Mathematics Magazine最新文献

{"title":"Schedules and Waitlists and Integer Programs, Oh My!","authors":"J. K. Denny","doi":"10.1080/0025570x.2023.2284419","DOIUrl":"https://doi.org/10.1080/0025570x.2023.2284419","url":null,"abstract":"","PeriodicalId":18344,"journal":{"name":"Mathematics Magazine","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-12-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138586927","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":"Maximum Overhang of Sticky Stacks","authors":"Zsolt Lengvárszky, Debbie Shepherd","doi":"10.1080/0025570x.2023.2266324","DOIUrl":"https://doi.org/10.1080/0025570x.2023.2266324","url":null,"abstract":"SummaryWe consider a variation of the “overhang” problem where blocks stick together.MSC: 70C20 AcknowledgmentsZsolt Lengvárszky is the recipient of the Miriam Sklar endowed professorship. This research was supported in part by the Louisiana Board of Regents Endowed Professor/Chair Program.Additional informationNotes on contributorsZsolt LengvárszkyZSOLT LENGVÁRSZKY (MR Author ID: 112490) received his degrees from the University of Szeged, Hungary, and the University of South Carolina. He joined the faculty of the Louisiana State University, Shreveport in 2008. His mathematical interests include lattice theory and the mathematics of paper folding.Debbie ShepherdDeborah K. Shepherd received her Ph. D. in Computational Analysis and Modeling from Louisiana Tech University in 2001. Her MS in Mathematics is from Southern Illinois University, Edwardsville. She is currently an associate professor at Louisiana State University, Shreveport. Her primary research interests are in statistical quality control.","PeriodicalId":18344,"journal":{"name":"Mathematics Magazine","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-11-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135136344","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 Visual Proof of Lehmer’s Arctangent Sum","authors":"Rex H. Wu","doi":"10.1080/0025570x.2023.2266313","DOIUrl":"https://doi.org/10.1080/0025570x.2023.2266313","url":null,"abstract":"SummaryWe provide a visual proof to Lehmer’s infinite sum of the arctangents of the inverse of the odd-indexed Fibonacci numbers. A few corollaries follow from the diagram, including Euler’s Machin-like formula and Strassnitzky’s formula.MSC: 11B39 Additional informationNotes on contributorsRex H. WuREX H. WU (MR Author ID: 1293646, ORCID 0000-0003-0970-3741) would like to thank the anonymous reviewer and the Editor for their many generous suggestions. Rex has been working with Garfield’s trapezoid for many years. He recently found more applications of it on the Fibonacci numbers. This article is one of them. Talking about Garfield’s trapezoid, which is named after president James A. Garfield for his proof on the Pythagorean theorem, Rex unexpectedly met his great-great-grandson Mr. Peter Garfield recently.","PeriodicalId":18344,"journal":{"name":"Mathematics Magazine","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-11-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135091891","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":"The Invisible Solutions of the Rubik’s Cube","authors":"Allen Charest, Ben Coté, Ward Heilman","doi":"10.1080/0025570x.2023.2266345","DOIUrl":"https://doi.org/10.1080/0025570x.2023.2266345","url":null,"abstract":"SummaryThe center cubies on the Rubik’s Cube can change orientation when the puzzle is brought from one solved state to another. The set of all possible reorientations of the center cubies creates what we call the invisible solutions group. We investigate the size and structure of the invisible solutions group for the Rubik’s Cube, Rubik’s Revenge, and the Professor’s Cube.MSC: 20-01 AcknowledgmentsThe authors would like to thank the Adrian Tinsley Program for Undergraduate Research and Creative Scholarship for funding and the anonymous referees for the helpful comments.Notes1 Online version of the article contains color diagrams.Additional informationNotes on contributorsAllen CharestALLEN CHAREST received a Bachelors in Mathematics and Secondary Education from Bridgewater State University in 2019. He currently works as STEAM Math Teacher at Greater Lawrence Technical School and is fascinated by group theory and nature.Ben CotéBEN COTÉ (MR Author ID: 951394, ORCID 0000-0003-2844-1935) received a Ph.D. in Mathematics from the University of California, Santa Barbara in 2016. He currently teaches at Western Oregon University. When not investigating recreational mathematics, he enjoys camping and gardening with his wife Brittany and sons Levi and Oliver.Ward HeilmanWARD HEILMAN received a Ph.D. in Mathematics from Northeastern University. He has been at Bridgewater State University (Mass.) since 1996. He is active in social justice, and fascinated by axioms, cryptology, basketball, Huxley, Kerouac and most recently Thomas Paine.","PeriodicalId":18344,"journal":{"name":"Mathematics Magazine","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-11-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135192196","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":"Generalized Sine Functions, Complexified","authors":"Pisheng Ding, Sunil K. Chebolu","doi":"10.1080/0025570x.2023.2266329","DOIUrl":"https://doi.org/10.1080/0025570x.2023.2266329","url":null,"abstract":"SummaryGeneralized sine functions, primarily viewed as real-valued functions, are studied herein as complex analytic functions. Their natural domains of analyticity are identified and their mapping properties are detailed. Some implications of this theory for calculus and geometry are explored.MSC:: 30-02 Notes* For z near 1, factor (1−z4)3/4 into g(z)(z−1)3/4 where g is continuous and nonzero at 1. Thus, it suffices to track the phase change of (z−1)3/4 as z traverses an arc in V¯4 from 1−ϵ to 1+ϵ.