Pub Date : 2023-08-01DOI: 10.1016/j.hm.2023.07.002
Alessandro Belcastro, Giuseppina Fenaroli
We discuss the probabilistic question faced by the Italian scholar Giovanni Rizzetti (1675–1751) and suggest this is a variant of what we refer to today as the “ballot sequences”, variant to which Catalan numbers offer a solution.
Rizzetti's search for a solution led him to produce an iterative rule which involved the consideration of Catalan numbers. Although coming up with these were not his final goal, the rule he elaborated allowed him to carry on calculating them as long as he wanted. As such, it is possible this was the first time such numbers were determined.
{"title":"A determination of Catalan numbers in 18th century Italy by Giovanni Rizzetti (1675–1751)","authors":"Alessandro Belcastro, Giuseppina Fenaroli","doi":"10.1016/j.hm.2023.07.002","DOIUrl":"https://doi.org/10.1016/j.hm.2023.07.002","url":null,"abstract":"<div><p>We discuss the probabilistic question faced by the Italian scholar Giovanni Rizzetti (1675–1751) and suggest this is a variant of what we refer to today as the “<em>ballot sequences</em>”, variant to which Catalan numbers offer a solution.</p><p>Rizzetti's search for a solution led him to produce an iterative rule which involved the consideration of Catalan numbers. Although coming up with these were not his final goal, the rule he elaborated allowed him to carry on calculating them as long as he wanted. As such, it is possible this was the first time such numbers were determined.</p></div>","PeriodicalId":51061,"journal":{"name":"Historia Mathematica","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2023-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"50190797","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 : 2023-08-01DOI: 10.1016/S0315-0860(23)00064-2
{"title":"Notes on contributors","authors":"","doi":"10.1016/S0315-0860(23)00064-2","DOIUrl":"https://doi.org/10.1016/S0315-0860(23)00064-2","url":null,"abstract":"","PeriodicalId":51061,"journal":{"name":"Historia Mathematica","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2023-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"50190798","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 : 2023-08-01DOI: 10.1016/j.hm.2023.06.001
Dominique Raynaud
This article aims at identifying the sources of fols. 395r and 686r-686v of the Codex Atlanticus. These anonymous folios, inserted in Leonardo da Vinci's notebooks, do not deal with the duplication of the cube proper, nor do they derive from Giorgio Valla's De expetendis et fugiendis rebus (1501), as has been claimed. They deal specifically with the extraction of the cube root by geometric methods. The analysis of the sources by the tracer method reveals that these fragments are taken from the Practica geometrie by Leonardo Fibonacci (1220) and, more precisely, from a volgarizzamento that appears in the Praticha d'arismetrica by Benedetto da Firenze (1463). Leonardo could have consulted this text in one of his two Florentine periods, around 1463-1482 or around 1503-1506.
本文旨在确定fols的来源。395r和686r-686v。这些匿名的对开本插入了达的笔记本中，并没有处理立方体本身的复制，也没有像人们所说的那样源自乔治·瓦拉的《De expetendis et fugiendis rebus》（1501）。它们专门处理通过几何方法提取立方根的问题。通过示踪法对来源的分析表明，这些碎片取自莱昂纳多·斐波那契（1220）的《几何实践》，更准确地说，取自贝内代托·达·弗伦泽（1463）的《阿里斯特里卡实践》中出现的一个volgarizzamento。莱昂纳多可能在他的两个佛罗伦萨时期中的一个时期，即1463-1482年左右或1503-1506年左右查阅了这篇文章。
{"title":"Da Vinci's Codex Atlanticus, fols. 395r and 686r–686v, refers to Leonardo Pisano volgarizzato, not to Giorgio Valla","authors":"Dominique Raynaud","doi":"10.1016/j.hm.2023.06.001","DOIUrl":"10.1016/j.hm.2023.06.001","url":null,"abstract":"<div><p>This article aims at identifying the sources of fols. 395r and 686r-686v of the <em>Codex Atlanticus</em>. These anonymous folios, inserted in Leonardo da Vinci's notebooks, do not deal with the duplication of the cube proper, nor do they derive from Giorgio Valla's <em>De expetendis et fugiendis rebus</em><span> (1501), as has been claimed. They deal specifically with the extraction of the cube root by geometric methods. The analysis of the sources by the tracer method reveals that these fragments are taken from the </span><em>Practica geometrie</em> by Leonardo Fibonacci (1220) and, more precisely, from a <em>volgarizzamento</em> that appears in the <em>Praticha d'arismetrica</em> by Benedetto da Firenze (1463). Leonardo could have consulted this text in one of his two Florentine periods, around 1463-1482 or around 1503-1506.</p></div>","PeriodicalId":51061,"journal":{"name":"Historia Mathematica","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2023-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45659503","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 : 2023-08-01DOI: 10.1016/j.hm.2023.06.002
Michael Wiescher
This paper evaluates possible reasons and motivations for 19th century geometer Julius Plücker's change in direction from his purely mathematical work to experimental physics. The author argues that this change did not happen suddenly in 1846 as is frequently suggested but rather, was a gradual change. This move took more than a decade and was triggered by Plücker's idea to apply his mathematical formalism to physical objects and phenomena, such as crystals and the trajectories of light in crystalline materials, a move which eventually led him to the newly discovered phenomena of diamagnetism.
