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Comprendre les math'ematiques pour comprendre Platon - th'e'et`ete (147d-148b) 理解数学来理解柏拉图- th'e'和' ete (147d-148b)
arXiv: History and Overview Pub Date : 2014-07-01 DOI: 10.20416/LSRSPS.V1I1.53
S. Ofman
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引用次数: 3
Mathematical Analysis of Melodies: Slope and Discrete Frechet Distance 旋律的数学分析:坡度和离散Frechet距离
arXiv: History and Overview Pub Date : 2014-06-21 DOI: 10.17654/FJMSJUL2015_583_615
F. Hazama
{"title":"Mathematical Analysis of Melodies: Slope and Discrete Frechet Distance","authors":"F. Hazama","doi":"10.17654/FJMSJUL2015_583_615","DOIUrl":"https://doi.org/10.17654/FJMSJUL2015_583_615","url":null,"abstract":"A directed graph, called an M-graph, is attached to every melody. Our chief concern in this paper is to investigate (1) how the positivity of the slope of the M-graph is related to singability of the melody, (2) when the M-graph has a symmetry, and (3) how we can detect a similarity between two melodies. For the third theme, we introduce the notion of transposed discrete Frechet distance, and show its relevance in the study of similarity detection among an arbitrary set of melodies.","PeriodicalId":429168,"journal":{"name":"arXiv: History and Overview","volume":"13 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2014-06-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"116808876","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}
引用次数: 0
Pythagoras at the Bat 毕达哥拉斯挥棒
arXiv: History and Overview Pub Date : 2014-05-29 DOI: 10.1007/978-3-319-08440-4_6
Steven J. Miller, Taylor C. Corcoran, Jennifer Gossels, Victor Luo, Jaclyn D. Porfilio
{"title":"Pythagoras at the Bat","authors":"Steven J. Miller, Taylor C. Corcoran, Jennifer Gossels, Victor Luo, Jaclyn D. Porfilio","doi":"10.1007/978-3-319-08440-4_6","DOIUrl":"https://doi.org/10.1007/978-3-319-08440-4_6","url":null,"abstract":"","PeriodicalId":429168,"journal":{"name":"arXiv: History and Overview","volume":"35 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2014-05-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"129464918","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}
引用次数: 5
The Anthyphairetic Revolutions of the Platonic Ideas 柏拉图思想的Anthyphairetic革命
arXiv: History and Overview Pub Date : 2014-05-16 DOI: 10.1515/9783110565959-013
S. Negrepontis
{"title":"The Anthyphairetic Revolutions of the Platonic Ideas","authors":"S. Negrepontis","doi":"10.1515/9783110565959-013","DOIUrl":"https://doi.org/10.1515/9783110565959-013","url":null,"abstract":"In the present work it is shown, by an examination of the Platonic dialogues Theaetetus, Sophistes, Politicus, and Philebus, that (a) a Platonic Idea is the philosophic analogue of a pair of lines incommensurable in length only, (b) the Division and Collection, the method by which humans obtain knowledge of a Platonic Idea, is the philosophic analogue of the palindromically periodic anthyphairesis of this pair, and (c) a Platonic Idea is One in the sense of the self-similarity induced by periodic anthyphairesis. \u0000A byproduct of the above analysis is that (d) Theaetetus had obtained a proof of the Proposition: The anthyphairesis of a dyad of lines incommensurable in length only is palindromically periodic. It is further verified that the concepts and tools contained in the Theaetetean Book X of the Elements suffice for the proof of the Proposition.","PeriodicalId":429168,"journal":{"name":"arXiv: History and Overview","volume":"36 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2014-05-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"124446964","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}
引用次数: 1
The Quaternion Group as a Symmetry Group 作为对称群的四元数群
arXiv: History and Overview Pub Date : 2014-04-25 DOI: 10.2307/j.ctvc778jw.17
Vi Hart, Henry Segerman
{"title":"The Quaternion Group as a Symmetry Group","authors":"Vi Hart, Henry Segerman","doi":"10.2307/j.ctvc778jw.17","DOIUrl":"https://doi.org/10.2307/j.ctvc778jw.17","url":null,"abstract":"We briefly review the distinction between abstract groups and symmetry groups of objects, and discuss the question of which groups have appeared as the symmetry groups of physical objects. To our knowledge, the quaternion group (a beautiful group with eight elements) has not appeared in this fashion. We describe the quaternion group, both formally and intuitively, and give our strategy for representing the quaternion group as the symmetry group of a physical sculpture.","PeriodicalId":429168,"journal":{"name":"arXiv: History and Overview","volume":"50 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2014-04-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"124547587","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}
