{"title":"Mathematics is beautiful by Heinz Klaus Strick, pp. 366, £24.99 (paper), ISBN 978-3-662-62688-7, £19.99 (eBook) ISBN 978-3-662-62689-4, Springer Verlag (2021)","authors":"Peter Giblin","doi":"10.1017/mag.2024.52","DOIUrl":"https://doi.org/10.1017/mag.2024.52","url":null,"abstract":"","PeriodicalId":22812,"journal":{"name":"The Mathematical Gazette","volume":"2 3","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-02-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139774741","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":"Irrationality and transcendence in number theory by David Angell , pp. 242, £59.99, (hard), ISBN 978-0-367-62837-6, Chapman and Hall/CRC (2022)","authors":"Peter Shiu","doi":"10.1017/mag.2024.47","DOIUrl":"https://doi.org/10.1017/mag.2024.47","url":null,"abstract":"","PeriodicalId":22812,"journal":{"name":"The Mathematical Gazette","volume":"115 16","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-02-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139776763","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":"42 6","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-02-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139775685","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 this work originally arose from a question pertaining to a laboratory experiment on circular motion in our departmental lab manual. The experiment itself involves rotating a bob along a horizontal circle (Figure 1), where the tension in the string attached to the bob provides the centripetal acceleration of the bob, the string itself passing through a smooth vertical pipe. It is assumed that the rotation is fast enough for the effect of gravity to be neglected and therefore the orientation of the part of the string between the top end of the pipe and the bob can be taken to be horizontal. The abovementioned question enquires what happens to the speed of the bob in the case that the bottom end of the string is hand-held and pulled slowly so that the radius of the circular orbit decreases. The answer to the question is straightforward. Either a work-energy argument or an argument involving the conservation of angular momentum provides the same correct answer.
{"title":"A slowly evolving conical pendulum","authors":"Subhranil De","doi":"10.1017/mag.2024.16","DOIUrl":"https://doi.org/10.1017/mag.2024.16","url":null,"abstract":"The idea of this work originally arose from a question pertaining to a laboratory experiment on circular motion in our departmental lab manual. The experiment itself involves rotating a bob along a horizontal circle (Figure 1), where the tension in the string attached to the bob provides the centripetal acceleration of the bob, the string itself passing through a smooth vertical pipe. It is assumed that the rotation is fast enough for the effect of gravity to be neglected and therefore the orientation of the part of the string between the top end of the pipe and the bob can be taken to be horizontal. The abovementioned question enquires what happens to the speed of the bob in the case that the bottom end of the string is hand-held and pulled slowly so that the radius of the circular orbit decreases. The answer to the question is straightforward. Either a work-energy argument or an argument involving the conservation of angular momentum provides the same correct answer.","PeriodicalId":22812,"journal":{"name":"The Mathematical Gazette","volume":"323 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-02-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139834610","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}
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.
欧拉的多项式 f (n) = n2 + n + 41 以连续替换 0、1、...、39 的值时产生 40 个不同的质数而闻名：见表 1。包括欧拉在内的一些学者更倾向于使用多项式 f (n - 1) = n2 - n + 41，其中 n = 1, ..., 40 为质数。由于 f (-n) = f (n - 1)，f (n) 在 n = -40，-39，...，39 时实际上取质数值（每个值重复一次）；等价多项式 f (n - 40) = n2 - 79n + 1601 在 n = 0，1，...，79 时取（重复）质数值。
{"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":"691 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-02-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139835435","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 are various combinatorial questions on rectangular arrays consisting of points, numbers, fields or, in general, of symbols such as chessboards, lattices, and graphs. Many such problems in enumerative combinatorics come from other branches of science and technology like physics, chemistry, computer sciences and engineering; for example the following two very challenging problems from chemistry: Problem 1: Dimer problem (Domino tiling) In chemistry, a large molecule composed repeatedly from monomers as a long chain is called a polymer and a dimer is composed of two monomers (where: mono = 1, di = 2, poly = many and mer = part).
{"title":"Walk on a grid","authors":"Manija Shahali, H. A. ShahAli","doi":"10.1017/mag.2024.17","DOIUrl":"https://doi.org/10.1017/mag.2024.17","url":null,"abstract":"There are various combinatorial questions on rectangular arrays consisting of points, numbers, fields or, in general, of symbols such as chessboards, lattices, and graphs. Many such problems in enumerative combinatorics come from other branches of science and technology like physics, chemistry, computer sciences and engineering; for example the following two very challenging problems from chemistry:\u0000Problem 1: Dimer problem (Domino tiling)\u0000In chemistry, a large molecule composed repeatedly from monomers as a long chain is called a polymer and a dimer is composed of two monomers (where: mono = 1, di = 2, poly = many and mer = part).","PeriodicalId":22812,"journal":{"name":"The Mathematical Gazette","volume":"664 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-02-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139835780","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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