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Historia Mathematica最新文献

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On the history of units in French elementary school arithmetic: The case of proportionality 论法国小学算术中单位的历史:以比例为例
IF 0.5 3区 哲学
Historia Mathematica Pub Date : 2022-05-01 DOI: 10.1016/j.hm.2021.04.003
Christine Chambris , Jana Visnovska
{"title":"On the history of units in French elementary school arithmetic: The case of proportionality","authors":"Christine Chambris ,&nbsp;Jana Visnovska","doi":"10.1016/j.hm.2021.04.003","DOIUrl":"10.1016/j.hm.2021.04.003","url":null,"abstract":"<div><p>The measurement of magnitudes was at the foundation of numbers and calculation in academic mathematics until the 19th century. It provided units and the concrete and abstract numbers that formed the basis of school arithmetic up to the mid-20th century in France. Our analysis of changes in teaching resources for proportionality (late 19th to the early 21st century) documents how the disappearance of magnitudes in academic knowledge was followed by the loss of the differentiation of the conceptual complexity of mathematical ideas related to proportionality. These changes made teaching and learning about proportionality considerably more difficult, and we later witness their gradual, but not yet systematic, reversal.</p></div>","PeriodicalId":51061,"journal":{"name":"Historia Mathematica","volume":"59 ","pages":"Pages 99-118"},"PeriodicalIF":0.5,"publicationDate":"2022-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42148964","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"哲学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 3
Measuring crops with the šukunnûm-number 用šukunnûm数测量作物
IF 0.5 3区 哲学
Historia Mathematica Pub Date : 2022-05-01 DOI: 10.1016/j.hm.2020.06.005
Baptiste Fiette
{"title":"Measuring crops with the šukunnûm-number","authors":"Baptiste Fiette","doi":"10.1016/j.hm.2020.06.005","DOIUrl":"10.1016/j.hm.2020.06.005","url":null,"abstract":"<div><p>Šamaš-hazir was the manager of the royal domain of Hammu-rabi, king of Babylon (1792-1750 BC), in southern Mesopotamia. Harvest registers and yield tables found in his archives take the form of tabular accounts in which an estimated yield rate is expressed by a number called <em>šukunnûm</em>. Although the <em>šukunnûm</em>-number is used to keep accounts of barley yield rates, it is never associated with a specific unit of measurement. In order to define the elaboration and the nature of the <em>šukunnûm</em>-number, this article will analyze its relation to surface and capacity units and its function in crop measurements.</p></div>","PeriodicalId":51061,"journal":{"name":"Historia Mathematica","volume":"59 ","pages":"Pages 71-98"},"PeriodicalIF":0.5,"publicationDate":"2022-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1016/j.hm.2020.06.005","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42438097","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"哲学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Introduction – A critical approach to the opposition between “concrete” and “abstract” numbers 引言——对“具体”数字和“抽象”数字对立的批判方法
IF 0.5 3区 哲学
Historia Mathematica Pub Date : 2022-05-01 DOI: 10.1016/j.hm.2022.05.001
Christine Proust, Eric Vandendriessche
{"title":"Introduction – A critical approach to the opposition between “concrete” and “abstract” numbers","authors":"Christine Proust,&nbsp;Eric Vandendriessche","doi":"10.1016/j.hm.2022.05.001","DOIUrl":"10.1016/j.hm.2022.05.001","url":null,"abstract":"","PeriodicalId":51061,"journal":{"name":"Historia Mathematica","volume":"59 ","pages":"Pages 3-11"},"PeriodicalIF":0.5,"publicationDate":"2022-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46739621","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"哲学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
“Complex numbers” and the problem of multiplication between quantities “复数”和数量之间的乘法问题
IF 0.5 3区 哲学
Historia Mathematica Pub Date : 2022-05-01 DOI: 10.1016/j.hm.2020.07.001
Débora Ferreira , Gert Schubring
