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Historia Mathematica最新文献

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Mathematical cognition related to the large numbers in early societies: A study based on 5th-century Buddhist Commentaries in Sri Lanka. 早期社会中与大数有关的数学认知：基于斯里兰卡 5 世纪佛教注释的研究。
IF 0.5 3区 哲学
Historia Mathematica Pub Date : 2024-06-01 DOI: 10.1016/j.hm.2024.02.002
Chandana Jayawardana
{"title":"Mathematical cognition related to the large numbers in early societies: A study based on 5th-century Buddhist Commentaries in Sri Lanka.","authors":"Chandana Jayawardana","doi":"10.1016/j.hm.2024.02.002","DOIUrl":"10.1016/j.hm.2024.02.002","url":null,"abstract":"<div><p>Universal presentations and interpretations of the history of mathematics have now been challenged, identifying the need of resurrecting hitherto marginalized contributions. In such studies, cognitive factors influencing the related development trajectories play a crucial role. Different societies would have had different mathematical cognitions contributing to the development of distinct forms of mathematics. This study attempts to surface the related cognitive contents of using large numbers. The principal source used for the study—the Buddhist Commentaries—determines the period and region covered. As such, it explores the conditions prevailed in 5th century CE (approximately) in Sri Lanka.</p><p>2000 Mathematics Subject Classification (MSC 2000) code: 01A07</p></div>","PeriodicalId":51061,"journal":{"name":"Historia Mathematica","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2024-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140199712","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
IF 0.5 3区 哲学
Historia Mathematica Pub Date : 2024-06-01 DOI: 10.1016/j.hm.2024.02.004
Jens Høyrup (Emeritus)
{"title":"","authors":"Jens Høyrup (Emeritus)","doi":"10.1016/j.hm.2024.02.004","DOIUrl":"https://doi.org/10.1016/j.hm.2024.02.004","url":null,"abstract":"","PeriodicalId":51061,"journal":{"name":"Historia Mathematica","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2024-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141314442","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 International commission on mathematical instruction, 1908–2008: People, events and challenges in mathematics education 国际数学教学委员会，1908-2008 年：数学教育中的人、事和挑战
IF 0.5 3区 哲学
Historia Mathematica Pub Date : 2024-06-01 DOI: 10.1016/j.hm.2024.02.007
Thomas Preveraud
{"title":"The International commission on mathematical instruction, 1908–2008: People, events and challenges in mathematics education","authors":"Thomas Preveraud","doi":"10.1016/j.hm.2024.02.007","DOIUrl":"10.1016/j.hm.2024.02.007","url":null,"abstract":"","PeriodicalId":51061,"journal":{"name":"Historia Mathematica","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2024-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140199716","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
Johannes Regiomontanus, Aufgaben und Übungen zur Algebrass, Jens Høyrup, Martin Hellmann, Erwin Rauner Verlag, Augsburg (2023), Essay review byed.
