Pub Date : 2023-01-01DOI: 10.5642/jhummath.gezg5395
Cristina Carr, Daniel Chioffi, Maya Glenn, Stefan Nita, V. Nita, Bogdan G. Nita
We analyze and model the neck of the classical harp based on the length of the strings, their tension and density. We then use the results to design new and innovative harp shapes by adjusting the parameters of the model
{"title":"The Mathematics of the Harp: Modeling the Classical Instrument and Designing Futuristic Ones","authors":"Cristina Carr, Daniel Chioffi, Maya Glenn, Stefan Nita, V. Nita, Bogdan G. Nita","doi":"10.5642/jhummath.gezg5395","DOIUrl":"https://doi.org/10.5642/jhummath.gezg5395","url":null,"abstract":"We analyze and model the neck of the classical harp based on the length of the strings, their tension and density. We then use the results to design new and innovative harp shapes by adjusting the parameters of the model","PeriodicalId":42411,"journal":{"name":"Journal of Humanistic Mathematics","volume":" ","pages":""},"PeriodicalIF":0.3,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48144016","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 : 2023-01-01DOI: 10.5642/jhummath.cdrw3514
G. Gentili, Luisa Simonutti, D. Struppa
In this article, we describe the invention of double-entry bookkeeping (or partita doppia as it was called in Italian) as a fertile intersection between mathematics and early commerce. We focus our attention on this seemingly simple technique that requires only minimal mathematical expertise, but whose discovery is clearly the result of a mathematical way of thinking, in order to make a conceptual point about the role of mathematics as the humus from which disciplines as different as operations research, computer science, and data science have evolved
{"title":"The Merchant and the Mathematician: Commerce and Accounting","authors":"G. Gentili, Luisa Simonutti, D. Struppa","doi":"10.5642/jhummath.cdrw3514","DOIUrl":"https://doi.org/10.5642/jhummath.cdrw3514","url":null,"abstract":"In this article, we describe the invention of double-entry bookkeeping (or partita doppia as it was called in Italian) as a fertile intersection between mathematics and early commerce. We focus our attention on this seemingly simple technique that requires only minimal mathematical expertise, but whose discovery is clearly the result of a mathematical way of thinking, in order to make a conceptual point about the role of mathematics as the humus from which disciplines as different as operations research, computer science, and data science have evolved","PeriodicalId":42411,"journal":{"name":"Journal of Humanistic Mathematics","volume":" ","pages":""},"PeriodicalIF":0.3,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42326908","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 : 2023-01-01DOI: 10.5642/jhummath.lmmv7107
O. Marrero
Synopsis We present the story of a theorem’s conception and birth. The tale begins with the circumstances in which the idea sprouted; then is the question’s origin; next comes the preliminary investigation, which led to the conjecture and the proof; finally, we state the theorem. Our discussion is accessible to anyone who knows mathematical induction. Therefore, this material can be used for instruction in a variety of courses. In particular, this story may be used in undergraduate courses as an example of how mathematicians do research. As a bonus, the proof by induction is not of the simplest kind, because it includes some preliminary work that facilitates the proof; therefore, the theorem can also serve as a nice exercise in induction. Additionally, we use well-known facts from calculus to clarify and enhance what is intrinsically a discrete problem. Making an unexpected but welcome explanatory appearance, the number e is pertinent.
