Pub Date : 2022-11-01DOI: 10.1016/S0315-0860(22)00086-6
{"title":"Notes on contributors","authors":"","doi":"10.1016/S0315-0860(22)00086-6","DOIUrl":"https://doi.org/10.1016/S0315-0860(22)00086-6","url":null,"abstract":"","PeriodicalId":51061,"journal":{"name":"Historia Mathematica","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2022-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"92057338","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}
Pub Date : 2022-11-01DOI: 10.1016/j.hm.2022.06.001
Hidetoshi Fukagawa , David Clark
This geometry problem rose to great prominence among Japan's mathematicians after it was posted on a sangaku in 1749. Several scholars presented solutions, most famously Ajima Naonobu in 1774. Here we present Ajima's celebrated solution, along with a modern interpretation of his analysis, which notably employs the computation of a determinant via cofactor expansion. This article consists, in large part, of a translation of a modern Japanese language reconstruction of Ajima's solution. Some historical context is also provided.
{"title":"Ajima's solution to the Gion shrine problem: A modern interpretation","authors":"Hidetoshi Fukagawa , David Clark","doi":"10.1016/j.hm.2022.06.001","DOIUrl":"10.1016/j.hm.2022.06.001","url":null,"abstract":"<div><p>This geometry problem rose to great prominence among Japan's mathematicians after it was posted on a <em>sangaku</em> in 1749. Several scholars presented solutions, most famously Ajima Naonobu in 1774. Here we present Ajima's celebrated solution, along with a modern interpretation of his analysis, which notably employs the computation of a determinant via cofactor expansion. This article consists, in large part, of a translation of a modern Japanese language reconstruction of Ajima's solution. Some historical context is also provided.</p></div>","PeriodicalId":51061,"journal":{"name":"Historia Mathematica","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2022-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44121583","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}
Pub Date : 2022-11-01DOI: 10.1016/j.hm.2022.05.002
J. Marshall Unger
Fukagawa and Rothman introduced a difficult wasan problem concerning an ellipse inscribed in a right triangle from an old travel diary. Like the famous Gion Shrine problem, it does not specify numerical data but asks only for an equation of a particular kind; moreover, modern solutions of the problem entail polynomial equations of degree greater than four. One may therefore wonder whether the problem was recorded correctly. A careful examination of the primary text suggests that problem may have been written in haste, and that the original problem may have been more tractable mathematically.
{"title":"Mathematics and philology: An example from wasan","authors":"J. Marshall Unger","doi":"10.1016/j.hm.2022.05.002","DOIUrl":"10.1016/j.hm.2022.05.002","url":null,"abstract":"<div><p>Fukagawa and Rothman introduced a difficult <em>wasan</em><span> problem concerning an ellipse<span> inscribed in a right triangle from an old travel diary. Like the famous Gion Shrine problem, it does not specify numerical data but asks only for an equation of a particular kind; moreover, modern solutions of the problem entail polynomial equations of degree greater than four. One may therefore wonder whether the problem was recorded correctly. A careful examination of the primary text suggests that problem may have been written in haste, and that the original problem may have been more tractable mathematically.</span></span></p></div>","PeriodicalId":51061,"journal":{"name":"Historia Mathematica","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2022-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42007488","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}
Pub Date : 2022-11-01DOI: 10.1016/j.hm.2022.08.003
Arrigo Pisati , Riccardo Rosso
We analyze the work on geometrical optics by Felice Casorati who contributed to the dissemination of Gaussian optics in Italy. In his approach to Gauss's (1840) Untersuchungen he applied determinants to describe multiple refractions in an optical system and he explored the extension of the theory to cover slightly non-centered optical systems for which he introduced the cardinal line, a straight line that replaces the optical axis in this framework.
