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ABC-triangles ABC 三角形
The Mathematical Gazette Pub Date : 2024-02-15 DOI: 10.1017/mag.2024.13
J. Griffiths
{"title":"ABC-triangles","authors":"J. Griffiths","doi":"10.1017/mag.2024.13","DOIUrl":"https://doi.org/10.1017/mag.2024.13","url":null,"abstract":"If we talk about the centre of a triangle, what might we be referring to? Any triangle has many different points that could regarded as its centre; in fact, Encyclopedia of Triangle Centres lists over 70 000 possibilities. Three of the most famous centres, that every triangle will possess (although they may coincide), are the incentre (where the three angle bisectors meet), the centroid (where the three medians meet) and the orthocentre (where the three altitudes meet). Proofs that these centres are well-defined and exist for every triangle are simple and satisfying, good examples of reasoning (if we are teachers) for our students. Proving the three altitudes of a triangle share a point using the scalar product of vectors is a wonderful demonstration of the power of this idea.","PeriodicalId":22812,"journal":{"name":"The Mathematical Gazette","volume":"33 21","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-02-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139775888","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
108.02 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
Science by simulation, volume 1 by Andrew French, pp 288, £40 (paper), ISBN 978-1-80061-121-4, World Scientific (2022) 模拟科学》第 1 卷，安德鲁-弗伦奇著，第 288 页，40 英镑（纸质），ISBN 978-1-80061-121-4，世界科学出版社（2022 年）。
The Mathematical Gazette Pub Date : 2024-02-15 DOI: 10.1017/mag.2024.50
Owen Toller
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引用次数: 0
Formulations: architecture, mathematics, culture by Andrew Witt , pp. 428, £23.15, (paper), ISBN 978-0-262-54300-2, Massachusetts Institute of Technology Press (2021) 公式：建筑、数学、文化》，安德鲁-威特著，第 428 页，23.15 英镑（纸质），ISBN 978-0-262-54300-2，麻省理工学院出版社 (2021)
The Mathematical Gazette Pub Date : 2024-02-15 DOI: 10.1017/mag.2024.45
T. Crilly
{"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":"26 11","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-02-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139775254","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
108.17 On a generalisation of the Lemoine axis 108.17 关于勒莫因轴的一般化
The Mathematical Gazette Pub Date : 2024-02-15 DOI: 10.1017/mag.2024.34
Hans Humenberger, Franz Embacher
{"title":"108.17 On a generalisation of the Lemoine axis","authors":"Hans Humenberger, Franz Embacher","doi":"10.1017/mag.2024.34","DOIUrl":"https://doi.org/10.1017/mag.2024.34","url":null,"abstract":"","PeriodicalId":22812,"journal":{"name":"The Mathematical Gazette","volume":"1 12","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-02-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139774682","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 characterisation of regular n-gons via (in)commensurability 通过（不）可通约性确定正则 n 形的特征
The Mathematical Gazette Pub Date : 2024-02-15 DOI: 10.1017/mag.2024.8
Silvano Rossetto, Giovanni Vincenzi
{"title":"A characterisation of regular n-gons via (in)commensurability","authors":"Silvano Rossetto, Giovanni Vincenzi","doi":"10.1017/mag.2024.8","DOIUrl":"https://doi.org/10.1017/mag.2024.8","url":null,"abstract":"In Euclidean geometry, a regular polygon is equiangular (all angles are equal in size) and equilateral (all sides have the same length) polygon. So regular polygons should be thought of as special polygons.","PeriodicalId":22812,"journal":{"name":"The Mathematical Gazette","volume":"34 32","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-02-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139776059","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
108.03 Remarks on perfect powers 108.03 关于完美权力的评论
The Mathematical Gazette Pub Date : 2024-02-15 DOI: 10.1017/mag.2024.20
H. A. ShahAli
{"title":"108.03 Remarks on perfect powers","authors":"H. A. ShahAli","doi":"10.1017/mag.2024.20","DOIUrl":"https://doi.org/10.1017/mag.2024.20","url":null,"abstract":"","PeriodicalId":22812,"journal":{"name":"The Mathematical Gazette","volume":"211 3","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-02-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139833662","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
Some generalisations and extensions of a remarkable geometry puzzle 非凡几何难题的一些概括和扩展
The Mathematical Gazette Pub Date : 2024-02-15 DOI: 10.1017/mag.2024.6
Quang Hung Tran
{"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":"241 ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-02-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139833769","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
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":"575 ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-02-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139834040","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
ABC-triangles ABC 三角形
The Mathematical Gazette Pub Date : 2024-02-15 DOI: 10.1017/mag.2024.13
J. Griffiths
{"title":"ABC-triangles","authors":"J. Griffiths","doi":"10.1017/mag.2024.13","DOIUrl":"https://doi.org/10.1017/mag.2024.13","url":null,"abstract":"If we talk about the centre of a triangle, what might we be referring to? Any triangle has many different points that could regarded as its centre; in fact, Encyclopedia of Triangle Centres lists over 70 000 possibilities. Three of the most famous centres, that every triangle will possess (although they may coincide), are the incentre (where the three angle bisectors meet), the centroid (where the three medians meet) and the orthocentre (where the three altitudes meet). Proofs that these centres are well-defined and exist for every triangle are simple and satisfying, good examples of reasoning (if we are teachers) for our students. Proving the three altitudes of a triangle share a point using the scalar product of vectors is a wonderful demonstration of the power of this idea.","PeriodicalId":22812,"journal":{"name":"The Mathematical Gazette","volume":"502 ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-02-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139835486","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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