Sourcebook in the Mathematics of Medieval Europe and North Africa

Author: Victor J. Katz,Menso Folkerts,Barnabas Hughes,Roi Wagner,J. Lennart Berggren

Publisher: Princeton University Press

ISBN: 1400883202

Category: Mathematics

Page: 592

View: 9892

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Medieval Europe was a meeting place for the Christian, Jewish, and Islamic civilizations, and the fertile intellectual exchange of these cultures can be seen in the mathematical developments of the time. This sourcebook presents original Latin, Hebrew, and Arabic sources of medieval mathematics, and shows their cross-cultural influences. Most of the Hebrew and Arabic sources appear here in translation for the first time. Readers will discover key mathematical revelations, foundational texts, and sophisticated writings by Latin, Hebrew, and Arabic-speaking mathematicians, including Abner of Burgos's elegant arguments proving results on the conchoid—a curve previously unknown in medieval Europe; Levi ben Gershon’s use of mathematical induction in combinatorial proofs; Al-Mu’taman Ibn Hūd’s extensive survey of mathematics, which included proofs of Heron’s Theorem and Ceva’s Theorem; and Muhyī al-Dīn al-Maghribī’s interesting proof of Euclid’s parallel postulate. The book includes a general introduction, section introductions, footnotes, and references. The Sourcebook in the Mathematics of Medieval Europe and North Africa will be indispensable to anyone seeking out the important historical sources of premodern mathematics.
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Making and Breaking Mathematical Sense

Histories and Philosophies of Mathematical Practice

Author: Roi Wagner

Publisher: Princeton University Press

ISBN: 1400883784

Category: Mathematics

Page: 256

View: 351

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In line with the emerging field of philosophy of mathematical practice, this book pushes the philosophy of mathematics away from questions about the reality and truth of mathematical entities and statements and toward a focus on what mathematicians actually do—and how that evolves and changes over time. How do new mathematical entities come to be? What internal, natural, cognitive, and social constraints shape mathematical cultures? How do mathematical signs form and reform their meanings? How can we model the cognitive processes at play in mathematical evolution? And how does mathematics tie together ideas, reality, and applications? Roi Wagner uniquely combines philosophical, historical, and cognitive studies to paint a fully rounded image of mathematics not as an absolute ideal but as a human endeavor that takes shape in specific social and institutional contexts. The book builds on ancient, medieval, and modern case studies to confront philosophical reconstructions and cutting-edge cognitive theories. It focuses on the contingent semiotic and interpretive dimensions of mathematical practice, rather than on mathematics' claim to universal or fundamental truths, in order to explore not only what mathematics is, but also what it could be. Along the way, Wagner challenges conventional views that mathematical signs represent fixed, ideal entities; that mathematical cognition is a rigid transfer of inferences between formal domains; and that mathematics’ exceptional consensus is due to the subject’s underlying reality. The result is a revisionist account of mathematical philosophy that will interest mathematicians, philosophers, and historians of science alike.
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Plato’s forms, mathematics and astronomy

Author: Theokritos Kouremenos

Publisher: Walter de Gruyter GmbH & Co KG

ISBN: 3110601486

Category: Literary Criticism

Page: 158

View: 8510

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Plato’s view that mathematics paves the way for his philosophy of forms is well known. This book attempts to flesh out the relationship between mathematics and philosophy as Plato conceived them by proposing that in his view, although it is philosophy that came up with the concept of beings, which he calls forms, and highlighted their importance, first to natural philosophy and then to ethics, the things that do qualify as beings are inchoately revealed by mathematics as the raw materials that must be further processed by philosophy (mathematicians, to use Plato’s simile in the Euthedemus, do not invent the theorems they prove but discover beings and, like hunters who must hand over what they catch to chefs if it is going to turn into something useful, they must hand over their discoveries to philosophers). Even those forms that do not bear names of mathematical objects, such as the famous forms of beauty and goodness, are in fact forms of mathematical objects. The first chapter is an attempt to defend this thesis. The second argues that for Plato philosophy’s crucial task of investigating the exfoliation of the forms into the sensible world, including the sphere of human private and public life, is already foreshadowed in one of its branches, astronomy.
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The Best Writing on Mathematics 2019

