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In Search of Comrade Agronomof: Some Tribonacci History 寻找农学家同志:一些Tribonacci的历史
IF 0.5 4区 数学
American Mathematical Monthly Pub Date : 2023-08-23 DOI: 10.1080/00029890.2023.2231796
H. Tuenter
{"title":"In Search of Comrade Agronomof: Some Tribonacci History","authors":"H. Tuenter","doi":"10.1080/00029890.2023.2231796","DOIUrl":"https://doi.org/10.1080/00029890.2023.2231796","url":null,"abstract":"Abstract A note from May 1914 by a certain Agronomof in the Belgian journal Mathesis is frequently cited in the context of the mathematical history of the Tribonacci number sequence. We round out the historical perspective by providing details on Agronomof’s life and work, and highlight two late-nineteenth-century occurrences of this number sequence. One occurrence is connected to Charles Darwin’s On the Origin of Species. Furthermore, we show that the main identity in Agronomof’s note can be leveraged to derive several nontrivial identities with surprising ease and elegance. Some of these identities have only recently been proven by different and more laborious methods; others are new.","PeriodicalId":7761,"journal":{"name":"American Mathematical Monthly","volume":"130 1","pages":"708 - 719"},"PeriodicalIF":0.5,"publicationDate":"2023-08-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41579303","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
A Combinatorial Proof of a Symmetric Group Character Involution 一类对称群字符对合的组合证明
IF 0.5 4区 数学
American Mathematical Monthly Pub Date : 2023-08-14 DOI: 10.1080/00029890.2023.2242042
P. Renteln
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引用次数: 0
The Determinant Mod p of a Circulant Matrix of Order pm pm阶循环矩阵的行列式Mod p
IF 0.5 4区 数学
American Mathematical Monthly Pub Date : 2023-08-14 DOI: 10.1080/00029890.2023.2240266
Tom Moshaiov
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引用次数: 0
A Tale of Two by Two Matrices 《两个矩阵的故事
IF 0.5 4区 数学
American Mathematical Monthly Pub Date : 2023-08-14 DOI: 10.1080/00029890.2023.2242039
D. Kalman, R. Mena
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引用次数: 0
Gagliardo-Nirenberg-Sobolev Inequality: An Induction Proof Gagliardo-Nirenberg-Sobolev不等式:一个归纳证明
IF 0.5 4区 数学
American Mathematical Monthly Pub Date : 2023-08-10 DOI: 10.1080/00029890.2023.2240683
Shibo Liu
{"title":"Gagliardo-Nirenberg-Sobolev Inequality: An Induction Proof","authors":"Shibo Liu","doi":"10.1080/00029890.2023.2240683","DOIUrl":"https://doi.org/10.1080/00029890.2023.2240683","url":null,"abstract":"Abstract This paper presents an induction proof of the G-N-S inequality when p = 1, which the author believes is much simpler and more transparent than other proofs found in the literature.","PeriodicalId":7761,"journal":{"name":"American Mathematical Monthly","volume":"1 1","pages":""},"PeriodicalIF":0.5,"publicationDate":"2023-08-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44822927","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Yueh-Gin Gung and Dr. Charles Y. Hu Award for 2023 to Victor J. Katz for Distinguished Service to Mathematics Yueh Gin Gung和Charles Y.Hu博士2023年数学杰出贡献奖授予Victor J.Katz
IF 0.5 4区 数学
American Mathematical Monthly Pub Date : 2023-08-04 DOI: 10.1080/00029890.2023.2190724
Vesta Coufal, Suzanne Dorée, T. Dray, Frank Farris, Amy Shell-Gellasch, Derek Smith
{"title":"Yueh-Gin Gung and Dr. Charles Y. Hu Award for 2023 to Victor J. Katz for Distinguished Service to Mathematics","authors":"Vesta Coufal, Suzanne Dorée, T. Dray, Frank Farris, Amy Shell-Gellasch, Derek Smith","doi":"10.1080/00029890.2023.2190724","DOIUrl":"https://doi.org/10.1080/00029890.2023.2190724","url":null,"abstract":"The Yueh-Gin Gung and Dr. Charles Y. Hu Award for Distinguished Service to Mathematics is the most prestigious award for service offered by the Mathematical Association of America. It celebrates contributions to the community that have influenced the field of mathematics in a significant and positive way. Victor Katz","PeriodicalId":7761,"journal":{"name":"American Mathematical Monthly","volume":"130 1","pages":"603 - 605"},"PeriodicalIF":0.5,"publicationDate":"2023-08-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45314360","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Billiard Circuits in Quadrilaterals 四边形台球回路
IF 0.5 4区 数学
American Mathematical Monthly Pub Date : 2023-08-02 DOI: 10.1080/00029890.2023.2230860
K. Knox