{"title":"The Genesis of a Theorem","authors":"O. Marrero","doi":"10.5642/jhummath.lmmv7107","DOIUrl":"https://doi.org/10.5642/jhummath.lmmv7107","url":null,"abstract":"Synopsis We present the story of a theorem’s conception and birth. The tale begins with the circumstances in which the idea sprouted; then is the question’s origin; next comes the preliminary investigation, which led to the conjecture and the proof; finally, we state the theorem. Our discussion is accessible to anyone who knows mathematical induction. Therefore, this material can be used for instruction in a variety of courses. In particular, this story may be used in undergraduate courses as an example of how mathematicians do research. As a bonus, the proof by induction is not of the simplest kind, because it includes some preliminary work that facilitates the proof; therefore, the theorem can also serve as a nice exercise in induction. Additionally, we use well-known facts from calculus to clarify and enhance what is intrinsically a discrete problem. Making an unexpected but welcome explanatory appearance, the number e is pertinent.","PeriodicalId":42411,"journal":{"name":"Journal of Humanistic Mathematics","volume":" ","pages":""},"PeriodicalIF":0.3,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46836193","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 : 2023-01-01DOI: 10.5642/jhummath.lmpq5945
Valentin A. B. Küchle, Shiv Karunakaran, Mariana Levin, John J. Smith III, Sarah D. Castle, Jihye Hwang, Yaomingxin Lu, R. Elmore
Humanistic geographers distinguish between space and place: "What begins as undifferentiated space becomes place as we get to know it better and endow it with value" [19, page 6]. In this essay, we seek to demonstrate how mathematics education researchers and mathematics instructors may find space and place il-luminating for understanding important aspects of students' learning experiences during the coronavirus pandemic - and possibly beyond. Specifically, after in-tro ducing the terms and relating them to the context of a university mathematics class, we exemplify how home and class places collided for three undergraduate mathematics students forced to deal with the abrupt transition to online educa-tion. We conclude by discussing implications of attending to space and place for designers and researchers of (pandemic) online instruction and make connections to how the pandemic and attending to space and place can serve as a catalyst for reshaping undergraduate mathematics education.
{"title":"Collapsing Spaces, Colliding Places: Leveraging Constructs from Humanistic Geography to Explore Mathematics Classes","authors":"Valentin A. B. Küchle, Shiv Karunakaran, Mariana Levin, John J. Smith III, Sarah D. Castle, Jihye Hwang, Yaomingxin Lu, R. Elmore","doi":"10.5642/jhummath.lmpq5945","DOIUrl":"https://doi.org/10.5642/jhummath.lmpq5945","url":null,"abstract":"Humanistic geographers distinguish between space and place: \"What begins as undifferentiated space becomes place as we get to know it better and endow it with value\" [19, page 6]. In this essay, we seek to demonstrate how mathematics education researchers and mathematics instructors may find space and place il-luminating for understanding important aspects of students' learning experiences during the coronavirus pandemic - and possibly beyond. Specifically, after in-tro ducing the terms and relating them to the context of a university mathematics class, we exemplify how home and class places collided for three undergraduate mathematics students forced to deal with the abrupt transition to online educa-tion. We conclude by discussing implications of attending to space and place for designers and researchers of (pandemic) online instruction and make connections to how the pandemic and attending to space and place can serve as a catalyst for reshaping undergraduate mathematics education.","PeriodicalId":42411,"journal":{"name":"Journal of Humanistic Mathematics","volume":"1 1","pages":""},"PeriodicalIF":0.3,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70801391","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 : 2023-01-01DOI: 10.5642/jhummath.podj4118
Szilárd Svitek
Synopsis Zero has (a) special role(s) in mathematics. In the current century, we take negative numbers and zero for granted, but we should also be aware that their acceptance and their emergence in mathematics, and their ubiquity today, have not come to happen as rapidly as, for example, for natural numbers. Students can quickly become confused by the question: is zero a natural number? The answer is simple: a matter of definition. The history of zero and that of negative numbers are closely linked. It was in the calculations of debts that the negative numbers first appeared, where the state of balance between positive and negative assets was also given. We now take them for granted, but the history of science shows that it was far from a smooth process, and interesting mistakes about zero still occur in education today. I present a few examples below, and how they have been resolved.
