A Chinese Mathematician in Plato's Cave. Virtual/Real Dimensions Of
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UNDERSTANDING MATHEMATICS to UNDERSTAND PLATO -THEAETEUS (147D-148B Salomon Ofman
UNDERSTANDING MATHEMATICS TO UNDERSTAND PLATO -THEAETEUS (147d-148b Salomon Ofman To cite this version: Salomon Ofman. UNDERSTANDING MATHEMATICS TO UNDERSTAND PLATO -THEAETEUS (147d-148b. Lato Sensu, revue de la Société de philosophie des sciences, Société de philosophie des sciences, 2014, 1 (1). hal-01305361 HAL Id: hal-01305361 https://hal.archives-ouvertes.fr/hal-01305361 Submitted on 20 Apr 2016 HAL is a multi-disciplinary open access L’archive ouverte pluridisciplinaire HAL, est archive for the deposit and dissemination of sci- destinée au dépôt et à la diffusion de documents entific research documents, whether they are pub- scientifiques de niveau recherche, publiés ou non, lished or not. The documents may come from émanant des établissements d’enseignement et de teaching and research institutions in France or recherche français ou étrangers, des laboratoires abroad, or from public or private research centers. publics ou privés. UNDERSTANDING MATHEMATICS TO UNDERSTAND PLATO - THEAETEUS (147d-148b) COMPRENDRE LES MATHÉMATIQUES POUR COMPRENDRE PLATON - THÉÉTÈTE (147d-148b) Salomon OFMAN Institut mathématique de Jussieu-PRG Histoire des Sciences mathématiques 4 Place Jussieu 75005 Paris [email protected] Abstract. This paper is an updated translation of an article published in French in the Journal Lato Sensu (I, 2014, p. 70-80). We study here the so- called ‘Mathematical part’ of Plato’s Theaetetus. Its subject concerns the incommensurability of certain magnitudes, in modern terms the question of the rationality or irrationality of the square roots of integers. As the most ancient text on the subject, and on Greek mathematics and mathematicians as well, its historical importance is enormous. -
The What and Why of Whole Number Arithmetic: Foundational Ideas from History, Language and Societal Changes
Portland State University PDXScholar Mathematics and Statistics Faculty Fariborz Maseeh Department of Mathematics Publications and Presentations and Statistics 3-2018 The What and Why of Whole Number Arithmetic: Foundational Ideas from History, Language and Societal Changes Xu Hu Sun University of Macau Christine Chambris Université de Cergy-Pontoise Judy Sayers Stockholm University Man Keung Siu University of Hong Kong Jason Cooper Weizmann Institute of Science SeeFollow next this page and for additional additional works authors at: https:/ /pdxscholar.library.pdx.edu/mth_fac Part of the Science and Mathematics Education Commons Let us know how access to this document benefits ou.y Citation Details Sun X.H. et al. (2018) The What and Why of Whole Number Arithmetic: Foundational Ideas from History, Language and Societal Changes. In: Bartolini Bussi M., Sun X. (eds) Building the Foundation: Whole Numbers in the Primary Grades. New ICMI Study Series. Springer, Cham This Book Chapter is brought to you for free and open access. It has been accepted for inclusion in Mathematics and Statistics Faculty Publications and Presentations by an authorized administrator of PDXScholar. Please contact us if we can make this document more accessible: [email protected]. Authors Xu Hu Sun, Christine Chambris, Judy Sayers, Man Keung Siu, Jason Cooper, Jean-Luc Dorier, Sarah Inés González de Lora Sued, Eva Thanheiser, Nadia Azrou, Lynn McGarvey, Catherine Houdement, and Lisser Rye Ejersbo This book chapter is available at PDXScholar: https://pdxscholar.library.pdx.edu/mth_fac/253 Chapter 5 The What and Why of Whole Number Arithmetic: Foundational Ideas from History, Language and Societal Changes Xu Hua Sun , Christine Chambris Judy Sayers, Man Keung Siu, Jason Cooper , Jean-Luc Dorier , Sarah Inés González de Lora Sued , Eva Thanheiser , Nadia Azrou , Lynn McGarvey , Catherine Houdement , and Lisser Rye Ejersbo 5.1 Introduction Mathematics learning and teaching are deeply embedded in history, language and culture (e.g. -
Writing the History of Mathematics: Interpretations of the Mathematics of the Past and Its Relation to the Mathematics of Today