{"title":"“Complex numbers” and the problem of multiplication between quantities","authors":"Débora Ferreira ,&nbsp;Gert Schubring","doi":"10.1016/j.hm.2020.07.001","DOIUrl":"10.1016/j.hm.2020.07.001","url":null,"abstract":"<div><p>This paper presents an analysis of a hitherto barely known conceptual problem in the foundations of arithmetic. An unknown type of number, so-called complex numbers, first emerged in 18th century France and became connected with the claim of non-commutativity of their multiplication. These first French practitioners are here analysed, along with examination of the impact of the introduction of the metric decimal system. International dissemination of the notion is then analysed, in particular in the case of Brazil. The paper concludes by looking at the mathematical foundations of multiplying (physical) quantities.</p></div>","PeriodicalId":51061,"journal":{"name":"Historia Mathematica","volume":"59 ","pages":"Pages 119-145"},"PeriodicalIF":0.5,"publicationDate":"2022-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1016/j.hm.2020.07.001","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42331581","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"哲学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
The sexagesimal place-value notation and abstract numbers in mathematical cuneiform texts 数学楔形文字文本中的六十进制位值符号和抽象数字
IF 0.5 3区 哲学
Historia Mathematica Pub Date : 2022-05-01 DOI: 10.1016/j.hm.2021.12.001
Christine Proust
{"title":"The sexagesimal place-value notation and abstract numbers in mathematical cuneiform texts","authors":"Christine Proust","doi":"10.1016/j.hm.2021.12.001","DOIUrl":"10.1016/j.hm.2021.12.001","url":null,"abstract":"<div><p>The discovery at the end of the 19<sup>th</sup> century of the mathematical cuneiform texts posed to historians the question of the nature of the numbers used in them, i.e. that of the sexagesimal place-value notation. This notation, although familiar to us today since it is the one we use to measure time, has, in the cuneiform texts, specificities which still raise challenges of interpretation. One of these specificities is the fact that the cuneiform writing does not indicate the order of magnitude of the numbers (for example, 1, 60, 1/60 or any other power of 60 are written in the same way). This article outlines the way in which historians of the late 19th and early 20th centuries interpreted this specificity. The focus here is on the interpretation proposed by the Assyriologist François Thureau-Dangin, who in 1930 considered numbers in sexagesimal place-value notation as “abstract numbers”, as opposed to “concrete numbers”.</p></div>","PeriodicalId":51061,"journal":{"name":"Historia Mathematica","volume":"59 ","pages":"Pages 54-70"},"PeriodicalIF":0.5,"publicationDate":"2022-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47681082","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"哲学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
The concrete numbers of “primitive” societies: A historiographical approach “原始”社会的具体数字:一种史学方法
IF 0.5 3区 哲学
Historia Mathematica Pub Date : 2022-05-01 DOI: 10.1016/j.hm.2022.01.006
Eric Vandendriessche
{"title":"The concrete numbers of “primitive” societies: A historiographical approach","authors":"Eric Vandendriessche","doi":"10.1016/j.hm.2022.01.006","DOIUrl":"10.1016/j.hm.2022.01.006","url":null,"abstract":"<div><p>From the 19<sup>th</sup> century onwards, some mathematicians and philosophers (G. Peacock, L. Conant, L. Lévy-Bruhl, L. Brunschvicg et al.), analyzed the numerical systems in use in so-called primitive societies as having a more “concrete” (or less “abstract”) character than those developed in more “advanced” societies. This article aims to better understand—and compare—what this opposition between “abstract numbers” and “concrete numbers” actually meant for these authors, as well as the characteristics of the “primitive mentality”—which they believed—this opposition would highlight.</p></div>","PeriodicalId":51061,"journal":{"name":"Historia Mathematica","volume":"59 ","pages":"Pages 12-34"},"PeriodicalIF":0.5,"publicationDate":"2022-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41299961","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"哲学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 1
Numeracy at the dawn of writing: Mesopotamia and beyond 文字诞生之初的计算能力:美索不达米亚及其他地区
IF 0.5 3区 哲学
Historia Mathematica Pub Date : 2022-05-01 DOI: 10.1016/j.hm.2020.08.002
Miguel Valério, Silvia Ferrara
