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The role of convexity in defining regular polyhedra 凸性在定义正多面体中的作用
The Mathematical Gazette Pub Date : 2024-02-15 DOI: 10.1017/mag.2024.10
Chris Ottewill
{"title":"The role of convexity in defining regular polyhedra","authors":"Chris Ottewill","doi":"10.1017/mag.2024.10","DOIUrl":"https://doi.org/10.1017/mag.2024.10","url":null,"abstract":"It is almost twenty years since Branko Grünbaum lamented that the ‘original sin’ in the theory of polyhedra is that from Euclid onwards “the writers failed to define what are the ‘polyhedra’ among which they are finding the ‘regular’ ones” ([1, p. 43]). Various definitions of ‘regular’ can be found in the literature with a condition of convexity often included (e.g. [2, p. 301], [3, p. 77], [4, p. 47], [5, p. 435], [6, p. 16]). The condition of convexity is usually cited to exclude regular self-intersecting polyhedra, i.e. the Kepler-Poinsot polyhedra, such as the ‘great dodecahedron’ consisting of twelve intersecting pentagonal faces shown in Figure 1 with one face shaded. Richeson also notes ([4, pp. 47-48]) that, for a particular definition of ‘regular’, convexity is needed to exclude the ‘punched-in’ icosahedron shown in Figure 2.","PeriodicalId":22812,"journal":{"name":"The Mathematical Gazette","volume":"59 20","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-02-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139775034","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
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":"59 29","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-02-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139775385","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
Relating constructions and properties through duality 通过二元性关联构造和属性
The Mathematical Gazette Pub Date : 2024-02-15 DOI: 10.1017/mag.2024.5
Steven J. Kilner, David L. Farnsworth
{"title":"Relating constructions and properties through duality","authors":"Steven J. Kilner, David L. Farnsworth","doi":"10.1017/mag.2024.5","DOIUrl":"https://doi.org/10.1017/mag.2024.5","url":null,"abstract":"Our goal is to find new constructions and properties of parabolas. Our strategy is to display the steps in a known construction or property, and then to take the dual of the steps in order to create a new construction or property.","PeriodicalId":22812,"journal":{"name":"The Mathematical Gazette","volume":"12 23","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-02-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139776213","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
108.11 Euler’s limit—revisited 108.11 欧拉极限重温
The Mathematical Gazette Pub Date : 2024-02-15 DOI: 10.1017/mag.2024.28
Bikash Chakraborty, Sagar Chakraborty
{"title":"108.11 Euler’s limit—revisited","authors":"Bikash Chakraborty, Sagar Chakraborty","doi":"10.1017/mag.2024.28","DOIUrl":"https://doi.org/10.1017/mag.2024.28","url":null,"abstract":"","PeriodicalId":22812,"journal":{"name":"The Mathematical Gazette","volume":"171 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-02-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139833567","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 Devil’s Advocate and the binomial expansion 魔鬼代言人与二项式展开
The Mathematical Gazette Pub Date : 2024-02-15 DOI: 10.1017/mag.2024.36
Nick Lord
{"title":"The Devil’s Advocate and the binomial expansion","authors":"Nick Lord","doi":"10.1017/mag.2024.36","DOIUrl":"https://doi.org/10.1017/mag.2024.36","url":null,"abstract":"","PeriodicalId":22812,"journal":{"name":"The Mathematical Gazette","volume":"362 4","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-02-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139834210","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
108.01 A use of Pythagorean triples in a problem in elementary geometry 108.01 勾股定理三段论在初等几何问题中的应用
The Mathematical Gazette Pub Date : 2024-02-15 DOI: 10.1017/mag.2024.18
Alexander Kronberg
{"title":"108.01 A use of Pythagorean triples in a problem in elementary geometry","authors":"Alexander Kronberg","doi":"10.1017/mag.2024.18","DOIUrl":"https://doi.org/10.1017/mag.2024.18","url":null,"abstract":"","PeriodicalId":22812,"journal":{"name":"The Mathematical Gazette","volume":"144 2","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-02-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139834783","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
{"title":"A cautionary tale about the pole of polar coordinates","authors":"Nick Lord","doi":"10.1017/mag.2024.37","DOIUrl":"https://doi.org/10.1017/mag.2024.37","url":null,"abstract":"","PeriodicalId":22812,"journal":{"name":"The Mathematical Gazette","volume":"105 2","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-02-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139834828","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
xy = cos (x + y) and other implicit equations that are surprisingly easy to plot xy = cos (x + y) 及其他隐式方程，绘制起来出奇地容易
The Mathematical Gazette Pub Date : 2024-02-15 DOI: 10.1017/mag.2024.2
Michael Jewess
{"title":"xy = cos (x + y) and other implicit equations that are surprisingly easy to plot","authors":"Michael Jewess","doi":"10.1017/mag.2024.2","DOIUrl":"https://doi.org/10.1017/mag.2024.2","url":null,"abstract":"The following equations relate y only implicitly to x:(1)(2) In both equations, y is a function of x for a continuous range of (x, y) values in the real x-y plane. (1) represents an ellipse. (2) has been designed by the author to have a solution in the real x-y plane at (−1, 2), and because the function on the left-hand side of (2) meets certain conditions regarding continuity and partial differentiability there must be a line of points in the real x-y plane satisfying (2) and passing continuously through (−1, 2) [1, pp. 23-28].","PeriodicalId":22812,"journal":{"name":"The Mathematical Gazette","volume":"117 10","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-02-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139835957","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
Relating constructions and properties through duality 通过二元性关联构造和属性
The Mathematical Gazette Pub Date : 2024-02-15 DOI: 10.1017/mag.2024.5
Steven J. Kilner, David L. Farnsworth
{"title":"Relating constructions and properties through duality","authors":"Steven J. Kilner, David L. Farnsworth","doi":"10.1017/mag.2024.5","DOIUrl":"https://doi.org/10.1017/mag.2024.5","url":null,"abstract":"Our goal is to find new constructions and properties of parabolas. Our strategy is to display the steps in a known construction or property, and then to take the dual of the steps in order to create a new construction or property.","PeriodicalId":22812,"journal":{"name":"The Mathematical Gazette","volume":"183 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-02-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139835974","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
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