Author: Mircea Pitici

Publisher: Princeton University Press

ISBN: 0691198357

Category: Crafts & Hobbies

Page: 304

View: 4912

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The year's finest mathematical writing from around the world This annual anthology brings together the year's finest mathematics writing from around the world. Featuring promising new voices alongside some of the foremost names in the field, The Best Writing on Mathematics 2019 makes available to a wide audience many articles not easily found anywhere else—and you don't need to be a mathematician to enjoy them. These essays delve into the history, philosophy, teaching, and everyday aspects of math, offering surprising insights into its nature, meaning, and practice—and taking readers behind the scenes of today's hottest mathematical debates. In this volume, Moon Duchin explains how geometric-statistical methods can be used to combat gerrymandering, Jeremy Avigad illustrates the growing use of computation in making and verifying mathematical hypotheses, and Kokichi Sugihara describes how to construct geometrical objects with unusual visual properties. In other essays, Neil Sloane presents some recent additions to the vast database of integer sequences he has catalogued, and Alessandro Di Bucchianico and his colleagues highlight how mathematical methods have been successfully applied to big-data problems. And there's much, much more. In addition to presenting the year's most memorable math writing, this must-have anthology includes an introduction by the editor and a bibliography of other notable writings on mathematics. This is a must-read for anyone interested in where math has taken us—and where it is headed.
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Great Circles

The Transits of Mathematics and Poetry

Author: Emily Rolfe Grosholz

Publisher: Springer

ISBN: 3319982311

Category: Mathematics

Page: 274

View: 4870

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This volume explores the interaction of poetry and mathematics by looking at analogies that link them. The form that distinguishes poetry from prose has mathematical structure (lifting language above the flow of time), as do the thoughtful ways in which poets bring the infinite into relation with the finite. The history of mathematics exhibits a dramatic narrative inspired by a kind of troping, as metaphor opens, metonymy and synecdoche elaborate, and irony closes off or shifts the growth of mathematical knowledge. The first part of the book is autobiographical, following the author through her discovery of these analogies, revealed by music, architecture, science fiction, philosophy, and the study of mathematics and poetry. The second part focuses on geometry, the circle and square, launching us from Shakespeare to Housman, from Euclid to Leibniz. The third part explores the study of dynamics, inertial motion and transcendental functions, from Descartes to Newton, and in 20th c. poetry. The final part contemplates infinity, as it emerges in modern set theory and topology, and in contemporary poems, including narrative poems about modern cosmology.
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The Holocaust in Historical Context

Author: Steven T. Katz

Publisher: Oxford University Press, USA

ISBN: N.A

Category: Antisemitism

Page: 720

View: 1942

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With this volume, Steven T. Katz initiates the provocative argument that the Holocaust is a singular event in human history. Unlike any previous work on the subject, The Holocaust in Historical Context maintains that the Holocaust is the only example of true genocide--a systematic attempt to kill all the members of a group--in history. In a richly documented, subtly argued, and amazingly wide-ranging comparative historical and phenomenological analysis, Katz explores the philosophical and historiographical implications of the uniqueness of the Holocaust. After he establishes the nature of genocide, Katz examines other occasions of mass death to which the Holocaust is regularly compared from slavery in the ancient world to the medieval persecution of heretics, from the depopulation of the New World to the Armenian massacres during World War I, and from the Gulag to Cambodia. In the first of three volumes, Katz, after setting the groundwork for his analysis with four chapters dealing with essential methodological issues, begins his comparative case studies with slavery in the ancient Greek and Roman world, and continues with such subjects as medieval antisemitism, the European witch craze, the medieval wars of religion, the medieval persecution of homosexuals, and the French campaign against Huguenots. Throughout this investigation of pre-modern Jewish and non-Jewish history, Katz looks at the ways in which the Holocaust has precedents and parallels, and in what way it stands alone as a singular, highly distinctive historical event.
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Encyclopaedia of the Arts

Author: Herbert Read

Publisher: N.A

ISBN: N.A

Category: Art

Page: 966

View: 4823

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Includes architecture, sculpture, applied arts, painting, graphic arts, literature, theatre, cinema, photography, music, opera, and ballet under biographies, titles, styles, schools, movements and groups, technical terms, techniques and materials.
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