Pub Date : 2023-12-21DOI: 10.1080/00029890.2023.2285695
Mario Gómez, Facundo Mémoli
Ptolemy’s inequality is a classic relationship between the distances among four points in Euclidean space. Another relationship between six distances is the 4-point condition, an inequality satisfi...
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Pub Date : 2023-12-21DOI: 10.1080/00029890.2024.2292451
Lola Thompson
{"title":"Reviews\u0000 An Introduction to the Circle Method\u0000 . By M. Ram Murty & Kaneenika Sinha, American Mathematical Society, 2023. 258 pp., ISBN 978-1-4704-7203-0, $59.00.","authors":"Lola Thompson","doi":"10.1080/00029890.2024.2292451","DOIUrl":"https://doi.org/10.1080/00029890.2024.2292451","url":null,"abstract":"","PeriodicalId":501497,"journal":{"name":"The American Mathematical Monthly","volume":"53 17","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-12-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138952392","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 : 2023-12-21DOI: 10.1080/00029890.2023.2284611
János Pach, Gábor Tardos
Let P be an N-element point set in the plane. Consider N (pointlike) grasshoppers sitting at different points of P. In a “legal” move, any one of them can jump over another, and land on its other s...
假设 P 是平面上的一个 N 元素点集。在一个 "合法 "的移动中，任何一只蚱蜢都可以跳过另一只蚱蜢，然后落在它的另一个点上。
{"title":"Where Have All the Grasshoppers Gone?","authors":"János Pach, Gábor Tardos","doi":"10.1080/00029890.2023.2284611","DOIUrl":"https://doi.org/10.1080/00029890.2023.2284611","url":null,"abstract":"Let P be an N-element point set in the plane. Consider N (pointlike) grasshoppers sitting at different points of P. In a “legal” move, any one of them can jump over another, and land on its other s...","PeriodicalId":501497,"journal":{"name":"The American Mathematical Monthly","volume":"19 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-12-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139018269","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 : 2023-12-18DOI: 10.1080/00029890.2023.2285200
Albin Fredriksson
A polyhedron is Rupert if it is possible to cut a hole in it and thread an identical polyhedron through the hole. It is known that all 5 Platonic solids, 10 of the 13 Archimedean solids, 9 of the 1...
{"title":"Optimizing for the Rupert Property","authors":"Albin Fredriksson","doi":"10.1080/00029890.2023.2285200","DOIUrl":"https://doi.org/10.1080/00029890.2023.2285200","url":null,"abstract":"A polyhedron is Rupert if it is possible to cut a hole in it and thread an identical polyhedron through the hole. It is known that all 5 Platonic solids, 10 of the 13 Archimedean solids, 9 of the 1...","PeriodicalId":501497,"journal":{"name":"The American Mathematical Monthly","volume":"3 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-12-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138715712","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 : 2023-12-18DOI: 10.1080/00029890.2023.2284607
Reza Farhadian, Vadim Ponomarenko
Published in The American Mathematical Monthly (Ahead of Print, 2023)
发表于《美国数学月刊》（2023 年提前出版）
{"title":"A Statistical Proof of Chebyshev’s Sum Inequality","authors":"Reza Farhadian, Vadim Ponomarenko","doi":"10.1080/00029890.2023.2284607","DOIUrl":"https://doi.org/10.1080/00029890.2023.2284607","url":null,"abstract":"Published in The American Mathematical Monthly (Ahead of Print, 2023)","PeriodicalId":501497,"journal":{"name":"The American Mathematical Monthly","volume":"65 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-12-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139018080","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 : 2023-12-15DOI: 10.1080/00029890.2023.2284634
John G. Ratcliffe, S. Tschantz
{"title":"On a Geometry Problem in Plato’s\u0000 Meno","authors":"John G. Ratcliffe, S. Tschantz","doi":"10.1080/00029890.2023.2284634","DOIUrl":"https://doi.org/10.1080/00029890.2023.2284634","url":null,"abstract":"","PeriodicalId":501497,"journal":{"name":"The American Mathematical Monthly","volume":"94 6","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-12-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139000409","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 : 2023-12-15DOI: 10.1080/00029890.2023.2286221
Christoph Börgers, Bruce Boghosian, Natasa Dragovic, Anna Haensch
Political candidates often shift their positions opportunistically in hopes of capturing more votes. When there are only two candidates, the best strategy for each of them is often to move toward t...
{"title":"A Blue Sky Bifurcation in the Dynamics of Political Candidates","authors":"Christoph Börgers, Bruce Boghosian, Natasa Dragovic, Anna Haensch","doi":"10.1080/00029890.2023.2286221","DOIUrl":"https://doi.org/10.1080/00029890.2023.2286221","url":null,"abstract":"Political candidates often shift their positions opportunistically in hopes of capturing more votes. When there are only two candidates, the best strategy for each of them is often to move toward t...","PeriodicalId":501497,"journal":{"name":"The American Mathematical Monthly","volume":"19 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-12-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139968795","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 : 2023-12-15DOI: 10.1080/00029890.2023.2286224
Anton Petrunin, Stephan Stadler
We survey known proofs of the Fáry–Milnor theorem; it states that any nontrivial knot makes at least two full turns.
我们研究了法里-米尔诺定理的已知证明；该定理指出，任何非难结都至少有两个完整的转折。
{"title":"Six Proofs of the Fáry–Milnor Theorem","authors":"Anton Petrunin, Stephan Stadler","doi":"10.1080/00029890.2023.2286224","DOIUrl":"https://doi.org/10.1080/00029890.2023.2286224","url":null,"abstract":"We survey known proofs of the Fáry–Milnor theorem; it states that any nontrivial knot makes at least two full turns.","PeriodicalId":501497,"journal":{"name":"The American Mathematical Monthly","volume":"52 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-12-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138715918","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 : 2023-12-14DOI: 10.1080/00029890.2023.2284609
Edited by Vadim Ponomarenko
Published in The American Mathematical Monthly (Ahead of Print, 2023)
发表于《美国数学月刊》（2023 年提前出版）
{"title":"100 Years Ago This Month in The American Mathematical Monthly","authors":"Edited by Vadim Ponomarenko","doi":"10.1080/00029890.2023.2284609","DOIUrl":"https://doi.org/10.1080/00029890.2023.2284609","url":null,"abstract":"Published in The American Mathematical Monthly (Ahead of Print, 2023)","PeriodicalId":501497,"journal":{"name":"The American Mathematical Monthly","volume":"17 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-12-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138691236","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 : 2023-12-01DOI: 10.1080/00029890.2023.2274239
Daniel Johnston, P. Mark Kayll, Cory Palmer
We introduce, and partially resolve, a conjecture that brings a three-centuries-old derangements phenomenon and its much younger two-decades-old analogue under the same umbrella. Our tools blend co...
{"title":"Deranged Matchings: Proofs and Conjectures","authors":"Daniel Johnston, P. Mark Kayll, Cory Palmer","doi":"10.1080/00029890.2023.2274239","DOIUrl":"https://doi.org/10.1080/00029890.2023.2274239","url":null,"abstract":"We introduce, and partially resolve, a conjecture that brings a three-centuries-old derangements phenomenon and its much younger two-decades-old analogue under the same umbrella. Our tools blend co...","PeriodicalId":501497,"journal":{"name":"The American Mathematical Monthly","volume":"17 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138535449","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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