* The Schwarz reflection principle also guarantees that the extended function is analytic on [O,B4).* At the other half of the vertices, i.e., the translates of the ω3kA3’s, the extended sin 3 is bounded and hence analytic by Riemann’s principle of removable singularity.Additional informationNotes on contributorsPisheng DingPISHENG DING (MR Author ID: 784635) studied physics and mathematics as an undergraduate at the legendary City College of New York, where Joseph Bak kindled in him a keen interest in complex analysis. He earned his doctorate in 2003 from the Courant Institute under the direction of Sylvain Cappell. So that his family could be under one roof, he joined Illinois State University in 2010 as an adjunct and has since remained in this position. While deploring the state of mathematics education in the United States, he currently enjoys teaching his 6th-grade daughter Elaine authentic Euclidean geometry.Sunil K. CheboluSUNIL CHEBOLU (MR Author ID: 781874) received his Ph.D. in mathematics from the University of Washington in 2005. After completing a three-year postdoctoral fellowship at the University of Western Ontario in Canada, he joined the faculty at Illinois State University in 2008. Although his primary research interests lie in algebra and number theory, he embraces all areas of mathematics. During his spare time, he enjoys playing his guitar or observing deep-sky objects through his telescope.","PeriodicalId":18344,"journal":{"name":"Mathematics Magazine","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-11-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135192482","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":"Buffon’s Leaf Problem","authors":"Ruka Iguchi, Hideaki Kida, Keisuke Matsuda, Miki Ono, Miu Shibata, Haruka Takano","doi":"10.1080/0025570x.2023.2266352","DOIUrl":"https://doi.org/10.1080/0025570x.2023.2266352","url":null,"abstract":"SummaryAccording to Buffon’s needle problem, you can approximate the value of π by throwing needles onto arrays of parallel lines and counting the number of needles crossing the lines. However, it is time-consuming to do the experiment in reality (in 1901, Lazzarini threw 3408 needles to approximate the value of π). In this paper, we tried to approximate the value of π from easily-accesible images of fallen leaves. We extended Buffon’s needle problem in two ways: instead of a simple needle we considered a complex shape, and instead of a uniform size we considered various sizes. After we confirmed the extension by a computer simulation, we approximated the value of π from the images we took experimentally and we while walking. From the experimentally-taken images (50 leaves/image × 20 images), the value of π was approximated as 3.1569. The approximated value of π using the images we took while walking was 3.5961 (the accuracy was not good because it was calculated from one image).MSC: 60-01 Notes1 Note that the online version of this article has color diagramsAdditional informationNotes on contributorsRuka IguchiRUKA IGUCHI is a 3rd-year high school student at Hiroshima University High School. She is a runner and has often participated in a marathon.Hideaki KidaHIDEAKI KIDA is a mathematics teacher at Hiroshima University High School. After receiving a Master of Education degree from Hiroshima University, he has been a high school teacher for 22 years.Keisuke MatsudaKEISUKE MATSUDA is a graduate student at Osaka University, studying beetle horn formation using mathematical modeling. He seeks the rules underlying the natural phenomena around us and the shapes of living things.Miki OnoMIKI ONO is a 3rd-year high school student at Hiroshima University High School and a singer who has an attractive voice.Miu ShibataMIU SHIBATA is a 3rd-year high school student at Hiroshima University High School and a violinist who is good at computer programming.Haruka TakanoHARUKA TAKANO is a 3rd-year high school student at Hiroshima University High School and a contrabassist who loves grilled meat and ice cream as much as mathematics.","PeriodicalId":18344,"journal":{"name":"Mathematics Magazine","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-11-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135432693","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":"Exploring Perpendicularity and Parallelism Through Play","authors":"Pentti Haukkanen, Timo Tossavainen","doi":"10.1080/0025570x.2023.2266334","DOIUrl":"https://doi.org/10.1080/0025570x.2023.2266334","url":null,"abstract":"SummaryWe introduce a set of axioms