Revolutions And Continuity In Greek Mathematics

Author : Michalis Sialaros
Publisher : Walter de Gruyter GmbH & Co KG
ISBN 13 : 3110565951
Total Pages : 401 pages
Book Rating : 4.59/5 ( download)

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Download or read book Revolutions and Continuity in Greek Mathematics written by Michalis Sialaros and published by Walter de Gruyter GmbH & Co KG. This book was released on 2018-04-23 with total page 401 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume brings together a number of leading scholars working in the field of ancient Greek mathematics to present their latest research. In their respective area of specialization, all contributors offer stimulating approaches to questions of historical and historiographical ‘revolutions’ and ‘continuity’. Taken together, they provide a powerful lens for evaluating the applicability of Thomas Kuhn’s ideas on ‘scientific revolutions’ to the discipline of ancient Greek mathematics. Besides the latest historiographical studies on ‘geometrical algebra’ and ‘premodern algebra’, the reader will find here some papers which offer new insights into the controversial relationship between Greek and pre-Hellenic mathematical practices. Some other contributions place emphasis on the other edge of the historical spectrum, by exploring historical lines of ‘continuity’ between ancient Greek, Byzantine and post-Hellenic mathematics. The terminology employed by Greek mathematicians, along with various non-textual and material elements, is another topic which some of the essays in the volume explore. Finally, the last three articles focus on a traditionally rich source on ancient Greek mathematics; namely the works of Plato and Aristotle.

Author : Michalis Sialaros
Publisher : Walter de Gruyter GmbH & Co KG
ISBN 13 : 3110565277
Total Pages : 401 pages
Book Rating : 4.70/5 ( download)

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Download or read book Revolutions and Continuity in Greek Mathematics written by Michalis Sialaros and published by Walter de Gruyter GmbH & Co KG. This book was released on 2018-04-23 with total page 401 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume brings together a number of leading scholars working in the field of ancient Greek mathematics to present their latest research. In their respective area of specialization, all contributors offer stimulating approaches to questions of historical and historiographical ‘revolutions’ and ‘continuity’. Taken together, they provide a powerful lens for evaluating the applicability of Thomas Kuhn’s ideas on ‘scientific revolutions’ to the discipline of ancient Greek mathematics. Besides the latest historiographical studies on ‘geometrical algebra’ and ‘premodern algebra’, the reader will find here some papers which offer new insights into the controversial relationship between Greek and pre-Hellenic mathematical practices. Some other contributions place emphasis on the other edge of the historical spectrum, by exploring historical lines of ‘continuity’ between ancient Greek, Byzantine and post-Hellenic mathematics. The terminology employed by Greek mathematicians, along with various non-textual and material elements, is another topic which some of the essays in the volume explore. Finally, the last three articles focus on a traditionally rich source on ancient Greek mathematics; namely the works of Plato and Aristotle.

Author :
Publisher : BRILL
ISBN 13 : 900446722X
Total Pages : 297 pages
Book Rating : 4.24/5 ( download)

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Download or read book Numbers and Numeracy in the Greek Polis written by and published by BRILL. This book was released on 2021-12-20 with total page 297 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is a wide-ranging study of numbers as a social and cultural phenomenon in ancient Greece, revealing both the instrumentality of numbers to polis life and the complex cultural meanings inherent in their use.

Author : Fabio Acerbi
Publisher : Springer Nature
ISBN 13 : 3030769593
Total Pages : 396 pages
Book Rating : 4.98/5 ( download)

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Download or read book The Logical Syntax of Greek Mathematics written by Fabio Acerbi and published by Springer Nature. This book was released on 2021-06-21 with total page 396 pages. Available in PDF, EPUB and Kindle. Book excerpt: The aim of this monograph is to describe Greek mathematics as a literary product, studying its style from a logico-syntactic point of view and setting parallels with logical and grammatical doctrines developed in antiquity. In this way, major philosophical themes such as the expression of mathematical generality and the selection of criteria of validity for arguments can be treated without anachronism. Thus, the book is of interest for both historians of ancient philosophy and specialists in Ancient Greek, in addition to historians of mathematics. This volume is divided into five parts, ordered in decreasing size of the linguistic units involved. The first part describes the three stylistic codes of Greek mathematics; the second expounds in detail the mechanism of "validation"; the third deals with the status of mathematical objects and the problem of mathematical generality; the fourth analyzes the main features of the "deductive machine," i.e. the suprasentential logical system dictated by the traditional division of a mathematical proposition into enunciation, setting-out, construction, and proof; and the fifth deals with the sentential logical system of a mathematical proposition, with special emphasis on quantification, modalities, and connectors. A number of complementary appendices are included as well.

