Pub Date : 2015-09-02DOI: 10.1080/17498430.2015.1036335
D. Jesseph
{"title":"The tangled origins of the Leibnizian calculus: a case study of a mathematical revolution, by Richard C Brown","authors":"D. Jesseph","doi":"10.1080/17498430.2015.1036335","DOIUrl":"https://doi.org/10.1080/17498430.2015.1036335","url":null,"abstract":"","PeriodicalId":211442,"journal":{"name":"BSHM Bulletin: Journal of the British Society for the History of Mathematics","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2015-09-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"134054710","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2015-09-02DOI: 10.1080/17498430.2015.1036336
Jonathan P. Bowen
will ‘show that some fairly esoteric Renaissance ideas nourished the seventeenth century climate that made Leibniz’s calculus possible’ (p 205). On the whole, this volume is a useful contribution to a large and growing literature. Readers not readily familiar with the contents of a university-level course in the calculus may find some of the material technically challenging, and those with reservations about the Kuhnian analysis of scientific change will likely find the historiographic orientation unsatisfying. I also found that Brown’s discussion tended to wander rather far afield—an impression heightened by the presence of six appendices that range over topics only very loosely connected to Brown’s main argument. Finally, the presence of numerous typographical errors through the text was occasionally distracting. Despite these shortcomings, the volume delivers a nuanced and technically sound account of the Leibnizian calculus and its intellectual context.
{"title":"It began with Babbage: the genesis of computer science, by Subrata Dasgupta","authors":"Jonathan P. Bowen","doi":"10.1080/17498430.2015.1036336","DOIUrl":"https://doi.org/10.1080/17498430.2015.1036336","url":null,"abstract":"will ‘show that some fairly esoteric Renaissance ideas nourished the seventeenth century climate that made Leibniz’s calculus possible’ (p 205). On the whole, this volume is a useful contribution to a large and growing literature. Readers not readily familiar with the contents of a university-level course in the calculus may find some of the material technically challenging, and those with reservations about the Kuhnian analysis of scientific change will likely find the historiographic orientation unsatisfying. I also found that Brown’s discussion tended to wander rather far afield—an impression heightened by the presence of six appendices that range over topics only very loosely connected to Brown’s main argument. Finally, the presence of numerous typographical errors through the text was occasionally distracting. Despite these shortcomings, the volume delivers a nuanced and technically sound account of the Leibnizian calculus and its intellectual context.","PeriodicalId":211442,"journal":{"name":"BSHM Bulletin: Journal of the British Society for the History of Mathematics","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2015-09-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"133550370","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2015-09-02DOI: 10.1080/17498430.2015.1055902
E. Robson
{"title":"Subverting expectations: memories of editing with Jackie","authors":"E. Robson","doi":"10.1080/17498430.2015.1055902","DOIUrl":"https://doi.org/10.1080/17498430.2015.1055902","url":null,"abstract":"","PeriodicalId":211442,"journal":{"name":"BSHM Bulletin: Journal of the British Society for the History of Mathematics","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2015-09-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"123232336","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2015-09-02DOI: 10.1080/17498430.2015.1035585
Fatma Kayan Fadlelmula
This study examines pre-service teachers’ points of view about learning history of mathematics during their undergraduate education. An open-ended questionnaire was administered to one hundred and twenty pre-service teachers, during the fall semester of the 2013–14 academic year. The participants indicated that learning history of mathematics could increase their content knowledge as they understand how formulas, theories and relations were developed over time. In addition, it could develop them intellectually as they learn life stories of mathematicians. Also, it could help them to hold the attention of students, and answer some of the why questions. Particularly, they reported using history of mathematics knowledge while teaching Geometry and Numbers.