引用次数: 14
Bridging knowing and proving in mathematics An essay from a didactical perspective 从教学角度出发的一篇文章
arXiv: History and Overview Pub Date : 2014-03-27 DOI: 10.1007/978-1-4419-0576-5_9
N. Balacheff
{"title":"Bridging knowing and proving in mathematics An essay from a didactical perspective","authors":"N. Balacheff","doi":"10.1007/978-1-4419-0576-5_9","DOIUrl":"https://doi.org/10.1007/978-1-4419-0576-5_9","url":null,"abstract":"","PeriodicalId":429168,"journal":{"name":"arXiv: History and Overview","volume":"58 8","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2014-03-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"113941076","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}
引用次数: 37
An American mathematician in Moscow, or how I destroyed the Soviet Union 一位在莫斯科的美国数学家，或是我如何摧毁苏联
arXiv: History and Overview Pub Date : 2014-02-01 DOI: 10.1090/NOTI1076
M. Nathanson
{"title":"An American mathematician in Moscow, or how I destroyed the Soviet Union","authors":"M. Nathanson","doi":"10.1090/NOTI1076","DOIUrl":"https://doi.org/10.1090/NOTI1076","url":null,"abstract":"Reminiscences about I. M. Gel'fand on the 100th anniversary of his birth, and about mathematical life in Moscow in the former Soviet Union.","PeriodicalId":429168,"journal":{"name":"arXiv: History and Overview","volume":"685 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2014-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"116955933","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}
引用次数: 0
Some Thoughts on the Teaching of Mathematics -- ten years later 关于数学教学的几点思考——十年后
arXiv: History and Overview Pub Date : 2014-01-04 DOI: 10.1090/NOTI1131
Igor Rivin
{"title":"Some Thoughts on the Teaching of Mathematics -- ten years later","authors":"Igor Rivin","doi":"10.1090/NOTI1131","DOIUrl":"https://doi.org/10.1090/NOTI1131","url":null,"abstract":"I describe some deep-seated problems in higher mathematical education, and give some ideas for their solution -- I advocate a move away from the traditional introduction of mathematics through calculus, and towards computation and discrete mathematics.","PeriodicalId":429168,"journal":{"name":"arXiv: History and Overview","volume":"32 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2014-01-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"131227805","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}
引用次数: 1
An interview with Tsuyoshi Ando 采访安藤刚
arXiv: History and Overview Pub Date : 2013-11-28 DOI: 10.15352/AFA/1396833513
R. Brualdi, M. Moslehian
{"title":"An interview with Tsuyoshi Ando","authors":"R. Brualdi, M. Moslehian","doi":"10.15352/AFA/1396833513","DOIUrl":"https://doi.org/10.15352/AFA/1396833513","url":null,"abstract":"In celebration of the distinguished achievements of Professor Tsuyoshi Ando in matrix analysis and operator theory, we conducted an interview with him via email. This paper presents Professor Ando's responses to several questions we gave him regarding his education and life as a mathematician.","PeriodicalId":429168,"journal":{"name":"arXiv: History and Overview","volume":"91 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2013-11-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"120858301","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}
引用次数: 0
On the life and scientific work of Gino Fano 论吉诺·法诺的生平和科学工作
arXiv: History and Overview Pub Date : 2013-11-27 DOI: 10.4310/ICCM.2014.V2.N1.A9
A. Collino, A. Conte, A. Verra
{"title":"On the life and scientific work of Gino Fano","authors":"A. Collino, A. Conte, A. Verra","doi":"10.4310/ICCM.2014.V2.N1.A9","DOIUrl":"https://doi.org/10.4310/ICCM.2014.V2.N1.A9","url":null,"abstract":"A collection of selected papers of Gino Fano, containing most of his research papers in Italian, is now available on line at the site of Biblioteca Digitale Italiana di Matematica. The address is: this http URL The realization of this collection on line is part of a joint project of Unione Matematica Italiana (UMI) and Societa' Italiana per la Matematica Applicata e Industriale (SIMAI). The present submission to arXiv is the introduction to the collection and an announcement of it as well.","PeriodicalId":429168,"journal":{"name":"arXiv: History and Overview","volume":"10 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2013-11-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"115106160","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}
引用次数: 1
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