Writing the History of Mathematics: Interpretations of the Mathematics of the Past and Its Relation to the Mathematics of Today Johanna Pejlare and Kajsa Bråting Contents Introduction.................................................................. 2 Traces of Mathematics of the First Humans........................................ 3 History of Ancient Mathematics: The First Written Sources........................... 6 History of Mathematics or Heritage of Mathematics?................................. 9 Further Views of the Past and Its Relation to the Present.............................. 15 Can History Be Recapitulated or Does Culture Matter?............................... 19 Concluding Remarks........................................................... 24 Cross-References.............................................................. 24 References................................................................... 24 Abstract In the present chapter, interpretations of the mathematics of the past are problematized, based on examples such as archeological artifacts, as well as written sources from the ancient Egyptian, Babylonian, and Greek civilizations. The distinction between history and heritage is considered in relation to Euler’s function concept, Cauchy’s sum theorem, and the Unguru debate. Also, the distinction between the historical past and the practical past,aswellasthe distinction between the historical and the nonhistorical relations to the past, are made concrete based on Torricelli’s result on an infinitely long solid from -
Library Trends V.55, No.3 Winter 2007
View metadata, citation and similar papers at core.ac.uk brought to you by CORE provided by Illinois Digital Environment for Access to Learning and... Badly Wanted, but Not for Reading: The Unending Odyssey of The Complete Library of Four Treasures of the Wensu Library Chengzhi Wang Abstract The Chinese book project Siku Quanshu (The Complete Library of Four Treasures) was conducted at the Emperor Qianlong’s command start- ing in 1772. Thirteen thousand two hundred fifty-four books were collected nationwide and thousands of scholars were involved; 3,462 books were selected to make up the Siku Quanshu proper. Over 4 million pages were transcribed by thousands of copyists. Out of the seven copies made, only three copies survived the dramatic histori- cal changes of the nineteenth and twentieth centuries almost intact. This article traces the odyssey of the Wenshu Ge copy, particularly in the rapidly changing sociopolitical and economic contexts of the twentieth century. The emphasis of the article is placed on the de- scription and analysis of its relocation in the early 1920s soon after China was transformed into a republic; in the 1960s at the height of the Cold War when China split from and confronted the USSR; and in particular, in the new era of reform and opening up for economic development since the late 1970s. After the turn of the century, the two-decade competition between Liaoning Province and Gansu Province for physically keeping the copy has become increasingly intense at the national, provincial, and local levels, and the competi- tion has created significant impacts on library building and cultural development in the two provinces and beyond. -
Ancient Rhetoric and Greek Mathematics: a Response to a Modern Historiographical Dilemma
Science in Context 16(3), 391–412 (2003). Copyright © Cambridge University Press DOI: 10.1017/S0269889703000863 Printed in the United Kingdom Ancient Rhetoric and Greek Mathematics: A Response to a Modern Historiographical Dilemma Alain Bernard Dibner Institute, Boston To the memory of three days in the Negev Argument In this article, I compare Sabetai Unguru’s and Wilbur Knorr’s views on the historiography of ancient Greek mathematics. Although they share the same concern for avoiding anach- ronisms, they take very different stands on the role mathematical readings should have in the interpretation of ancient mathematics. While Unguru refuses any intrusion of mathematical practice into history, Knorr believes this practice to be a key tool for understanding the ancient tradition of geometry. Thus modern historians have to find their way between these opposing views while avoiding an unsatisfactory compromise. One approach to this, I propose, is to take ancient rhetoric into account. I illustrate this proposal