Author : Bharath Sriraman
Publisher : Springer Nature
ISBN 13 : 3031408462
Total Pages : 3221 pages
Book Rating : 4.65/5 ( download)

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Download or read book Handbook of the History and Philosophy of Mathematical Practice written by Bharath Sriraman and published by Springer Nature. This book was released on with total page 3221 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Author : Niccolò Guicciardini
Publisher : Cambridge University Press
ISBN 13 : 1108883281
Total Pages : 394 pages
Book Rating : 4.83/5 ( download)

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Download or read book Anachronisms in the History of Mathematics written by Niccolò Guicciardini and published by Cambridge University Press. This book was released on 2021-07-22 with total page 394 pages. Available in PDF, EPUB and Kindle. Book excerpt: The controversial matters surrounding the notion of anachronism are difficult ones: they have been broached by literary and art critics, by philosophers, as well as by historians of science. This book adopts a bottom-up approach to the many problems concerning anachronism in the history of mathematics. Some of the leading scholars in the field of history of mathematics reflect on the applicability of present-day mathematical language, concepts, standards, disciplinary boundaries, indeed notions of mathematics itself, to well-chosen historical case studies belonging to the mathematics of the past, in European and non-European cultures. A detailed introduction describes the key themes and binds the various chapters together. The interdisciplinary and transcultural approach adopted allows this volume to cover topics important for history of mathematics, history of the physical sciences, history of science, philosophy of mathematics, history of philosophy, methodology of history, non-European science, and the transmission of mathematical knowledge across cultures.

Author : S. G. Dani
Publisher : Springer Nature
ISBN 13 : 3030136094
Total Pages : 759 pages
Book Rating : 4.93/5 ( download)

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Download or read book Geometry in History written by S. G. Dani and published by Springer Nature. This book was released on 2019-10-18 with total page 759 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is a collection of surveys on important mathematical ideas, their origin, their evolution and their impact in current research. The authors are mathematicians who are leading experts in their fields. The book is addressed to all mathematicians, from undergraduate students to senior researchers, regardless of the specialty.

Author : Matteo Valleriani
Publisher : Springer Nature
ISBN 13 : 3031113179
Total Pages : 369 pages
Book Rating : 4.78/5 ( download)

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Download or read book Scientific Visual Representations in History written by Matteo Valleriani and published by Springer Nature. This book was released on 2023-01-01 with total page 369 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book explores continuity and ruptures in the historical use of visual representations in science and related disciplines such as art history and anthropology. The book also considers more recent developments that attest to the unprecedented importance of scientific visualizations, such as video recordings, animations, simulations, graphs, and enhanced realities. The volume collects historical reflections concerned with the use of visual material, visualization, and vision in science from a historical perspective, ranging across multiple cultures from antiquity until present day. The focus is on visual representations such as drawings, prints, tables, mathematical symbols, photos, data visualizations, mapping processes, and (on a meta-level) visualizations of data extracted from historical sources to visually support the historical research itself. Continuity and ruptures between the past and present use of visual material are presented against the backdrop of the epistemic functions of visual material in science. The function of visual material is defined according to three major epistemic categories: exploration, transformation, and transmission of knowledge.

Author : Jean Christianidis
Publisher : Taylor & Francis
ISBN 13 : 1351694979
Total Pages : 891 pages
Book Rating : 4.71/5 ( download)

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Download or read book The Arithmetica of Diophantus written by Jean Christianidis and published by Taylor & Francis. This book was released on 2022-11-01 with total page 891 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume offers an English translation of all ten extant books of Diophantus of Alexandria’s Arithmetica, along with a comprehensive conceptual, historical, and mathematical commentary. Before his work became the inspiration for the emerging field of number theory in the seventeenth century, Diophantus (ca. 3rd c. CE) was known primarily as an algebraist. This volume explains how his method of solving arithmetical problems agrees both conceptually and procedurally with the premodern algebra later practiced in Arabic, Latin, and European vernaculars, and how this algebra differs radically from the modern algebra initiated by François Viète and René Descartes. It also discusses other surviving traces of ancient Greek algebra and follows the influence of the Arithmetica in medieval Islam, Byzantium, and the European Renaissance down to the 1621 publication of Claude-Gaspard Bachet’s edition. After the English translation the book provides a problem-by-problem commentary explaining the solutions in a manner compatible with Diophantus’s mode of thought. The Arithmetica of Diophantus provides an invaluable resource for historians of mathematics, science, and technology, as well as those studying ancient Greek, medieval Islamic and Byzantine, and Renaissance history. In addition, the volume is also suitable for mathematicians and mathematics educators.

Author : Carlo Cellucci
Publisher : Springer Nature
ISBN 13 : 3030897311
Total Pages : 457 pages
Book Rating : 4.14/5 ( download)

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Download or read book The Making of Mathematics written by Carlo Cellucci and published by Springer Nature. This book was released on 2022-03-07 with total page 457 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book offers an alternative to current philosophy of mathematics: heuristic philosophy of mathematics. In accordance with the heuristic approach, the philosophy of mathematics must concern itself with the making of mathematics and in particular with mathematical discovery. In the past century, mainstream philosophy of mathematics has claimed that the philosophy of mathematics cannot concern itself with the making of mathematics but only with finished mathematics, namely mathematics as presented in published works. On this basis, mainstream philosophy of mathematics has maintained that mathematics is theorem proving by the axiomatic method. This view has turned out to be untenable because of Gödel’s incompleteness theorems, which have shown that the view that mathematics is theorem proving by the axiomatic method does not account for a large number of basic features of mathematics. By using the heuristic approach, this book argues that mathematics is not theorem proving by the axiomatic method, but is rather problem solving by the analytic method. The author argues that this view can account for the main items of the mathematical process, those being: mathematical objects, demonstrations, definitions, diagrams, notations, explanations, applicability, beauty, and the role of mathematical knowledge.