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Historia Mathematica最新文献

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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
Ubiratan D'Ambrosio (1932–2021) 乌比拉坦·丹布罗西奥（1932–2021）
IF 0.5 3区 哲学
Historia Mathematica Pub Date : 2022-02-01 DOI: 10.1016/j.hm.2022.01.002
Patrick Scott
{"title":"Ubiratan D'Ambrosio (1932–2021)","authors":"Patrick Scott","doi":"10.1016/j.hm.2022.01.002","DOIUrl":"10.1016/j.hm.2022.01.002","url":null,"abstract":"","PeriodicalId":51061,"journal":{"name":"Historia Mathematica","volume":"58 ","pages":"Pages 3-6"},"PeriodicalIF":0.5,"publicationDate":"2022-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S0315086022000027/pdfft?md5=bea999b7b693b75904342dc81bca36ac&pid=1-s2.0-S0315086022000027-main.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42073265","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: 0
In memoriam: Richard P. Lorch (1942–2021) 纪念:理查德·p·洛奇(1942-2021)
IF 0.5 3区 哲学
Historia Mathematica Pub Date : 2022-02-01 DOI: 10.1016/j.hm.2022.01.003
Henry Zepeda, Benno van Dalen, Menso Folkerts
{"title":"In memoriam: Richard P. Lorch (1942–2021)","authors":"Henry Zepeda,&nbsp;Benno van Dalen,&nbsp;Menso Folkerts","doi":"10.1016/j.hm.2022.01.003","DOIUrl":"10.1016/j.hm.2022.01.003","url":null,"abstract":"","PeriodicalId":51061,"journal":{"name":"Historia Mathematica","volume":"58 ","pages":"Pages 7-16"},"PeriodicalIF":0.5,"publicationDate":"2022-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S0315086022000039/pdfft?md5=f5490f0cc53093de78ebbe54d4d2599a&pid=1-s2.0-S0315086022000039-main.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42156895","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: 0
François Viète's method for calculating the eccentricity in a bisected model and its possible application to Kepler's Vicarious Hypothesis 弗朗索瓦·维<e:1>特在等分模型中计算偏心率的方法及其在开普勒替代假说中的可能应用
IF 0.5 3区 哲学
Historia Mathematica Pub Date : 2022-02-01 DOI: 10.1016/j.hm.2021.09.002
Christián C. Carman
{"title":"François Viète's method for calculating the eccentricity in a bisected model and its possible application to Kepler's Vicarious Hypothesis","authors":"Christián C. Carman","doi":"10.1016/j.hm.2021.09.002","DOIUrl":"10.1016/j.hm.2021.09.002","url":null,"abstract":"<div><p>According to Kepler's own words in <em>Astronomia Nova</em>, he invested five years trying to find the values for the eccentricities for his “vicarious” hypothesis. At some point, he asked Herwart von Hohenburg, to ask François Viète's help to solve his problem, but there is no evidence that Viète received this request. At that time, Viète was working on his unpublished <em>Ad harmonicon coeleste</em>. In it, he proposes a new method for bisected models, which can easily be extended to non-bisected models. In this paper, I describe Viète's method, analyze its accuracy, and show how to extend it to non-bisected models, making it suitable for solving Kepler's problem.</p></div>","PeriodicalId":51061,"journal":{"name":"Historia Mathematica","volume":"58 ","pages":"Pages 71-91"},"PeriodicalIF":0.5,"publicationDate":"2022-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41537447","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
Small numerical variations in a set of similar problems from Nippur on the area of the square 尼普尔在正方形面积上的一组类似问题中的小数值变化
IF 0.5 3区 哲学
Historia Mathematica Pub Date : 2022-02-01 DOI: 10.1016/j.hm.2021.07.004
Charlotte de Varent
{"title":"Small numerical variations in a set of similar problems from Nippur on the area of the square","authors":"Charlotte de Varent","doi":"10.1016/j.hm.2021.07.004","DOIUrl":"10.1016/j.hm.2021.07.004","url":null,"abstract":"<div><p>This study is based on a set of six tablets dated to the Old-Babylonian period in Mesopotamia, written in cuneiform script, and relating to problems on the areas of squares. Their content is very similar, except for the length measurement of the side of the square. The issue of hypothetical pedagogical issues involved in the choice of numerical values in the statements is addressed by detailing the tasks they imply in the process of problem solving.</p></div>","PeriodicalId":51061,"journal":{"name":"Historia Mathematica","volume":"58 ","pages":"Pages 35-70"},"PeriodicalIF":0.5,"publicationDate":"2022-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41929531","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
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