{"title":"Fibonacci Convolutions","authors":"David Nacin","doi":"10.1080/0025570X.2023.2201547","DOIUrl":"https://doi.org/10.1080/0025570X.2023.2201547","url":null,"abstract":"Summary We present visual proofs of two results on convolutions of the Fibonacci numbers with related sequences.","PeriodicalId":18344,"journal":{"name":"Mathematics Magazine","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-04-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46875738","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":"Infinitely Many New Derivations of the Geometric Expectation","authors":"L. Hong","doi":"10.1080/0025570X.2023.2199722","DOIUrl":"https://doi.org/10.1080/0025570X.2023.2199722","url":null,"abstract":"Summary Several derivations of the geometric expectation have been proposed by previous authors. This article gives infinitely many new derivations of the geometric expectation.","PeriodicalId":18344,"journal":{"name":"Mathematics Magazine","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-04-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43033608","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":"Sums of Consecutive Odd Numbers","authors":"R. Nelsen","doi":"10.1080/0025570x.2023.2199753","DOIUrl":"https://doi.org/10.1080/0025570x.2023.2199753","url":null,"abstract":"Summary We show visually that certain pairs of consecutive subsets of consecutive odd numbers have equal sums.","PeriodicalId":18344,"journal":{"name":"Mathematics Magazine","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-04-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49096369","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":"A Novel Proof of the Desnanot-Jacobi Determinant Identity","authors":"J. Vrbik, Paul Vrbik","doi":"10.1080/0025570X.2023.2199721","DOIUrl":"https://doi.org/10.1080/0025570X.2023.2199721","url":null,"abstract":"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.","PeriodicalId":18344,"journal":{"name":"Mathematics Magazine","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-04-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45218825","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":"Identities for Pell Numbers: A Visual Sampler","authors":"R. Nelsen","doi":"10.1080/0025570X.2023.2199675","DOIUrl":"https://doi.org/10.1080/0025570X.2023.2199675","url":null,"abstract":"Summary We present some visual arguments for various Pell and Pell-Lucas number identities.","PeriodicalId":18344,"journal":{"name":"Mathematics Magazine","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-04-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46919510","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":"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}
{"title":"Report on the 63rd Annual International Mathematical Olympiad","authors":"B. Bajnok","doi":"10.1080/0025570X.2023.2177035","DOIUrl":"https://doi.org/10.1080/0025570X.2023.2177035","url":null,"abstract":"Summary We present the problems and solutions to the 63rd Annual International Mathematical Olympiad.","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":"44559956","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":"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}
{"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}
{"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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