Pub Date : 2023-04-24DOI: 10.1080/0025570X.2023.2201547
David Nacin
Summary We present visual proofs of two results on convolutions of the Fibonacci numbers with related sequences.
摘要我们给出了Fibonacci数和相关序列卷积的两个结果的可视化证明。
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Pub Date : 2023-04-24DOI: 10.1080/0025570X.2023.2199722
L. Hong
Summary Several derivations of the geometric expectation have been proposed by previous authors. This article gives infinitely many new derivations of the geometric expectation.
以前的作者已经提出了几个几何期望的推导。本文给出了无穷多个几何期望的新推导。
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Pub Date : 2023-04-24DOI: 10.1080/0025570x.2023.2199753
R. Nelsen
Summary We show visually that certain pairs of consecutive subsets of consecutive odd numbers have equal sums.
摘要我们直观地展示了某些对连续奇数的连续子集具有相等的和。
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Pub Date : 2023-04-24DOI: 10.1080/0025570X.2023.2199721
J. Vrbik, Paul Vrbik
Summary We present an alternate proof for the Desnanot-Jacobi identity using induction, basic matrix algebra and elementary differential calculus. It is an instructive demonstration of how it is occasionally necessary to utilize results from different fields of mathematics to solve a specific problem.
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Pub Date : 2023-04-19DOI: 10.1080/0025570X.2023.2199675
R. Nelsen
Summary We present some visual arguments for various Pell and Pell-Lucas number identities.
摘要我们给出了各种Pell和Pell-Lucas数恒等式的一些直观论证。
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Pub Date : 2023-03-15DOI: 10.1080/0025570x.2023.2180979
J. Rosenhouse
their analysis on tricuspid regurgitation (TR) improvement following cardiac resynchronization therapy (CRT) and associated findings of improved functional outcomes in this cohort.
他们对心脏再同步化治疗（CRT）后三尖瓣反流（TR）改善的分析以及该队列中功能结果改善的相关发现。
{"title":"Letter from the Editor","authors":"J. Rosenhouse","doi":"10.1080/0025570x.2023.2180979","DOIUrl":"https://doi.org/10.1080/0025570x.2023.2180979","url":null,"abstract":"their analysis on tricuspid regurgitation (TR) improvement following cardiac resynchronization therapy (CRT) and associated findings of improved functional outcomes in this cohort.","PeriodicalId":18344,"journal":{"name":"Mathematics Magazine","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-03-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42935644","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}
Pub Date : 2023-03-15DOI: 10.1080/0025570X.2023.2177035
B. Bajnok
Summary We present the problems and solutions to the 63rd Annual International Mathematical Olympiad.
摘要我们向第63届国际数学奥林匹克年会提出问题和解决办法。
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Pub Date : 2023-03-15DOI: 10.1080/0025570x.2023.2177036
{"title":"Problems and Solutions","authors":"","doi":"10.1080/0025570x.2023.2177036","DOIUrl":"https://doi.org/10.1080/0025570x.2023.2177036","url":null,"abstract":"","PeriodicalId":18344,"journal":{"name":"Mathematics Magazine","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-03-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135698259","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}
Pub Date : 2023-03-13DOI: 10.1080/0025570X.2023.2176101
Alissa S. Crans, Glen T. Whitney
Summary For four decades, Mathematics Magazine has chronicled the quest to find all convex pentagons that tile the plane. Illustrating this story physically leads to the question: What integer-sided convex pentagons tile the plane? Using results from classical number theory along with convexity and continuity principles, we provide a complete answer to this question.
{"title":"Integral Tiling Pentagons","authors":"Alissa S. Crans, Glen T. Whitney","doi":"10.1080/0025570X.2023.2176101","DOIUrl":"https://doi.org/10.1080/0025570X.2023.2176101","url":null,"abstract":"Summary For four decades, Mathematics Magazine has chronicled the quest to find all convex pentagons that tile the plane. Illustrating this story physically leads to the question: What integer-sided convex pentagons tile the plane? Using results from classical number theory along with convexity and continuity principles, we provide a complete answer to this question.","PeriodicalId":18344,"journal":{"name":"Mathematics Magazine","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-03-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46405232","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}
Pub Date : 2023-03-10DOI: 10.1080/0025570X.2023.2176684
Veselin Jungić
Summary The Moser spindle, a seemingly simple geometric object with seven vertices and 11 line segments of unit distance, was first introduced in the early 1960s. This article shows that the Moser spindle still plays a major role in the search for solutions to some of the most intriguing open problems in discrete geometry. Specifically, the problem of finding the chromatic number of the plane and the problem of finding the fractional chromatic number of the plane.
{"title":"Still Spinning: The Moser Spindle at Sixty","authors":"Veselin Jungić","doi":"10.1080/0025570X.2023.2176684","DOIUrl":"https://doi.org/10.1080/0025570X.2023.2176684","url":null,"abstract":"Summary The Moser spindle, a seemingly simple geometric object with seven vertices and 11 line segments of unit distance, was first introduced in the early 1960s. This article shows that the Moser spindle still plays a major role in the search for solutions to some of the most intriguing open problems in discrete geometry. Specifically, the problem of finding the chromatic number of the plane and the problem of finding the fractional chromatic number of the plane.","PeriodicalId":18344,"journal":{"name":"Mathematics Magazine","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-03-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41345435","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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