{"title":"Billiard Circuits in Quadrilaterals","authors":"K. Knox","doi":"10.1080/00029890.2023.2230860","DOIUrl":"https://doi.org/10.1080/00029890.2023.2230860","url":null,"abstract":"Abstract A quadrilateral contains a closed billiard circuit that bounces consecutively on the interiors of its sides each exactly once per cycle, if and only if it is cyclic and its interior contains the center of its circumscribed circle.","PeriodicalId":7761,"journal":{"name":"American Mathematical Monthly","volume":"130 1","pages":"755 - 759"},"PeriodicalIF":0.5,"publicationDate":"2023-08-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49140242","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Sum of a Geometric Series Via the Integral 几何级数的积分和
IF 0.5 4区 数学
American Mathematical Monthly Pub Date : 2023-07-26 DOI: 10.1080/00029890.2023.2231164
B. Chakraborty
{"title":"Sum of a Geometric Series Via the Integral","authors":"B. Chakraborty","doi":"10.1080/00029890.2023.2231164","DOIUrl":"https://doi.org/10.1080/00029890.2023.2231164","url":null,"abstract":"","PeriodicalId":7761,"journal":{"name":"American Mathematical Monthly","volume":"130 1","pages":"764 - 764"},"PeriodicalIF":0.5,"publicationDate":"2023-07-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48060015","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
An Arithmetic Proof of a Theorem of Chan, Long, and Yang Chan、Long和Yang定理的算术证明
IF 0.5 4区 数学
American Mathematical Monthly Pub Date : 2023-07-24 DOI: 10.1080/00029890.2023.2230836
K. Williams
{"title":"An Arithmetic Proof of a Theorem of Chan, Long, and Yang","authors":"K. Williams","doi":"10.1080/00029890.2023.2230836","DOIUrl":"https://doi.org/10.1080/00029890.2023.2230836","url":null,"abstract":"Abstract We present a short arithmetic proof of the theorem of Chan, Long, and Yang proved in the Monthly in 2011, which gives explicit formulas for integers x and y such that , where p is a prime satisfying .","PeriodicalId":7761,"journal":{"name":"American Mathematical Monthly","volume":"130 1","pages":"760 - 763"},"PeriodicalIF":0.5,"publicationDate":"2023-07-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46694907","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Reviews 评论
IF 0.5 4区 数学
American Mathematical Monthly Pub Date : 2023-07-24 DOI: 10.1080/00029890.2023.2231826
Brian Hopkins
{"title":"Reviews","authors":"Brian Hopkins","doi":"10.1080/00029890.2023.2231826","DOIUrl":"https://doi.org/10.1080/00029890.2023.2231826","url":null,"abstract":"The most revelatory experience of my undergraduate mathematics degree was a writing course offered by James Vick. Well on his way to becoming a vice president in the University of Texas administration, Vick still managed to teach the occasional class. This one, “Proofs, Conjectures, and Controversies,” showed us that mathematics was not always as absolute as implied in our other courses. In particular, there is not always consensus about what constitutes a valid proof and what tools are allowed. One example of controversy was the 1976 computer-assisted proof of the four color theorem, establishing that the countries of every map can be colored with at most four colors so that no two neighboring countries are colored the same. The class readings included the recent Dover edition of Saaty and Kainan’s book [18] on the “assaults and conquest” of that graph theory problem and Leonard Gillman’s celebrated guide to mathematical writing [5]. What an honor to learn about recent and contentious research developments while developing skills in mathematical exposition. The year 1976 was an important year for both the United States and graph theory. In that year of the American bicentennial, Kenneth Appel and Wolfgang Haken of the University of Illinois solved Francis Guthrie’s 1852 four color conjecture. This was one of the rare mathematical results to be mentioned (eventually) in The New York Times [19, p. 209]. Another milestone for graph theory that year was the publication of the first book on its history, Graph Theory 1736–1936 by Norman Biggs, Keith Lloyd, and Robin Wilson [2]. That book opened a sort of trilogy on the history of graph theory, all involving the talented and prolific expositor Robin Wilson. The second book was a 2002 solo effort Four Colors Suffice [19]. The third book, based on the 2012 dissertation of David Parks [16] and also featuring John Watkins, focuses on the period 1876–1976 with an emphasis on US and Canadian contributions to the field. This review will focus on the 2023 book while also discussing it in relation to its two predecessors.","PeriodicalId":7761,"journal":{"name":"American Mathematical Monthly","volume":"130 1","pages":"779 - 784"},"PeriodicalIF":0.5,"publicationDate":"2023-07-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44201560","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","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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