by showing how rhetorical categories can help us to analyze mathematical texts. I finally show that such an approach accommodates Knorr’s concern about ancient mathematical practice as well as the standards for modern historical research set by Unguru 25 years ago. Introduction The title of the present paper indicates that this work concerns the relationship between ancient rhetoric and ancient Greek mathematics. Such a title obviously raises a simple question: Is there such a relationship? The usual appreciation of ancient science and philosophy is at odds with such an idea. This appreciation is rooted in the pregnant categorization that ranks rhetoric and science at very different levels. -
Life, Thought and Image of Wang Zheng, a Confucian-Christian in Late Ming China
Life, Thought and Image of Wang Zheng, a Confucian-Christian in Late Ming China Inaugural-Dissertation zur Erlangung der Doktorwürde der Philosophischen Fakultät der Rheinischen Friedrich-Wilhelms-Universität zu Bonn vorgelegt von Ruizhong Ding aus Qishan, VR. China Bonn, 2019 Gedruckt mit der Genehmigung der Philosophischen Fakultät der Rheinischen Friedrich-Wilhelms-Universität Bonn Zusammensetzung der Prüfungskommission: Prof. Dr. Dr. Manfred Hutter, Institut für Orient- und Asienwissenschaften (Vorsitzender) Prof. Dr. Wolfgang Kubin, Institut für Orient- und Asienwissenschaften (Betreuer und Gutachter) Prof. Dr. Ralph Kauz, Institut für Orient- und Asienwissenschaften (Gutachter) Prof. Dr. Veronika Veit, Institut für Orient- und Asienwissenschaften (weiteres prüfungsberechtigtes Mitglied) Tag der mündlichen Prüfung:22.07.2019 Acknowledgements Currently, when this dissertation is finished, I look out of the window with joyfulness and I would like to express many words to all of you who helped me. Prof. Wolfgang Kubin accepted me as his Ph.D student and in these years he warmly helped me a lot, not only with my research but also with my life. In every meeting, I am impressed by his personality and erudition deeply. I remember one time in his seminar he pointed out my minor errors in the speech paper frankly and patiently. I am indulged in his beautiful German and brilliant poetry. His translations are full of insightful wisdom. Every time when I meet him, I hope it is a long time. I am so grateful that Prof. Ralph Kauz in the past years gave me unlimited help. In his seminars, his academic methods and sights opened my horizons. Usually, he supported and encouraged me to study more fields of research. -
Solving a System of Linear Equations Using Ancient Chinese Methods
Solving a System of Linear Equations Using Ancient Chinese Methods Mary Flagg University of St. Thomas Houston, TX JMM January 2018 Mary Flagg (University of St. Thomas Houston,Solving TX) a System of Linear Equations Using Ancient ChineseJMM Methods January 2018 1 / 22 Outline 1 Gaussian Elimination 2 Chinese Methods 3 The Project 4 TRIUMPHS Mary Flagg (University of St. Thomas Houston,Solving TX) a System of Linear Equations Using Ancient ChineseJMM Methods January 2018 2 / 22 Gaussian Elimination Question History Question Who invented Gaussian Elimination? When was Gaussian Elimination developed? Carl Friedrick Gauss lived from 1777-1855. Arthur Cayley was one of the first to create matrix algebra in 1858. Mary Flagg (University of St. Thomas Houston,Solving TX) a System of Linear Equations Using Ancient ChineseJMM Methods January 2018 3 / 22 Gaussian Elimination Ancient Chinese Origins Juizhang Suanshu The Nine Chapters on the Mathematical Art is an anonymous text compiled during the Qin and Han dynasties 221 BCE - 220 AD. It consists of 246 problems and their solutions arranged in 9 chapters by topic. Fangcheng Chapter 8 of the Nine Chapters is translated as Rectangular Arrays. It concerns the solution of systems of linear equations. Liu Hui The Chinese mathematician Liu Hui published an annotated version of The Nine Chapters in 263 AD. His comments contain a detailed explanation of the Fangcheng Rule Mary Flagg (University of St. Thomas Houston,Solving TX) a System of Linear Equations Using Ancient ChineseJMM Methods January 2018 4 / 22 Chinese Methods Counting Rods The ancient Chinese used counting rods to represent numbers and perform arithmetic. -
The Function of Diorism in Ancient Greek Analysis