that define two relations: planar perpendicularity and parallelism. We show how these relations can be explored informally through play with secondary school students. Our aim is to demonstrate that axiomatic thinking can be made accessible and fun even for young learners.MSC: Primary 97-01Secondary 51M04 Additional informationNotes on contributorsPentti HaukkanenPentti Haukkanen (MR Author ID: 82550) received his PhD in mathematics from the University of Tampere, Finland, under the supervision of Seppo Hyyrö. Currently, he is a university lecturer of mathematics at Tampere University in Finland. In his spare time, he enjoys various sports and culture.Timo TossavainenTimo Tossavainen (MR Author ID: 664009) received his PhD in mathematics from Jyväskylä University, Finland, under the supervision of Pekka Koskela. Currently, he is a professor of mathematics education at the Lulea University of Technology in Sweden. Among his proudest accomplishments is having learnt to play the guitar solo to the smash hit “The Final Countdown” by the Swedish rock band Europe.","PeriodicalId":18344,"journal":{"name":"Mathematics Magazine","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-11-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135474603","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 Mathematical Connection Between Single-Elimination Sports Tournaments and Evolutionary Trees","authors":"Matthew C. King, Noah A. Rosenberg","doi":"10.1080/0025570x.2023.2266389","DOIUrl":"https://doi.org/10.1080/0025570x.2023.2266389","url":null,"abstract":"How many ways are there to arrange the sequence of games in a single-elimination sports tournament? We consider the connection between this enumeration problem and the enumeration of “labeled histories,” or sequences of asynchronous branching events, in mathematical phylogenetics. The possibility of playing multiple games simultaneously in different arenas suggests an extension of the enumeration of labeled histories to scenarios in which multiple branching events occur simultaneously. We provide a recursive result enumerating game sequences and labeled histories in which simultaneity is allowed. For a March Madness basketball tournament of 68 labeled teams, the number of possible sequences of games is ∼1.91×1078 if arbitrarily many arenas are available, but only ∼3.60×1068 if all games must be played sequentially in the same arena.","PeriodicalId":18344,"journal":{"name":"Mathematics Magazine","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-11-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135589104","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":"Counting Triangles with Combinatorics","authors":"Matthew Glomski, K. Peter Krog, Mason Nakamura, Elizabeth M. Reid","doi":"10.1080/0025570x.2023.2266346","DOIUrl":"https://doi.org/10.1080/0025570x.2023.2266346","url":null,"abstract":"SummaryInspired by a problem presented in a New York Times essay, we consider the number of triangles formed by a finite collection of lines in the plane, under the restrictions that no more than two lines intersect at any point and that no two are parallel. We explore the ramifications of relaxing each of these requirements, and we derive a ‘unified triangle counting formula’ for any arrangement of finitely many lines in the plane.MSC: 05B30 Additional informationNotes on contributorsMatthew GlomskiMATTHEW GLOMSKI earned his Ph.D. at the University at Buffalo and joined the mathematics faculty of Marist College. In his spare time he enjoys hiking in the nearby Catskill Mountains.K. Peter KrogK. PETER KROG earned his Ph.D. at the University of Connecticut and joined the mathematics faculty at Marist College in 1996. His mathematical interests include group theory, statistics, and combinatorics.Mason NakamuraMASON NAKAMURA is an applied mathematics student at Marist College and plans to pursue his doctorate. He enjoys golfing, hiking, and snorkeling during his time away from mathematics.Elizabeth M. ReidELIZABETH M. REID is a member of the mathematics faculty at Marist College. She earned her Ph.D. at the University at Buffalo and enjoys hiking in her spare time.","PeriodicalId":18344,"journal":{"name":"Mathematics Magazine","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-11-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135933836","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":"Two Geometric Series","authors":"Tom Edgar","doi":"10.1080/0025570x.2023.2266415","DOIUrl":"https://doi.org/10.1080/0025570x.2023.2266415","url":null,"abstract":"SummaryWe use a square inside another to provide two geometric series dissection proofs. Notes1 Note that the online version of this article has color diagramsAdditional informationNotes on contributorsTom EdgarTOM EDGAR (MR Author ID: 821633) is a professor of mathematics at Pacific Lutheran University and the editor of Math Horizons. He has recently been animating his favorite visual proofs on his YouTube channel www.youtube.com/@MathVisualProofs/.","PeriodicalId":18344,"journal":{"name":"Mathematics Magazine","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135270601","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}