Babylonian Mathematical Astronomy: Procedure Texts

Author: Mathieu Ossendrijver

Publisher: Springer Science & Business Media

ISBN: 1461437822

Category: Mathematics

Page: 618

View: 595

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This book contains new translations and a new analysis of the procedure texts of Babylonian mathematical astronomy, the earliest known form of mathematical astronomy of the ancient world. The translations are based on a modern approach incorporating recent insights from Assyriology and translation science. The work contains updated and expanded interpretations of the astronomical algorithms and investigations of previously ignored linguistic, mathematical and other aspects of the procedure texts. Special attention is paid to issues of mathematical representation and over 100 photos of cuneiform tablets dating from 350-50 BCE are presented. In 2-3 years, the author intends to continue his study of Babylonian mathematical astronomy with a new publication which will contain new editions and reconstructions of approx. 250 tabular texts and a new philological, astronomical and mathematical analysis of these texts. Tabular texts are end products of Babylonian math astronomy, computed with algorithms that are formulated in the present volume, Procedure Texts.

A Remarkable Collection of Babylonian Mathematical Texts

Manuscripts in the Schøyen Collection: Cuneiform Texts I

Author: Jöran Friberg

Publisher: Springer Science & Business Media

ISBN: 0387345434

Category: Mathematics

Page: 533

View: 6401

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The book analyzes the mathematical tablets from the private collection of Martin Schoyen. It includes analyses of tablets which have never been studied before. This provides new insight into Babylonian understanding of sophisticated mathematical objects. The book is carefully written and organized. The tablets are classified according to mathematical content and purpose, while drawings and pictures are provided for the most interesting tablets.

Lengths, Widths, Surfaces

A Portrait of Old Babylonian Algebra and Its Kin

Author: Jens Høyrup

Publisher: Springer Science & Business Media

ISBN: 1475736851

Category: Mathematics

Page: 462

View: 3819

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In this examination of the Babylonian cuneiform "algebra" texts, based on a detailed investigation of the terminology and discursive organization of the texts, Jens Høyrup proposes that the traditional interpretation must be rejected. The texts turn out to speak not of pure numbers, but of the dimensions and areas of rectangles and other measurable geometrical magnitudes, often serving as representatives of other magnitudes (prices, workdays, etc...), much as pure numbers represent concrete magnitudes in modern applied algebra. Moreover, the geometrical procedures are seen to be reasoned to the same extent as the solutions of modern equation algebra, though not built on any explicit deductive structure.

A History of Ancient Mathematical Astronomy

Author: O. Neugebauer

Publisher: Springer Science & Business Media

ISBN: 364261910X

Category: Science

Page: 1456

View: 3202

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From the reviews: "This monumental work will henceforth be the standard interpretation of ancient mathematical astronomy. It is easy to point out its many virtues: comprehensiveness and common sense are two of the most important. Neugebauer has studied profoundly every relevant text in Akkadian, Egyptian, Greek, and Latin, no matter how fragmentary; [...] With the combination of mathematical rigor and a sober sense of the true nature of the evidence, he has penetrated the astronomical and the historical significance of his material. [...] His work has been and will remain the most admired model for those working with mathematical and astronomical texts. D. Pingree in Bibliotheca Orientalis, 1977 "... a work that is a landmark, not only for the history of science, but for the history of scholarship. HAMA [History of Ancient Mathematical Astronomy] places the history of ancient Astronomy on a entirely new foundation. We shall not soon see its equal. N.M. Swerdlow in Historia Mathematica, 1979

