Pub Date : 2022-07-01DOI: 10.5642/jhummath.cpqt6604
D. Neel
Synopsis A historical meditation on non-Euclidean geometry, three Jesuits, a radical egalitarian mathematical philosopher, and the atom bomb, structured by word-count with attention to divisors of 441 and the Fano plane.
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Pub Date : 2022-07-01DOI: 10.5642/jhummath.hetv3416
Evandro il Cinico
{"title":"Ode to delta","authors":"Evandro il Cinico","doi":"10.5642/jhummath.hetv3416","DOIUrl":"https://doi.org/10.5642/jhummath.hetv3416","url":null,"abstract":"","PeriodicalId":42411,"journal":{"name":"Journal of Humanistic Mathematics","volume":" ","pages":""},"PeriodicalIF":0.3,"publicationDate":"2022-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48245535","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 : 2022-01-01DOI: 10.5642/jhummath.202201.23
G. Krause
In this piece I propose a perspective shift, from a simplified view of mathematics story problems to a more academically rigorous perspective that integrates mathematical proficiency and language practices crucial for educating bilingual students. The data presented in this article provide a window into what preparing bilingual pre-service teachers to teach mathematics might involve. I discuss issues that arise in the context of preparing Spanish-English bilingual pre-service teachers in a way that can inform their practice in linguistically and culturally diverse classrooms.
{"title":"The Problem of Words: Learning to Teach Mathematics When Numbers and Languages Mix","authors":"G. Krause","doi":"10.5642/jhummath.202201.23","DOIUrl":"https://doi.org/10.5642/jhummath.202201.23","url":null,"abstract":"In this piece I propose a perspective shift, from a simplified view of mathematics story problems to a more academically rigorous perspective that integrates mathematical proficiency and language practices crucial for educating bilingual students. The data presented in this article provide a window into what preparing bilingual pre-service teachers to teach mathematics might involve. I discuss issues that arise in the context of preparing Spanish-English bilingual pre-service teachers in a way that can inform their practice in linguistically and culturally diverse classrooms.","PeriodicalId":42411,"journal":{"name":"Journal of Humanistic Mathematics","volume":" ","pages":""},"PeriodicalIF":0.3,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42702179","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 : 2022-01-01DOI: 10.5642/jhummath.202201.16
R. Haas
Early in the COVID-19 pandemic, when spring began to make itself felt, photos showed New Yorkers enjoying the outdoors, while properly socially distanced, by sitting on the grass in a square lattice of circles. But the planners should have consulted a mathematician for the design, because significantly more people (over 15% more) could enjoy the same area safely if the circles were closer packed into a hexagonal lattice.
{"title":"On the Mathematics of Social Distancing","authors":"R. Haas","doi":"10.5642/jhummath.202201.16","DOIUrl":"https://doi.org/10.5642/jhummath.202201.16","url":null,"abstract":"Early in the COVID-19 pandemic, when spring began to make itself felt, photos showed New Yorkers enjoying the outdoors, while properly socially distanced, by sitting on the grass in a square lattice of circles. But the planners should have consulted a mathematician for the design, because significantly more people (over 15% more) could enjoy the same area safely if the circles were closer packed into a hexagonal lattice.","PeriodicalId":42411,"journal":{"name":"Journal of Humanistic Mathematics","volume":" ","pages":""},"PeriodicalIF":0.3,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47998203","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 : 2022-01-01DOI: 10.5642/jhummath.202201.26
Firdous Ahmad Mala
{"title":"Alice’s Adventures in Wonderland: Carroll’s Symbolic Attack on Mathematical Symbolism","authors":"Firdous Ahmad Mala","doi":"10.5642/jhummath.202201.26","DOIUrl":"https://doi.org/10.5642/jhummath.202201.26","url":null,"abstract":"","PeriodicalId":42411,"journal":{"name":"Journal of Humanistic Mathematics","volume":" ","pages":""},"PeriodicalIF":0.3,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42324629","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 : 2022-01-01DOI: 10.5642/jhummath.202201.18
Carlos Alfaro
Synopsis We report on the top ten mathematicians with the highest number of articles, citations, and students, based on data from MathSciNet and the Mathematics Genealogy Project.
我们根据MathSciNet和数学谱系项目的数据，报道文章、引用和学生数量最多的前十位数学家。
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Pub Date : 2022-01-01DOI: 10.5642/jhummath.202201.30
Kyle Singh, Veselin Jungić, Jun Mei
Synopsis This interview, conducted in November 2020, explores the fascinating life and work of Ramsey theorist Thomas Craig Brown. We hope, through our conversation with Dr. Brown, to show that mathematics is not a discipline that is only concerned with numbers, but that it is, in a fundamental way, also about people and connections. In November 2020, we, the authors, had the chance to interview Ramsey the-orist Professor Thomas Craig Brown. In the following, we present this fascinating conversation. We discover that Dr. Brown’s dedication to mathematics and learning has always been at the heart of his work.