{"title":"Pre-service teachers' point of views about learning history of mathematics: a case study in Turkey","authors":"Fatma Kayan Fadlelmula","doi":"10.1080/17498430.2015.1035585","DOIUrl":"https://doi.org/10.1080/17498430.2015.1035585","url":null,"abstract":"This study examines pre-service teachers’ points of view about learning history of mathematics during their undergraduate education. An open-ended questionnaire was administered to one hundred and twenty pre-service teachers, during the fall semester of the 2013–14 academic year. The participants indicated that learning history of mathematics could increase their content knowledge as they understand how formulas, theories and relations were developed over time. In addition, it could develop them intellectually as they learn life stories of mathematicians. Also, it could help them to hold the attention of students, and answer some of the why questions. Particularly, they reported using history of mathematics knowledge while teaching Geometry and Numbers.","PeriodicalId":211442,"journal":{"name":"BSHM Bulletin: Journal of the British Society for the History of Mathematics","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2015-09-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"116461089","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2015-09-02DOI: 10.1080/17498430.2015.1057008
A. Whitaker
{"title":"The Third Irish History of Mathematics Conference","authors":"A. Whitaker","doi":"10.1080/17498430.2015.1057008","DOIUrl":"https://doi.org/10.1080/17498430.2015.1057008","url":null,"abstract":"","PeriodicalId":211442,"journal":{"name":"BSHM Bulletin: Journal of the British Society for the History of Mathematics","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2015-09-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"125415794","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2015-09-02DOI: 10.1080/17498430.2015.1086071
Robin Wilson
spreading the word amongst those without an educated background but with a thirst for knowledge. In being a very determined educator, De Morgan published intelligent comments and made suggestions, particularly in logic. In this way he was one of the first people to bring to general attention some things that we now regard as fundamental, for example mathematical induction (which he called ‘Successive Induction’ (1838)), the De Morgan laws and Boolean duality, quantifiers and their domains of relational logic. He championed a move to decimal currency in the 1850s (witness the introduction of the florin, two shillings, or a tenth of a pound) a move which at the time went nowhere. De Morgan’s ideas were explained in non-technical terms, how these things are important, and what they owe to him. According to Wilfrid Hodges, De Morgan was not to be compared with Boole whose work in logic was fresh, new, and full of insights, or even to Avicenna, an Islamic scholar of the early eleventh century. Primarily a teacher, De Morgan published widely in such journals as The Athenæum and the Penny Cyclopaedia, and was ready to give a helping hand to his students whether in mathematics or acting as wise tutor. As to De Morgan’s mathematical influence, the speaker neatly turned the question around and wondered what developments of today De Morgan would approve. Tony Crilly http://dx.doi.org/10.1080/17498430.2015.1055089
{"title":"Sixth BSHM–CSHPM Joint Meeting","authors":"Robin Wilson","doi":"10.1080/17498430.2015.1086071","DOIUrl":"https://doi.org/10.1080/17498430.2015.1086071","url":null,"abstract":"spreading the word amongst those without an educated background but with a thirst for knowledge. In being a very determined educator, De Morgan published intelligent comments and made suggestions, particularly in logic. In this way he was one of the first people to bring to general attention some things that we now regard as fundamental, for example mathematical induction (which he called ‘Successive Induction’ (1838)), the De Morgan laws and Boolean duality, quantifiers and their domains of relational logic. He championed a move to decimal currency in the 1850s (witness the introduction of the florin, two shillings, or a tenth of a pound) a move which at the time went nowhere. De Morgan’s ideas were explained in non-technical terms, how these things are important, and what they owe to him. According to Wilfrid Hodges, De Morgan was not to be compared with Boole whose work in logic was fresh, new, and full of insights, or even to Avicenna, an Islamic scholar of the early eleventh century. Primarily a teacher, De Morgan published widely in such journals as The Athenæum and the Penny Cyclopaedia, and was ready to give a helping hand to his students whether in mathematics or acting as wise tutor. As to De Morgan’s mathematical influence, the speaker neatly turned the question around and wondered what developments of today De Morgan would approve. Tony Crilly http://dx.doi.org/10.1080/17498430.2015.1055089","PeriodicalId":211442,"journal":{"name":"BSHM Bulletin: Journal of the British Society for the History of Mathematics","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2015-09-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"123401068","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2015-08-28DOI: 10.1080/17498430.2015.1044697
Fabio Bellissima
In this article, I try to show how the operation of compounding of ratios as performed with the method of Proposition VIII.4 of Euclid's Elements, has possibly taken shape from experiments on the monochord. This fact, together with the systematic and exclusive use of Proposition VIII.4 in the harmonic field, strengthens the thesis concerning the connection between harmonic theory and Book VIII. A misinterpretation by Zarlino, the most important music theorist of the Renaissance, will help us explain how the musical model may have been partially responsible for the disconnection between compounding and multiplication present in the Elements in spite of the link established by Proposition VIII.5.