New Mathematical Cuneiform Texts

Author: Jöran Friberg,Farouk N.H. Al-Rawi

Publisher: Springer

ISBN: 3319445979

Category: Mathematics

Page: 553

View: 7396

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This monograph presents in great detail a large number of both unpublished and previously published Babylonian mathematical texts in the cuneiform script. It is a continuation of the work A Remarkable Collection of Babylonian Mathematical Texts (Springer 2007) written by Jöran Friberg, the leading expert on Babylonian mathematics. Focussing on the big picture, Friberg explores in this book several Late Babylonian arithmetical and metro-mathematical table texts from the sites of Babylon, Uruk and Sippar, collections of mathematical exercises from four Old Babylonian sites, as well as a new text from Early Dynastic/Early Sargonic Umma, which is the oldest known collection of mathematical exercises. A table of reciprocals from the end of the third millennium BC, differing radically from well-documented but younger tables of reciprocals from the Neo-Sumerian and Old-Babylonian periods, as well as a fragment of a Neo-Sumerian clay tablet showing a new type of a labyrinth are also discussed. The material is presented in the form of photos, hand copies, transliterations and translations, accompanied by exhaustive explanations. The previously unpublished mathematical cuneiform texts presented in this book were discovered by Farouk Al-Rawi, who also made numerous beautiful hand copies of most of the clay tablets. Historians of mathematics and the Mesopotamian civilization, linguists and those interested in ancient labyrinths will find New Mathematical Cuneiform Texts particularly valuable. The book contains many texts of previously unknown types and material that is not available elsewhere.

New Mathematical Cuneiform Texts

Author: Jöran Friberg,Farouk N.H. Al-Rawi

Publisher: Springer

ISBN: 3319445979

Category: Mathematics

Page: 553

View: 3836

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This monograph presents in great detail a large number of both unpublished and previously published Babylonian mathematical texts in the cuneiform script. It is a continuation of the work A Remarkable Collection of Babylonian Mathematical Texts (Springer 2007) written by Jöran Friberg, the leading expert on Babylonian mathematics. Focussing on the big picture, Friberg explores in this book several Late Babylonian arithmetical and metro-mathematical table texts from the sites of Babylon, Uruk and Sippar, collections of mathematical exercises from four Old Babylonian sites, as well as a new text from Early Dynastic/Early Sargonic Umma, which is the oldest known collection of mathematical exercises. A table of reciprocals from the end of the third millennium BC, differing radically from well-documented but younger tables of reciprocals from the Neo-Sumerian and Old-Babylonian periods, as well as a fragment of a Neo-Sumerian clay tablet showing a new type of a labyrinth are also discussed. The material is presented in the form of photos, hand copies, transliterations and translations, accompanied by exhaustive explanations. The previously unpublished mathematical cuneiform texts presented in this book were discovered by Farouk Al-Rawi, who also made numerous beautiful hand copies of most of the clay tablets. Historians of mathematics and the Mesopotamian civilization, linguists and those interested in ancient labyrinths will find New Mathematical Cuneiform Texts particularly valuable. The book contains many texts of previously unknown types and material that is not available elsewhere.

What's Happening in the Mathematical Sciences

Author: Barry Cipra

Publisher: American Mathematical Soc.

ISBN: 9780821889985

Category: Science

Page: 51

View: 638

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After rave reviews for last year's issue of What's Happening, volume 2 has been eagerly awaited. Very well written, '' said one reader of volume 1. The writing is brilliant, positively brilliant.'' A terrific publication, '' said another. This is a wonderful tool for showing people what mathematics is about and what mathematicians can do.'' One reader called it a must for all mathematics department reading and coffee lounges.'' Volume 2 of What's Happening features the same lively writing and all new topics. Here you can read about a new class of solitons, the contributions wavelets are making to solving scientific problems, how mathematics is improving medical imaging, and Andrew Wiles's acclaimed work on Fermat's Last Theorem. What's Happening is great for mathematics undergraduates, graduate students, and mathematics clubs---not to mention mathematics faculty, who will enjoy reading about recent developments in fields other than their own. Highlighting the excitement and wonder of mathematics, What's Happening is in a class by itself.

Astronomical Cuneiform Texts

Babylonian Ephemerides of the Seleucid Period for the Motion of the Sun, the Moon, and the Planets

Author: O. Neugebauer

Publisher: Springer Science & Business Media

ISBN: 1461255074

Category: Mathematics

Page: 802

View: 4828

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THE MOON IX PREFACE TO THE SPRINGER EDITION When this collection of Babylonian astronomical purpose of column of the lunar ephemerides (by texts was published in 1955 (a date omitted by Aaboe) and the explanation of the method of computing the eclipse text ACT No. 6o (by Hamilton mistake from the title page), it contained all texts of this type that I could lay my hands on. As was to be and Aaboe). Some of these advances I have tried to incorporate into my History of Ancient Mathematical expected, the past 25 years provided more fragments, identified by A. Sachs and A. Aaboe in the British Astronomy (1975), which should be used as a guide to Museum and listed below. Also, some new joins the more recent literature. could be made and some errors of mine corrected. My sincerest thanks go to Springer-Verlag for Nevertheless, I think one still can consider the making this work again available to students of material of 1955 to be representative of what has been ancient astronomy. The Institute for Advanced preserved of the mathematical astronomy of the Study, which together with Brown University has Seleucid period. supported my work for more than four decades, has In the meantime, far more progress has been made graciously given its permission for this reprint. in our understanding of Babylonian astronomy, mainly by the publications of Aaboe, Hamilton, Maeyama, Sachs, van der Waerden, and others. As an Princeton 0.