IF 0.5 3区 哲学
Historia Mathematica Pub Date : 2024-03-01 DOI: 10.1016/j.hm.2023.11.001
Jens Høyrup
{"title":"","authors":"Jens Høyrup","doi":"10.1016/j.hm.2023.11.001","DOIUrl":"10.1016/j.hm.2023.11.001","url":null,"abstract":"","PeriodicalId":51061,"journal":{"name":"Historia Mathematica","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2024-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S0315086023000691/pdfft?md5=0a08d721743b6fdbb5314fdc1c07cd18&pid=1-s2.0-S0315086023000691-main.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138580424","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
Decimal fractional numeration and the decimal point in 15th-century Italy 15 世纪意大利的小数点法和小数点
IF 0.5 3区 哲学
Historia Mathematica Pub Date : 2024-03-01 DOI: 10.1016/j.hm.2024.01.001
Glen Van Brummelen
{"title":"Decimal fractional numeration and the decimal point in 15th-century Italy","authors":"Glen Van Brummelen","doi":"10.1016/j.hm.2024.01.001","DOIUrl":"10.1016/j.hm.2024.01.001","url":null,"abstract":"<div><p>The earliest known appearance of the decimal point was in the interpolation column of a sine table in Christopher Clavius's <em>Astrolabium</em> (1593). But this is a curious place to introduce such a significant new idea, and the fact that Clavius never took advantage of it in his own later writings has remained unexplained. We trace Clavius's use of decimal fractional numeration and the decimal point back to the work of Giovanni Bianchini (1440s), whose decimal system was a distinguishing feature of his calculations in spherical astronomy and metrology. While one needed to operate with Bianchini's decimal system to work with his astronomy, Regiomontanus copied it only in part. The rest of the European astronomical community followed Regiomontanus, and Bianchini's system reappeared only with its revival by Clavius.</p><p>La première apparition connue du point décimal se trouve dans la colonne d'interpolation d'une table de sinus dans l’<em>Astrolabium</em> de Christopher <span>Clavius (1593)</span>. Mais il s'agit là d'un endroit curieux pour introduire une nouvelle idée aussi importante, et le fait que Clavius n'en ait jamais tiré parti dans ses écrits ultérieurs reste inexpliqué. L'utilisation par Clavius de la numération fractionnaire décimale et du point décimal remonte aux travaux de Giovanni Bianchini (années 1440), dont le système décimal était une caractéristique distinctive de ses calculs en astronomie sphérique et en métrologie. Alors qu'il fallait utiliser le système décimal de Bianchini pour travailler avec son astronomie, Regiomontanus ne l'a copié qu'en partie. Le reste de la communauté astronomique européenne suivit Regiomontanus, et le système de Bianchini ne réapparut qu'avec Clavius.</p></div>","PeriodicalId":51061,"journal":{"name":"Historia Mathematica","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2024-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S0315086024000016/pdfft?md5=59df168ecdede94165b4e34ed494da77&pid=1-s2.0-S0315086024000016-main.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139917984","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
The saṃyoga-meru: A combinatorial tool in the Saṅgīta-ratnākara 萨迦瑜伽髓：萨迦摩尼宝典》中的组合工具
IF 0.5 3区 哲学
Historia Mathematica Pub Date : 2024-03-01 DOI: 10.1016/j.hm.2024.02.003
G Sreeram, Aditya Kolachana
{"title":"The saṃyoga-meru: A combinatorial tool in the Saṅgīta-ratnākara","authors":"G Sreeram,&nbsp;Aditya Kolachana","doi":"10.1016/j.hm.2024.02.003","DOIUrl":"https://doi.org/10.1016/j.hm.2024.02.003","url":null,"abstract":"<div><p>The <em>Saṅgīta-ratnākara</em> (Ocean of Music) of Śārṅgadeva (c. 1225 CE) is a 13th century text on musicology in Sanskrit. The fifth chapter of the <em>Saṅgīta-ratnākara</em> deals with a general analysis of all possible rhythms (<em>tāla</em>s) which can be obtained by combining a set of basic rhythmic components known as <em>tālāṅga</em>s. Here, Śārṅgadeva describes the construction of the <em>saṃyoga-meru</em> (Table of Combinations), a tool that tabulates the total number of possible <em>tāla</em>s of a given duration which are obtained by combining elements of different subsets of <em>tālāṅga</em>s. In this paper, we discuss the mathematical rationale employed by Śārṅgadeva in the construction of the <em>saṃyoga-meru</em>.</p></div>","PeriodicalId":51061,"journal":{"name":"Historia Mathematica","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2024-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S0315086024000053/pdfft?md5=1e9ed71e46f5239130c59d4c493d2de7&pid=1-s2.0-S0315086024000053-main.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140190887","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