View metadata, citation and similar papers at core.ac.uk brought to you by CORE provided by Elsevier - Publisher Connector Available online at www.sciencedirect.com Historia Mathematica 37 (2010) 579–614 www.elsevier.com/locate/yhmat The function of diorism in ancient Greek analysis Ken Saito a, Nathan Sidoli b, a Department of Human Sciences, Osaka Prefecture University, Japan b School of International Liberal Studies, Waseda University, Japan Available online 26 May 2010 Abstract This paper is a contribution to our knowledge of Greek geometric analysis. In particular, we investi- gate the aspect of analysis know as diorism, which treats the conditions, arrangement, and totality of solutions to a given geometric problem, and we claim that diorism must be understood in a broader sense than historians of mathematics have generally admitted. In particular, we show that diorism was a type of mathematical investigation, not only of the limitation of a geometric solution, but also of the total number of solutions and of their arrangement. Because of the logical assumptions made in the analysis, the diorism was necessarily a separate investigation which could only be carried out after the analysis was complete. Ó 2009 Elsevier Inc. All rights reserved. Re´sume´ Cet article vise a` contribuer a` notre compre´hension de l’analyse geometrique grecque. En particulier, nous examinons un aspect de l’analyse de´signe´ par le terme diorisme, qui traite des conditions, de l’arrangement et de la totalite´ des solutions d’un proble`me ge´ome´trique donne´, et nous affirmons que le diorisme doit eˆtre saisi dans un sens plus large que celui pre´ce´demment admis par les historiens des mathe´matiques. -
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Advances in Social Science, Education and Humanities Research, volume 283 International Conference on Contemporary Education, Social Sciences and Ecological Studies (CESSES 2018) Quantitative Estimation and Use Condition of Learning Materials for Official Ci Poetry in Ming Dynasty* Xuan Liu School of Language and Literature Harbin Institute of Technology, Weihai Weihai, China 264209 Yan Teng Jiaoling Jin School of Language and Literature School of Language and Literature Harbin Institute of Technology, Weihai Harbin Institute of Technology, Weihai Weihai, China 264209 Weihai, China 264209 Abstract—There were abundant learning materials of Ci reading these comments, learners learned what kind of Ci poetry in Ming Dynasty, which were mainly concentrated in the poems the authorities think were good works and what kind of palace, central departments, local government offices and Ci poems were not good, so as to establish their own imperial vassals’ residence. These materials can be read and sold evaluation criteria. Fourth, it is score of Ci. The Song Dynasty in printed form, promoting the study of people in the Ming also had Ci scores. Those were music scores, used to sing. But Dynasty and improving the creation of Ci poetry. Due to the scholars of the Ming Dynasty have been unable to understand dynastic change from Ming Dynasty to Qing Dynasty, it greatly such scores, so they compiled some more easily destroyed learning materials of Ci poetry in Ming Dynasty, and understandable metrical scores. Beginners could complete a Ci some precious and rare materials were lost. However, the poem according to the tone and format marked by the score. materials with large sales were preserved, which provided the Fifth, it is Ci rhyme. -
A Mathematician Reads Plutarch: Plato's Criticism of Geometers of His Time
View metadata, citation and similar papers at core.ac.uk brought to you by CORE provided by Scholarship@Claremont Journal of Humanistic Mathematics Volume 7 | Issue 2 July 2017 A Mathematician Reads Plutarch: Plato's Criticism of Geometers of His Time John B. Little College of the Holy Cross Follow this and additional works at: https://scholarship.claremont.edu/jhm Part of the Ancient History, Greek and Roman through Late Antiquity Commons, and the Mathematics Commons Recommended Citation Little, J. B. "A Mathematician Reads Plutarch: Plato's Criticism of Geometers of His Time," Journal of Humanistic Mathematics, Volume 7 Issue 2 (July 2017), pages 269-293. DOI: 10.5642/ jhummath.201702.13 . Available at: https://scholarship.claremont.edu/jhm/vol7/iss2/13 ©2017 by the authors. This work is licensed under a Creative Commons License. JHM is an open access bi-annual journal sponsored by the Claremont Center for the Mathematical Sciences and published by the Claremont Colleges Library | ISSN 2159-8118 | http://scholarship.claremont.edu/jhm/ The editorial staff of JHM works hard to make sure the scholarship disseminated in JHM is accurate and upholds professional ethical guidelines. However the views and opinions expressed in each published manuscript belong exclusively to the individual contributor(s). The publisher and the editors do not endorse or accept responsibility for them. See https://scholarship.claremont.edu/jhm/policies.html for more information. A Mathematician Reads Plutarch: Plato's Criticism of Geometers of His Time Cover Page Footnote This essay originated as an assignment for Professor Thomas Martin's Plutarch seminar at Holy Cross in Fall 2016. -
The Influence of Chinese Mathematical Arts on Seki Kowa
THE INFLUENCE OF CHINESE MATHEMATICAL ARTS ON SEKI KOWA b y SHIGERU JOCHI, M.A. (Tokai) Thesis submitted for the degree of Ph.D. School of Oriental and African Studies, University of London. 1 9 9 3 ProQuest Number: 10673061 All rights reserved INFORMATION TO ALL USERS The quality of this reproduction is dependent upon the quality of the copy submitted. In the unlikely event that the author did not send a com plete manuscript and there are missing pages, these will be noted. Also, if material had to be removed, a note will indicate the deletion. uest ProQuest 10673061 Published by ProQuest LLC(2017). Copyright of the Dissertation is held by the Author. All rights reserved. This work is protected against unauthorized copying under Title 17, United States C ode Microform Edition © ProQuest LLC. ProQuest LLC. 789 East Eisenhower Parkway P.O. Box 1346 Ann Arbor, Ml 48106- 1346 ABSTRACT I will consider the influence of Chinese mathematics on Seki Kowa. For this purpose, my thesis is constructed in four parts, introduction, I the studies of editions; Shu Shn Jin Zhang and Yang Uni S u m Fa, II the conception and extension of method for making magic squares, and 1 the analysis for solving indeterminate equations. In the introduction, I will explain some similarities between Chinese mathematics in the Song dynasty and Seki Kowa's works. It will become clear that the latter was influenced by Chinese mathematics. Then I introduce some former opinions concerning which Chinese mathematical book influenced him. I shall show that two Chinese mathematical books, Shn Shn Jin Zhang and Yang Hni S u m Fa, are particularly important. -
Tool 44: Prime Numbers
PART IV: Cinematography & Mathematics AGE RANGE: 13-15 1 TOOL 44: PRIME NUMBERS - THE MAN WHO KNEW INFINITY Sandgärdskolan This project has been funded with support from the European Commission. This publication reflects the views only of the author, and the Commission cannot be held responsible for any use which may be made of the information contained therein. Educator’s Guide Title: The man who knew infinity – prime numbers Age Range: 13-15 years old Duration: 2 hours Mathematical Concepts: Prime numbers, Infinity Artistic Concepts: Movie genres, Marvel heroes, vanishing point General Objectives: This task will make you learn more about infinity. It wants you to think for yourself about the word infinity. What does it say to you? It will also show you the connection between infinity and prime numbers. Resources: This tool provides pictures and videos for you to use in your classroom. The topics addressed in these resources will also be an inspiration for you to find other materials that you might find relevant in order to personalize and give nuance to your lesson. Tips for the educator: Learning by doing has proven to be very efficient, especially with young learners with lower attention span and learning difficulties. Don’t forget to 2 always explain what each math concept is useful for, practically. Desirable Outcomes and Competences: At the end of this tool, the student will be able to: Understand prime numbers and infinity in an improved way. Explore super hero movies. Debriefing and Evaluation: Write 3 aspects that you liked about this 1. activity: 2. 3.