{"title":"Numeracy at the dawn of writing: Mesopotamia and beyond","authors":"Miguel Valério,&nbsp;Silvia Ferrara","doi":"10.1016/j.hm.2020.08.002","DOIUrl":"10.1016/j.hm.2020.08.002","url":null,"abstract":"<div><p>Numeracy and writing constitute different phenomena, whose paths of formation often appear intertwined. Here we reassess the theory that numeracy evolved universally from a concrete to an abstract concept of number, and that that shift is correlated with the invention of writing. First, we gather contemporary linguistic data and early Mesopotamian epigraphic evidence that indicates that the ‘concrete’ vs. ‘abstract’ dichotomy is not useful to understand the emergence of numbers. Then, we discuss evidence from other regions where writing was probably invented independently, in order to investigate the conceptualization and formation of early numerical notations.</p></div>","PeriodicalId":51061,"journal":{"name":"Historia Mathematica","volume":"59 ","pages":"Pages 35-53"},"PeriodicalIF":0.5,"publicationDate":"2022-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1016/j.hm.2020.08.002","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42956845","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"哲学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 3
“Denominate numbers” in mathematics school textbooks by Stefan Banach 数学教科书中的“为数字命名”，作者是Stefan Banach
IF 0.5 3区 哲学
Historia Mathematica Pub Date : 2022-05-01 DOI: 10.1016/j.hm.2021.01.001
Karolina Karpińska
{"title":"“Denominate numbers” in mathematics school textbooks by Stefan Banach","authors":"Karolina Karpińska","doi":"10.1016/j.hm.2021.01.001","DOIUrl":"10.1016/j.hm.2021.01.001","url":null,"abstract":"<div><p>The paper is dedicated to analyzing the role of “denominate numbers” in textbooks for Polish schools, whose author or co-author was Stefan Banach. Banach used the concepts of “number” and “denominate number” in his textbooks. The ways of introducing these concepts, as well as the associated manner of understanding numeration, are analyzed in the paper. The methods of manipulating “denominate numbers” through various procedures are also discussed. The analysis is carried out in the context of the Polish ministerial ordinances related to teaching mathematics and the content of other textbooks, especially those used by Banach as a secondary school student.</p></div>","PeriodicalId":51061,"journal":{"name":"Historia Mathematica","volume":"59 ","pages":"Pages 164-196"},"PeriodicalIF":0.5,"publicationDate":"2022-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48902307","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"哲学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Notes on contributors 贡献者说明
IF 0.5 3区 哲学
Historia Mathematica Pub Date : 2022-05-01 DOI: 10.1016/S0315-0860(22)00042-8
{"title":"Notes on contributors","authors":"","doi":"10.1016/S0315-0860(22)00042-8","DOIUrl":"https://doi.org/10.1016/S0315-0860(22)00042-8","url":null,"abstract":"","PeriodicalId":51061,"journal":{"name":"Historia Mathematica","volume":"59 ","pages":"Pages 215-217"},"PeriodicalIF":0.5,"publicationDate":"2022-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138407907","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"哲学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
How Jean-Baptiste Delambre read ancient Greek arithmetic on the basis of the arithmetic of “complex numbers” at the turn of the 19th century 让-巴蒂斯特·德朗布尔是如何在19世纪之交的“复数”算术的基础上解读古希腊算术的
IF 0.5 3区 哲学
Historia Mathematica Pub Date : 2022-05-01 DOI: 10.1016/j.hm.2020.12.002
Xiaofei Wang
{"title":"How Jean-Baptiste Delambre read ancient Greek arithmetic on the basis of the arithmetic of “complex numbers” at the turn of the 19th century","authors":"Xiaofei Wang","doi":"10.1016/j.hm.2020.12.002","DOIUrl":"10.1016/j.hm.2020.12.002","url":null,"abstract":"<div><p>At the turn of the 19th century, arithmetic underwent a reform. Lagrange and Delambre developed diverse reflections on this discipline and contributed to the revival of the study of the ancient Greeks' mathematics. Through analyzing Lagrange's lectures on arithmetic and the popular arithmetic treatises, I reestablish how Lagrange's innovative ideas were adopted in the later books. Moreover, this paper clarifies the role that “complex numbers” played in these treatises and investigates Delambre's memoir on the ancient Greek arithmetic, so as to reveal the way in which Delambre read the ancients' texts and reconstructed their arithmetic using “complex numbers”.</p></div>","PeriodicalId":51061,"journal":{"name":"Historia Mathematica","volume":"59 ","pages":"Pages 146-163"},"PeriodicalIF":0.5,"publicationDate":"2022-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1016/j.hm.2020.12.002","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41490667","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"哲学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 1
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