“On the Unviability of Interpreting Leibniz's Infinitesimals through Non-standard analysis” "论通过非标准分析解读莱布尼茨无穷小的不可行性
IF 0.5 3区 哲学
Historia Mathematica Pub Date : 2024-03-01 DOI: 10.1016/j.hm.2023.12.001
Richard Arthur , David Rabouin
{"title":"“On the Unviability of Interpreting Leibniz's Infinitesimals through Non-standard analysis”","authors":"Richard Arthur ,&nbsp;David Rabouin","doi":"10.1016/j.hm.2023.12.001","DOIUrl":"10.1016/j.hm.2023.12.001","url":null,"abstract":"<div><p>Non-standard analysis has often been presented as the proper framework for expressing rigorously Leibniz's conception of infinitesimals. This paper intends to study this interpretation from an historical point of view and to dispel a series of misunderstandings on which it rests. In order to do so, we propose to go back to Leibniz's conception of quantity, number and magnitude, an approach which has not been developed yet in the literature.</p></div>","PeriodicalId":51061,"journal":{"name":"Historia Mathematica","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2024-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S031508602300085X/pdfft?md5=53a9a9c365002d97a94a541442d00233&pid=1-s2.0-S031508602300085X-main.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139577895","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
反动数学：纯粹性谱系》，马西莫-马佐蒂，芝加哥大学出版社（2023 年）
IF 0.5 3区 哲学
Historia Mathematica Pub Date : 2024-03-01 DOI: 10.1016/j.hm.2023.11.002
Davide Crippa
{"title":"","authors":"Davide Crippa","doi":"10.1016/j.hm.2023.11.002","DOIUrl":"10.1016/j.hm.2023.11.002","url":null,"abstract":"","PeriodicalId":51061,"journal":{"name":"Historia Mathematica","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2024-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S0315086023000708/pdfft?md5=19dd4fd5d92d0ca679a5aa0fdf81b7e7&pid=1-s2.0-S0315086023000708-main.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139056421","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
Cyclic quadrilaterals: Solutions of two Japanese problems and their proofs 循环四边形：两个日本问题的解决方案及其证明
IF 0.5 3区 哲学
Historia Mathematica Pub Date : 2023-11-01 DOI: 10.1016/j.hm.2023.08.001
J. Marshall Unger
{"title":"Cyclic quadrilaterals: Solutions of two Japanese problems and their proofs","authors":"J. Marshall Unger","doi":"10.1016/j.hm.2023.08.001","DOIUrl":"10.1016/j.hm.2023.08.001","url":null,"abstract":"<div><p>Late 18th and early 19th century Japanese mathematicians (<em>wasanka</em>) found solutions of two problems concerning the incircles of the quarter-triangles and skewed sectors of cyclic quadrilaterals. There is a modern proof of the first solution, but it makes extensive use of trigonometry and is therefore unlikely to be what a <em>wasanka</em> would have written. As for the second solution, Aida Yasuaki (1747–1817) gave two proofs for it, the second of which has been summarized in Japanese, but not the first. All three proofs are presented here together with commentary on their mathematical and historical significance.</p></div>","PeriodicalId":51061,"journal":{"name":"Historia Mathematica","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2023-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135408478","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
Newton on constructions in geometry 牛顿论几何学中的构造
IF 0.5 3区 哲学
Historia Mathematica Pub Date : 2023-11-01 DOI: 10.1016/j.hm.2023.09.002
Viktor Blåsjö
{"title":"Newton on constructions in geometry","authors":"Viktor Blåsjö","doi":"10.1016/j.hm.2023.09.002","DOIUrl":"10.1016/j.hm.2023.09.002","url":null,"abstract":"<div><p>Newton was critical of Descartes's constructivist vision of the foundations of geometry organised around certain curve-tracing principles. In unpublished work, Newton outlined a constructivist program of his own, based on his “organic” method of curve tracing, which subsumes Descartes's emblematic turning-ruler-and-moving-curve construction method as a special case, but does not suffer from the latter's flaw of being unable to trace all conics. This Newtonian program has been little studied and is more thoughtful and technically substantive than is commonly recognised. It also clashes with, and arguably supersedes and improves upon, Newton's perhaps better known earlier statements on the subject.</p></div>","PeriodicalId":51061,"journal":{"name":"Historia Mathematica","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2023-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S0315086023000666/pdfft?md5=cfffb05a2f2f6ca7ed57de11fa0b2c09&pid=1-s2.0-S0315086023000666-main.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135614706","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
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