in the Math Museum by Colin Adams, pp 209, $35 (paperback), ISBN 978-1-47046-858-3, American Mathematical Society (2022) 迷失在数学博物馆》，科林-亚当斯著，第 209 页，35 美元（平装本），国际标准书号 978-1-47046-858-3，美国数学学会（2022 年）。
The Mathematical Gazette Pub Date : 2024-02-15 DOI: 10.1017/mag.2024.53
Mark Hunacek
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引用次数: 0
108.14 A triangle number identity 108.14 三角形数字特征
The Mathematical Gazette Pub Date : 2024-02-15 DOI: 10.1017/mag.2024.31
Paul Stephenson
{"title":"108.14 A triangle number identity","authors":"Paul Stephenson","doi":"10.1017/mag.2024.31","DOIUrl":"https://doi.org/10.1017/mag.2024.31","url":null,"abstract":"","PeriodicalId":22812,"journal":{"name":"The Mathematical Gazette","volume":"382 2","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-02-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139835420","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}
引用次数: 0
The one true logic: a monist manifesto, by Owen Griffiths and A. C. Paseau, pp 232, ISBN 978-0-19-882971-3, Oxford University Press (2022). 唯一真实的逻辑：一元论宣言》，欧文-格里菲斯和 A. C. 帕索著，第 232 页，国际标准书号 978-0-19-882971-3，牛津大学出版社（2022 年）。
The Mathematical Gazette Pub Date : 2024-02-15 DOI: 10.1017/mag.2024.51
Alan Slomson
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引用次数: 0
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