{"title":"Life of a Working Ramsey Theorist: Conversation With Thomas C. Brown","authors":"Kyle Singh, Veselin Jungić, Jun Mei","doi":"10.5642/jhummath.202201.30","DOIUrl":"https://doi.org/10.5642/jhummath.202201.30","url":null,"abstract":"Synopsis This interview, conducted in November 2020, explores the fascinating life and work of Ramsey theorist Thomas Craig Brown. We hope, through our conversation with Dr. Brown, to show that mathematics is not a discipline that is only concerned with numbers, but that it is, in a fundamental way, also about people and connections. In November 2020, we, the authors, had the chance to interview Ramsey the-orist Professor Thomas Craig Brown. In the following, we present this fascinating conversation. We discover that Dr. Brown’s dedication to mathematics and learning has always been at the heart of his work.","PeriodicalId":42411,"journal":{"name":"Journal of Humanistic Mathematics","volume":" ","pages":""},"PeriodicalIF":0.3,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45678517","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 : 2022-01-01DOI: 10.5642/jhummath.202201.05
Amber Simpson,Signe Kastberg
In this paper, we argue that making activities within non-formal learning environments (e.g., museums, libraries) provide opportunities to engage youth in what we define as mathematical practices for making, everyday mathematical practices within the context of making activities. The mathematical practices identified from two non-formal school-based contexts highlighted three mathematical practices for making: informal measurement, spatial reasoning, and curiosity. These practices are identified in prior scholarship as being beneficial and foundational for the understanding of mathematical concepts. As educators and researchers turn to non-formal and informal contexts, with an eye toward understanding ways youth engage in the activity of making, descriptions of mathematical practices for making build upon prior everyday mathematical practices and open up a new landscape of inquiry.
{"title":"Makers Do Math! Legitimizing Informal Mathematical Practices Within Making Contexts","authors":"Amber Simpson,Signe Kastberg","doi":"10.5642/jhummath.202201.05","DOIUrl":"https://doi.org/10.5642/jhummath.202201.05","url":null,"abstract":"In this paper, we argue that making activities within non-formal learning environments (e.g., museums, libraries) provide opportunities to engage youth in what we define as mathematical practices for making, everyday mathematical practices within the context of making activities. The mathematical practices identified from two non-formal school-based contexts highlighted three mathematical practices for making: informal measurement, spatial reasoning, and curiosity. These practices are identified in prior scholarship as being beneficial and foundational for the understanding of mathematical concepts. As educators and researchers turn to non-formal and informal contexts, with an eye toward understanding ways youth engage in the activity of making, descriptions of mathematical practices for making build upon prior everyday mathematical practices and open up a new landscape of inquiry.","PeriodicalId":42411,"journal":{"name":"Journal of Humanistic Mathematics","volume":"21 1","pages":"40-75"},"PeriodicalIF":0.3,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138494834","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 : 2022-01-01DOI: 10.5642/jhummath.202201.10
Eric Grinberg
Reopening a cold case, inspector Echelon, high-ranking in the Row Operations Center, is searching for a lost linear map, known to be nilpotent. When a partially decomposed matrix is unearthed, he reconstructs its reduced form, finding it singular. But were its roots nilpotent? 1. Early In the Investigation In teaching Linear Algebra, the first topic often is row reduction [1, 7], including Row Reduced Echelon Form (RREF); its applicability is broad and growing. Another topic, surprisingly popular with beginning students, is nilpotent matrices. One naturally wonders about their intersection. For instance, one would expect to find a book exercise asking: What can be said about the RREF of a nilpotent matrix? In the early days of the Covid-19 pandemic, as test delivery went remote, demand grew for new, Internet-resistant problems. A limited literature search for the Nilpotent-RREF connection came up short, suggesting potential for take-home final exam questions, hence the note at hand. We’ll first explore examples sufficient to settle the 3×3 case, then consider the general situation. The upshot is the row reduction eliminates all traces of nilpotence. 2. Stumbling On Evidence We refer to [1, 2] for general background on RREF and rank. Recall that a square matrix M is nilpotent if some power of M , say M, is the zero matrix; the smallest such k is called the niloptent index or just index of M . For instance, the rightmost matrix in (2) below is nilpotent, of index 3. Indeed, every strictly upper-triangular matrix (square, with zeros on
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