{"title":"The Nothing That Really Matters","authors":"Szilárd Svitek","doi":"10.5642/jhummath.podj4118","DOIUrl":"https://doi.org/10.5642/jhummath.podj4118","url":null,"abstract":"Synopsis Zero has (a) special role(s) in mathematics. In the current century, we take negative numbers and zero for granted, but we should also be aware that their acceptance and their emergence in mathematics, and their ubiquity today, have not come to happen as rapidly as, for example, for natural numbers. Students can quickly become confused by the question: is zero a natural number? The answer is simple: a matter of definition. The history of zero and that of negative numbers are closely linked. It was in the calculations of debts that the negative numbers first appeared, where the state of balance between positive and negative assets was also given. We now take them for granted, but the history of science shows that it was far from a smooth process, and interesting mistakes about zero still occur in education today. I present a few examples below, and how they have been resolved.","PeriodicalId":42411,"journal":{"name":"Journal of Humanistic Mathematics","volume":"116 1","pages":""},"PeriodicalIF":0.3,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70801394","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 : 2023-01-01DOI: 10.5642/jhummath.bffk4651
J. Grabiner
{"title":"Book Review: Algebra the Beautiful: An Ode to Math’s Least-Loved Subject by G. Arnell Williams","authors":"J. Grabiner","doi":"10.5642/jhummath.bffk4651","DOIUrl":"https://doi.org/10.5642/jhummath.bffk4651","url":null,"abstract":"","PeriodicalId":42411,"journal":{"name":"Journal of Humanistic Mathematics","volume":" ","pages":""},"PeriodicalIF":0.3,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47903884","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 : 2023-01-01DOI: 10.5642/jhummath.bgui1643
Vijay Fafat
{"title":"The Babelogic of Mathematics","authors":"Vijay Fafat","doi":"10.5642/jhummath.bgui1643","DOIUrl":"https://doi.org/10.5642/jhummath.bgui1643","url":null,"abstract":"","PeriodicalId":42411,"journal":{"name":"Journal of Humanistic Mathematics","volume":" ","pages":""},"PeriodicalIF":0.3,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49152334","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 : 2023-01-01DOI: 10.5642/jhummath.xjfo9325
M. Huber, Gizem Karaali
{"title":"Where Does Mathematics Come From? Really, Where?","authors":"M. Huber, Gizem Karaali","doi":"10.5642/jhummath.xjfo9325","DOIUrl":"https://doi.org/10.5642/jhummath.xjfo9325","url":null,"abstract":"","PeriodicalId":42411,"journal":{"name":"Journal of Humanistic Mathematics","volume":" ","pages":""},"PeriodicalIF":0.3,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46312549","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 : 2022-07-01DOI: 10.5642/jhummath.sqek5024
Peter Appelbaum, C. Stathopoulou, Constantinos Xenofontos
Synopsis We argue that scholars and practitioners of mathematics education need to find new directions through recognition of its dystopic characteristics, and embrace these characteristics as both the source of challenges and method of response. This contrasts with the generally utopic approach of most scholarship in the field. We offer critical ethnomathematics education as a model, since it has its own origins in lingering dystopic legacies. A perpetual hopelessness and disempower-ment is one implicit curriculum of contemporary mathematics education, where the mathematics one learns might help to describe things, yet hardly assists in transforming the reification of power and agency in society. Embracing dystopia rather than trying to circumvent it generates new questions and pathways.
{"title":"Mathematics Education as Dystopia: A Future Beyond","authors":"Peter Appelbaum, C. Stathopoulou, Constantinos Xenofontos","doi":"10.5642/jhummath.sqek5024","DOIUrl":"https://doi.org/10.5642/jhummath.sqek5024","url":null,"abstract":"Synopsis We argue that scholars and practitioners of mathematics education need to find new directions through recognition of its dystopic characteristics, and embrace these characteristics as both the source of challenges and method of response. This contrasts with the generally utopic approach of most scholarship in the field. We offer critical ethnomathematics education as a model, since it has its own origins in lingering dystopic legacies. A perpetual hopelessness and disempower-ment is one implicit curriculum of contemporary mathematics education, where the mathematics one learns might help to describe things, yet hardly assists in transforming the reification of power and agency in society. Embracing dystopia rather than trying to circumvent it generates new questions and pathways.","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":"48384118","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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