Finding Zero

A Mathematician's Odyssey to Uncover the Origins of Numbers

Author: Amir D. Aczel

Publisher: St. Martin's Press

ISBN: 1466879106

Category: Mathematics

Page: 256

View: 5331

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The invention of numerals is perhaps the greatest abstraction the human mind has ever created. Virtually everything in our lives is digital, numerical, or quantified. The story of how and where we got these numerals, which we so depend on, has for thousands of years been shrouded in mystery. Finding Zero is an adventure filled saga of Amir Aczel's lifelong obsession: to find the original sources of our numerals. Aczel has doggedly crisscrossed the ancient world, scouring dusty, moldy texts, cross examining so-called scholars who offered wildly differing sets of facts, and ultimately penetrating deep into a Cambodian jungle to find a definitive proof. Here, he takes the reader along for the ride. The history begins with the early Babylonian cuneiform numbers, followed by the later Greek and Roman letter numerals. Then Aczel asks the key question: where do the numbers we use today, the so-called Hindu-Arabic numerals, come from? It is this search that leads him to explore uncharted territory, to go on a grand quest into India, Thailand, Laos, Vietnam, and ultimately into the wilds of Cambodia. There he is blown away to find the earliest zero—the keystone of our entire system of numbers—on a crumbling, vine-covered wall of a seventh-century temple adorned with eaten-away erotic sculptures. While on this odyssey, Aczel meets a host of fascinating characters: academics in search of truth, jungle trekkers looking for adventure, surprisingly honest politicians, shameless smugglers, and treacherous archaeological thieves—who finally reveal where our numbers come from.

Handbook on the History of Mathematics Education

Author: Alexander Karp,Gert Schubring

Publisher: Springer Science & Business Media

ISBN: 146149155X

Category: Mathematics

Page: 634

View: 821

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This is the first comprehensive International Handbook on the History of Mathematics Education, covering a wide spectrum of epochs and civilizations, countries and cultures. Until now, much of the research into the rich and varied history of mathematics education has remained inaccessible to the vast majority of scholars, not least because it has been written in the language, and for readers, of an individual country. And yet a historical overview, however brief, has become an indispensable element of nearly every dissertation and scholarly article. This handbook provides, for the first time, a comprehensive and systematic aid for researchers around the world in finding the information they need about historical developments in mathematics education, not only in their own countries, but globally as well. Although written primarily for mathematics educators, this handbook will also be of interest to researchers of the history of education in general, as well as specialists in cultural and even social history.

Mathematical Tablets from Tell Harmal

Author: Carlos Gonçalves

Publisher: Springer

ISBN: 3319225243

Category: Mathematics

Page: 141

View: 9334

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This work offers a re-edition of twelve mathematical tablets from the site of Tell Harmal, in the borders of present-day Baghdad. In ancient times, Tell Harmal was Šaduppûm, a city representative of the region of the Diyala river and of the kingdom of Ešnunna, to which it belonged for a time. These twelve tablets were originally published in separate articles in the beginning of the 1950s and mostly contain solved problem texts. Some of the problems deal with abstract matters such as triangles and rectangles with no reference to daily life, while others are stated in explicitly empirical contexts, such as the transportation of a load of bricks, the size of a vessel, the number of men needed to build a wall and the acquisition of oil and lard. This new edition of the texts is the first to group them, and takes into account all the recent developments of the research in the history of Mesopotamian mathematics. Its introductory chapters are directed to readers interested in an overview of the mathematical contents of these tablets and the language issues involved in their interpretation, while a chapter of synthesis discusses the ways history of mathematics has typically dealt with the mathematical evidence and inquires how and to what degree mathematical tablets can be made part of a picture of the larger social context. Furthermore, the volume contributes to a geography of the Old Babylonian mathematical practices, by evidencing that scribes at Šaduppûm made use of cultural material that was locally available. The edited texts are accompanied by translations, philological, and mathematical commentaries.