{"title":"Propositions VIII.4–5 of Euclid's Elements and the compounding of ratios on the monochord","authors":"Fabio Bellissima","doi":"10.1080/17498430.2015.1044697","DOIUrl":"https://doi.org/10.1080/17498430.2015.1044697","url":null,"abstract":"In this article, I try to show how the operation of compounding of ratios as performed with the method of Proposition VIII.4 of Euclid's Elements, has possibly taken shape from experiments on the monochord. This fact, together with the systematic and exclusive use of Proposition VIII.4 in the harmonic field, strengthens the thesis concerning the connection between harmonic theory and Book VIII. A misinterpretation by Zarlino, the most important music theorist of the Renaissance, will help us explain how the musical model may have been partially responsible for the disconnection between compounding and multiplication present in the Elements in spite of the link established by Proposition VIII.5.","PeriodicalId":211442,"journal":{"name":"BSHM Bulletin: Journal of the British Society for the History of Mathematics","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2015-08-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"121232334","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2015-07-20DOI: 10.1080/17498430.2015.1044161
D. Ball
L eaving aside Lewis Carroll, George Eliot was almost certainly the most mathematically proficient novelist of the mid-Victorian age. She also had a strong interest and belief in education, particularly mathematics education. As a woman, Eliot was inevitably an autodidact, and the need for and value of independent learning is reflected in her views about effective education. I shall demonstrate how she expressed these views within her novels, and conclude by discussing her depiction of the education of girls. In order to go far with mathematics, Eliot as a woman would have needed to have taken control of her own learning, and so posing her own mathematics problems was a necessity. But in this she was like her father, a farmer and eventually an estate manager. John Cross, Eliot’s widower, wrote about Eliot’s father’s ability to ‘calculate with almost absolute precision the quantity of timber in a standing tree’ (Cross 1885, 1:9). Eliot clearly admired this ability and alluded to it in her first novel when describing Adam Bede.
{"title":"‘Thick-rinded fruit of the tree of knowledge’: mathematics education in George Eliot's novels","authors":"D. Ball","doi":"10.1080/17498430.2015.1044161","DOIUrl":"https://doi.org/10.1080/17498430.2015.1044161","url":null,"abstract":"L eaving aside Lewis Carroll, George Eliot was almost certainly the most mathematically proficient novelist of the mid-Victorian age. She also had a strong interest and belief in education, particularly mathematics education. As a woman, Eliot was inevitably an autodidact, and the need for and value of independent learning is reflected in her views about effective education. I shall demonstrate how she expressed these views within her novels, and conclude by discussing her depiction of the education of girls. In order to go far with mathematics, Eliot as a woman would have needed to have taken control of her own learning, and so posing her own mathematics problems was a necessity. But in this she was like her father, a farmer and eventually an estate manager. John Cross, Eliot’s widower, wrote about Eliot’s father’s ability to ‘calculate with almost absolute precision the quantity of timber in a standing tree’ (Cross 1885, 1:9). Eliot clearly admired this ability and alluded to it in her first novel when describing Adam Bede.","PeriodicalId":211442,"journal":{"name":"BSHM Bulletin: Journal of the British Society for the History of Mathematics","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2015-07-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"128767544","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2015-06-05DOI: 10.1080/17498430.2015.1041072
J. Hunt, John . Sharp
We have been studying the geometry of anamorphic art which is a particular form of perspective where the picture has to be viewed from a special point in order to make sense of the image. Part of this work has been developing methods for resolving such images using a computer. In our work on one of the most famous anamorphic images, William Scrots’ 1546 portrait of Edward VI, the mathematics has been quite challenging. The results show that Scrots’ mastery of geometry was superb, and we make some suggestions as to how he might have constructed the painting especially the ellipses.
{"title":"Decoding William Scrots' anamorphic portrait of Edward VI","authors":"J. Hunt, John . Sharp","doi":"10.1080/17498430.2015.1041072","DOIUrl":"https://doi.org/10.1080/17498430.2015.1041072","url":null,"abstract":"We have been studying the geometry of anamorphic art which is a particular form of perspective where the picture has to be viewed from a special point in order to make sense of the image. Part of this work has been developing methods for resolving such images using a computer. In our work on one of the most famous anamorphic images, William Scrots’ 1546 portrait of Edward VI, the mathematics has been quite challenging. The results show that Scrots’ mastery of geometry was superb, and we make some suggestions as to how he might have constructed the painting especially the ellipses.","PeriodicalId":211442,"journal":{"name":"BSHM Bulletin: Journal of the British Society for the History of Mathematics","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2015-06-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"115842810","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2015-05-04DOI: 10.1080/17498430.2015.1036337
J. Schwermer
{"title":"Emil Artin's Iceland Journal 1925: “A World of Good”, edited by Tom Artin (ed) and Karin Tate (trans)","authors":"J. Schwermer","doi":"10.1080/17498430.2015.1036337","DOIUrl":"https://doi.org/10.1080/17498430.2015.1036337","url":null,"abstract":"","PeriodicalId":211442,"journal":{"name":"BSHM Bulletin: Journal of the British Society for the History of Mathematics","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2015-05-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"123868076","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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