{"title":"Felice Casorati and the reception of Gaussian optics in Italy","authors":"Arrigo Pisati , Riccardo Rosso","doi":"10.1016/j.hm.2022.08.003","DOIUrl":"https://doi.org/10.1016/j.hm.2022.08.003","url":null,"abstract":"<div><p>We analyze the work on geometrical optics by Felice Casorati who contributed to the dissemination of Gaussian optics in Italy. In his approach to <span>Gauss</span>'s (<span>1840</span>) <em>Untersuchungen</em> he applied determinants to describe multiple refractions in an optical system and he explored the extension of the theory to cover slightly non-centered optical systems for which he introduced the cardinal line, a straight line that replaces the optical axis in this framework.</p></div>","PeriodicalId":51061,"journal":{"name":"Historia Mathematica","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2022-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136921969","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}
Pub Date : 2022-10-01DOI: 10.1016/j.hm.2022.08.002
D. Buckle
{"title":"How the estimate of 2 on YBC 7289 may have been calculated","authors":"D. Buckle","doi":"10.1016/j.hm.2022.08.002","DOIUrl":"https://doi.org/10.1016/j.hm.2022.08.002","url":null,"abstract":"","PeriodicalId":51061,"journal":{"name":"Historia Mathematica","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2022-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49120669","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}
Pub Date : 2022-08-01DOI: 10.1016/S0315-0860(22)00064-7
{"title":"Notes on contributors","authors":"","doi":"10.1016/S0315-0860(22)00064-7","DOIUrl":"https://doi.org/10.1016/S0315-0860(22)00064-7","url":null,"abstract":"","PeriodicalId":51061,"journal":{"name":"Historia Mathematica","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2022-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136544181","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}
Pub Date : 2022-08-01DOI: 10.1016/j.hm.2022.07.001
Reinhard Siegmund-Schultze
{"title":"Felix Hausdorff's Collected Works – a meta-review","authors":"Reinhard Siegmund-Schultze","doi":"10.1016/j.hm.2022.07.001","DOIUrl":"10.1016/j.hm.2022.07.001","url":null,"abstract":"","PeriodicalId":51061,"journal":{"name":"Historia Mathematica","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2022-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49263022","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}
Pub Date : 2022-08-01DOI: 10.1016/j.hm.2022.03.001
M.G. Lugaresi , C. D'Alterio
Federigo Enriques (1871-1946) was a protagonist of mathematical culture in the early twentieth century. The handbook prepared for one of his university courses at the University of Bologna, Lezioni di geometria proiettiva, constitutes probably the most representative work of his early teaching years. This book has influenced several Enriques' researches, and in particular those relating to the foundations of geometry. The use of the synthetic approach in setting up the handbook leads Enriques to a new arrangement of the contents. The proposed analysis explores this aspect, showing in particular the law of duality, the postulate of continuity and the fundamental theorem of projectivity, without neglecting the importance that Enriques attributes to the historical developments of mathematics.
{"title":"Federigo Enriques (1871-1946): A critical study of Lezioni di geometria proiettiva","authors":"M.G. Lugaresi , C. D'Alterio","doi":"10.1016/j.hm.2022.03.001","DOIUrl":"10.1016/j.hm.2022.03.001","url":null,"abstract":"<div><p>Federigo Enriques (1871-1946) was a protagonist of mathematical culture in the early twentieth century. The handbook prepared for one of his university courses at the University of Bologna, <em>Lezioni di geometria proiettiva</em><span>, constitutes probably the most representative work of his early teaching years. This book has influenced several Enriques' researches, and in particular those relating to the foundations of geometry. The use of the synthetic approach in setting up the handbook leads Enriques to a new arrangement of the contents. The proposed analysis explores this aspect, showing in particular the law of duality, the postulate of continuity and the fundamental theorem of projectivity, without neglecting the importance that Enriques attributes to the historical developments of mathematics.</span></p></div>","PeriodicalId":51061,"journal":{"name":"Historia Mathematica","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2022-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44601723","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}
Pub Date : 2022-08-01DOI: 10.1016/j.hm.2021.11.002
Siu A. Chin
The feud between Robert Hooke and Isaac Newton, over whether Newton should have acknowledged Hooke's influence on his graphical method of constructing planet orbits, the celebrated Proposition 1, Theorem 1 of the Principia, has remained ongoing among their respective supporters, even after 300 years. The drama has escalated in recent decades, with a claim that Hooke may have used the same method and obtained an elliptical orbit for a linear force, a feat that some considered Newton never did for the inverse-square force. Modern understanding of Newton's graphical method as a symplectic integrator can now shed light on whether this claim is creditable.
{"title":"Modern light on ancient feud: Robert Hooke and Newton's graphical method","authors":"Siu A. Chin","doi":"10.1016/j.hm.2021.11.002","DOIUrl":"10.1016/j.hm.2021.11.002","url":null,"abstract":"<div><p><span><span>The feud between Robert Hooke and Isaac Newton, over whether Newton should have acknowledged Hooke's influence on his graphical method of constructing planet orbits, the celebrated </span>Proposition 1, Theorem 1 of the </span><span><em>Principia</em></span><span>, has remained ongoing among their respective supporters, even after 300 years. The drama has escalated in recent decades, with a claim that Hooke may have used the same method and obtained an elliptical orbit for a linear force, a feat that some considered Newton never did for the inverse-square force. Modern understanding of Newton's graphical method as a symplectic integrator can now shed light on whether this claim is creditable.</span></p></div>","PeriodicalId":51061,"journal":{"name":"Historia Mathematica","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2022-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42260091","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}
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