Scientific Sources and Teaching Contexts Throughout History: Problems and Perspectives

Author: Alain Bernard,Christine Proust

Publisher: Springer Science & Business Media

ISBN: 9400751222

Category: Science

Page: 334

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This book examines the textual, social, cultural, practical and institutional environments to which the expression “teaching and learning contexts” refers. It reflects on the extent to which studying such environments helps us to better understand ancient or modern sources, and how notions of “teaching” and “learning” are to be understood. Tackling two problems: the first, is that of certain sources of scientific knowledge being studied without taking into account the various “contexts” of transmission that gave this knowledge a long-lasting meaning. The second is that other sources are related to teaching and learning activities, but without being too precise and demonstrative about the existence and nature of this “teaching context”. In other words, this book makes clear what is meant by “context” and highlights the complexity of the practice hidden by the words “teaching” and “learning”. Divided into three parts, the book makes accessible teaching and learning situations, presents comparatist approaches, and emphasizes the notion of teaching as projects embedded in coherent treatises or productions.

From Aristotle to Augustine

Author: David J. Furley

Publisher: Psychology Press

ISBN: 0415308747

Category: Philosophy

Page: 457

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From Aristotle to Augustine surveys the work of philosophers who wrote in Greek and Latin from the mid-4th century BC to the 5th century AD. This second volume opens with Aristotle's immense influence on philosophy from the beginnings of Christian philosophy in the 5th century AD.

The Exact Sciences in Antiquity

Author: Otto Neugebauer

Publisher: Courier Corporation

ISBN: 9780486223322

Category: Science

Page: 240

View: 3998

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Based on a series of lectures delivered at Cornell University in the fall of 1949, and since revised, this is the standard non-technical coverage of Egyptian and Babylonian mathematics and astronomy, and their transmission to the Hellenistic world. Entirely modern in its data and conclusions, it reveals the surprising sophistication of certain areas of early science, particularly Babylonian mathematics. After a discussion of the number systems used in the ancient Near East (contrasting the Egyptian method of additive computations with unit fractions and Babylonian place values), Dr. Neugebauer covers Babylonian tables for numerical computation, approximations of the square root of 2 (with implications that the Pythagorean Theorem was known more than a thousand years before Pythagoras), Pythagorean numbers, quadratic equations with two unknowns, special cases of logarithms and various other algebraic and geometric cases. Babylonian strength in algebraic and numerical work reveals a level of mathematical development in many aspects comparable to the mathematics of the early Renaissance in Europe. This is in contrast to the relatively primitive Egyptian mathematics. In the realm of astronomy, too, Dr. Neugebauer describes an unexpected sophistication, which is interpreted less as the result of millennia of observations (as used to be the interpretation) than as a competent mathematical apparatus. The transmission of this early science and its further development in Hellenistic times is also described. An Appendix discusses certain aspects of Greek astronomy and the indebtedness of the Copernican system to Ptolemaic and Islamic methods. Dr. Neugebauer has long enjoyed an international reputation as one of the foremost workers in the area of premodern science. Many of his discoveries have revolutionized earlier understandings. In this volume he presents a non-technical survey, with much material unique on this level, which can be read with great profit by all interested in the history of science or history of culture. 14 plates. 52 figures.

Texts, Textual Acts and the History of Science

Author: Karine Chemla,Jacques Virbel

Publisher: Springer

ISBN: 3319164449

Category: Science

Page: 430

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The book presents the outcomes of an innovative research programme in the history of science and implements a Text Act Theory which extends Speech Act Theory, in order to illustrate a new approach to texts and textual communicative acts. It examines assertives (absolute or conditional statements, forecasts, insurance, etc.), directives, declarations and enumerations, as well as different types of textual units allowing authors to perform these acts: algorithms, recipes, prescriptions, lexical templates for terminological studies and enumerative structures. The book relies on the study of a broad range of documents of the past dealing with various domains: mathematics, zoology, medicine, lexicography. The documents examined come from scholarly sources from different parts of the world, such as China, Europe, India, Mesopotamia and are written in a variety of European languages as well as Chinese, Cuneiform and Sanskrit. This approach proves fruitful in both history of science and Text Act Theory.