{"title":"Julius Plücker – A path from geometry to optics","authors":"Michael Wiescher","doi":"10.1016/j.hm.2023.06.002","DOIUrl":"10.1016/j.hm.2023.06.002","url":null,"abstract":"<div><p>This paper evaluates possible reasons and motivations for 19<sup>th</sup><span> century geometer Julius Plücker's change in direction from his purely mathematical work to experimental physics. The author argues that this change did not happen suddenly in 1846 as is frequently suggested but rather, was a gradual change. This move took more than a decade and was triggered by Plücker's idea to apply his mathematical formalism to physical objects and phenomena, such as crystals and the trajectories of light in crystalline materials, a move which eventually led him to the newly discovered phenomena of diamagnetism.</span></p></div>","PeriodicalId":51061,"journal":{"name":"Historia Mathematica","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2023-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42901203","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 : 2023-05-01DOI: 10.1016/S0315-0860(23)00033-2
{"title":"Notes on contributors","authors":"","doi":"10.1016/S0315-0860(23)00033-2","DOIUrl":"https://doi.org/10.1016/S0315-0860(23)00033-2","url":null,"abstract":"","PeriodicalId":51061,"journal":{"name":"Historia Mathematica","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2023-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"50193717","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 : 2023-05-01DOI: 10.1016/j.hm.2023.05.003
Henning Heller
This article concerns a lecture course on Galois theory held by Felix Klein in summer 1886 at the University of Göttingen. Klein's commitment to teaching the theory of equations from Galois's advanced point of view forms a remarkable exception within the European curriculum. Klein's heuristic methodology, in which mathematical theory is extracted from a gradually advancing set of examples, allowed him for an efficient introduction of the main principles of Galois theory. At the same time, the lecture was difficult to follow and its immediate success remains questionable. The lecture furthermore provided Klein the possibility to further advertise his so-called Hypergalois vision for algebra, and prepared further lecture courses in that field. Through the commissioned lecture notes and Klein's engagement in the faculty, it also provided the means for a period of stability in the teaching of algebra at the University of Göttingen.
{"title":"Felix Klein's teaching of Galois theory","authors":"Henning Heller","doi":"10.1016/j.hm.2023.05.003","DOIUrl":"10.1016/j.hm.2023.05.003","url":null,"abstract":"<div><p>This article concerns a lecture course on Galois theory held by Felix Klein in summer 1886 at the University of Göttingen. Klein's commitment to teaching the theory of equations from Galois's advanced point of view forms a remarkable exception within the European curriculum. Klein's heuristic methodology, in which mathematical theory is extracted from a gradually advancing set of examples, allowed him for an efficient introduction of the main principles of Galois theory. At the same time, the lecture was difficult to follow and its immediate success remains questionable. The lecture furthermore provided Klein the possibility to further advertise his so-called <em>Hypergalois</em> vision for algebra, and prepared further lecture courses in that field. Through the commissioned lecture notes and Klein's engagement in the faculty, it also provided the means for a period of stability in the teaching of algebra at the University of Göttingen.</p></div>","PeriodicalId":51061,"journal":{"name":"Historia Mathematica","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2023-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41712321","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 : 2023-05-01DOI: 10.1016/j.hm.2023.02.002
David E. Rowe
{"title":"","authors":"David E. Rowe","doi":"10.1016/j.hm.2023.02.002","DOIUrl":"https://doi.org/10.1016/j.hm.2023.02.002","url":null,"abstract":"","PeriodicalId":51061,"journal":{"name":"Historia Mathematica","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2023-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"50193720","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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