Pub Date : 2024-05-20DOI: 10.1080/00029890.2024.2351727
Edited by Daniel H. Ullman, Daniel J. Velleman, Stan Wagon, Douglas B. West
Published in The American Mathematical Monthly (Ahead of Print, 2024)
发表于《美国数学月刊》（2024 年提前出版）
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Pub Date : 2024-05-13DOI: 10.1080/00029890.2024.2346070
Mathias Sonnleitner
Combination locks are widely used to secure bicycles. We consider a combination lock consisting of adjacent rotating dials with the first nonnegative integers printed on each of them. Assuming that...
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Pub Date : 2024-05-08DOI: 10.1080/00029890.2024.2345573
Edited by Vadim Ponomarenko
Published in The American Mathematical Monthly (Ahead of Print, 2024)
发表于《美国数学月刊》（2024 年提前出版）
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Pub Date : 2024-05-07DOI: 10.1080/00029890.2024.2344409
Mathew Kushelman, Peter McGrath
A theorem of Liouville asserts that the simplest angle-preserving transformations on Euclidean space—translations, dilations, reflections, and inversions—generate all angle-preserving transformatio...
{"title":"On Liouville’s Theorem for Conformal Maps","authors":"Mathew Kushelman, Peter McGrath","doi":"10.1080/00029890.2024.2344409","DOIUrl":"https://doi.org/10.1080/00029890.2024.2344409","url":null,"abstract":"A theorem of Liouville asserts that the simplest angle-preserving transformations on Euclidean space—translations, dilations, reflections, and inversions—generate all angle-preserving transformatio...","PeriodicalId":501497,"journal":{"name":"The American Mathematical Monthly","volume":"56 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-05-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140888438","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 : 2024-05-07DOI: 10.1080/00029890.2024.2344421
Ishan Banerjee, Amites Sarkar
In 1972, John Brillhart described an algorithm for expressing a prime p≡1 (mod4) as the sum of two squares. Brillhart’s algorithm, which is based on the Euclidean algorithm, is simplicity itself. H...
{"title":"Sums of Two Squares Visualized","authors":"Ishan Banerjee, Amites Sarkar","doi":"10.1080/00029890.2024.2344421","DOIUrl":"https://doi.org/10.1080/00029890.2024.2344421","url":null,"abstract":"In 1972, John Brillhart described an algorithm for expressing a prime p≡1 (mod4) as the sum of two squares. Brillhart’s algorithm, which is based on the Euclidean algorithm, is simplicity itself. H...","PeriodicalId":501497,"journal":{"name":"The American Mathematical Monthly","volume":"26 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-05-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141151406","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 : 2024-05-07DOI: 10.1080/00029890.2024.2347163
Shamil Asgarli, Michael Hartglass, Daniel Ostrov, Byron Walden
Two possibly unfair n-sided dice, both labeled 1,2,…,n, are rolled, and the sum is recorded. How should the dice’s sides be weighted so that the resulting sum is closest to the uniform distribution...
掷两颗可能不公平的 n 面骰子（均标有 1、2、...、n），并记录总和。骰子的边数应该如何加权，才能使所得的和最接近均匀分布？
{"title":"A Fair Shake: How Close Can The Sum Of n-Sided Dice Be To A Uniform Distribution?","authors":"Shamil Asgarli, Michael Hartglass, Daniel Ostrov, Byron Walden","doi":"10.1080/00029890.2024.2347163","DOIUrl":"https://doi.org/10.1080/00029890.2024.2347163","url":null,"abstract":"Two possibly unfair n-sided dice, both labeled 1,2,…,n, are rolled, and the sum is recorded. How should the dice’s sides be weighted so that the resulting sum is closest to the uniform distribution...","PeriodicalId":501497,"journal":{"name":"The American Mathematical Monthly","volume":"26 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-05-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141151409","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 : 2024-05-03DOI: 10.1080/00029890.2024.2344412
I. Pinelis
{"title":"An Exact Bound for the Inner Product of Vectors in ℂ\u0000 n","authors":"I. Pinelis","doi":"10.1080/00029890.2024.2344412","DOIUrl":"https://doi.org/10.1080/00029890.2024.2344412","url":null,"abstract":"","PeriodicalId":501497,"journal":{"name":"The American Mathematical Monthly","volume":"89 8","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-05-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141016262","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 : 2024-05-03DOI: 10.1080/00029890.2024.2344411
L. Bougoffa
{"title":"A Generalization of Wayment’s Mean Value Theorem for Integrals","authors":"L. Bougoffa","doi":"10.1080/00029890.2024.2344411","DOIUrl":"https://doi.org/10.1080/00029890.2024.2344411","url":null,"abstract":"","PeriodicalId":501497,"journal":{"name":"The American Mathematical Monthly","volume":"46 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-05-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141015820","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 : 2024-04-02DOI: 10.1080/00029890.2024.2323902
Elias Dubno
Even though Zaremba’s conjecture remains open, Bourgain and Kontorovich solved the problem for a full density subset. Nevertheless, there are only a handful of explicit sequences known to satisfy t...
{"title":"Zaremba’s Conjecture for Geometric Sequences: An Algorithm","authors":"Elias Dubno","doi":"10.1080/00029890.2024.2323902","DOIUrl":"https://doi.org/10.1080/00029890.2024.2323902","url":null,"abstract":"Even though Zaremba’s conjecture remains open, Bourgain and Kontorovich solved the problem for a full density subset. Nevertheless, there are only a handful of explicit sequences known to satisfy t...","PeriodicalId":501497,"journal":{"name":"The American Mathematical Monthly","volume":"21 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-04-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141151402","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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