Mathematics in Ancient Egypt

A Contextual History

Author: Annette Imhausen

Publisher: Princeton University Press

ISBN: 1400874300

Category: Mathematics

Page: 248

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Mathematics in Ancient Egypt traces the development of Egyptian mathematics, from the end of the fourth millennium BC—and the earliest hints of writing and number notation—to the end of the pharaonic period in Greco-Roman times. Drawing from mathematical texts, architectural drawings, administrative documents, and other sources, Annette Imhausen surveys three thousand years of Egyptian history to present an integrated picture of theoretical mathematics in relation to the daily practices of Egyptian life and social structures. Imhausen shows that from the earliest beginnings, pharaonic civilization used numerical techniques to efficiently control and use their material resources and labor. Even during the Old Kingdom, a variety of metrological systems had already been devised. By the Middle Kingdom, procedures had been established to teach mathematical techniques to scribes in order to make them proficient administrators for their king. Imhausen looks at counterparts to the notation of zero, suggests an explanation for the evolution of unit fractions, and analyzes concepts of arithmetic techniques. She draws connections and comparisons to Mesopotamian mathematics, examines which individuals in Egyptian society held mathematical knowledge, and considers which scribes were trained in mathematical ideas and why. Of interest to historians of mathematics, mathematicians, Egyptologists, and all those curious about Egyptian culture, Mathematics in Ancient Egypt sheds new light on a civilization's unique mathematical evolution.

Pappus of Alexandria Book 7 of the Collection

Part 1. Introduction, Text, and Translation

Author: N.A

Publisher: Springer Science & Business Media

ISBN: 1461249082

Category: Mathematics

Page: 749

View: 4784

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The seventh book of Pappus's Collection, his commentary on the Domain (or Treasury) of Analysis, figures prominently in the history of both ancient and modern mathematics: as our chief source of information concerning several lost works of the Greek geometers Euclid and Apollonius, and as a book that inspired later mathematicians, among them Viete, Newton, and Chasles, to original discoveries in their pursuit of the lost science of antiquity. This presentation of it is concerned solely with recovering what can be learned from Pappus about Greek mathematics. The main part of it comprises a new edition of Book 7; a literal translation; and a commentary on textual, historical, and mathematical aspects of the book. It proved to be convenient to divide the commentary into two parts, the notes to the text and translation, and essays about the lost works that Pappus discusses. The first function of an edition of this kind is, not to expose new discoveries, but to present a reliable text and organize the accumulated knowledge about it for the reader's convenience. Nevertheless there are novelties here. The text is based on a fresh transcription of Vat. gr. 218, the archetype of all extant manuscripts, and in it I have adopted numerous readings, on manuscript authority or by emendation, that differ from those of the old edition of Hultsch. Moreover, many difficult parts of the work have received little or no commentary hitherto.

Writings of Early Scholars in the Ancient Near East, Egypt, Rome, and Greece

Translating Ancient Scientific Texts

Author: Annette Imhausen,Tanja Pommerening

Publisher: Walter de Gruyter

ISBN: 3110229927

Category: Language Arts & Disciplines

Page: 436

View: 2413

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Medicine, astronomy, dealing with numbers even the cultures of the pre-modern world offer a rich spectrum of scientific texts. But how are they best translated? Is it sufficient to translate the sources into modern scientific language, and thereby, above all, to identify their deficits? Or would it be better to adopt the perspective of the sources themselves, strange as they are, only for them not to be properly understood by modern readers? Renowned representatives of various disciplines and traditions present a controversial and constructive discussion of these problems."

Mathematical Time Capsules

Historical Modules for the Mathematics Classroom

Author: Dick Jardine

Publisher: MAA

ISBN: 088385984X

Category: MATHEMATICS

Page: 204

View: 8867

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Mathematical Time Capsules offers teachers historical modules for immediate use in the mathematics classroom. Readers will find articles and activities from mathematics history that enhance the learning of topics covered in the undergraduate or secondary mathematics curricula. Each capsule presents at least one topic or a historical thread that can be used throughout a course. The capsules were written by experienced practitioners to provide teachers with historical background and classroom activities designed for immediate use in the classroom, along with further references and resources on the chapter subject. --Publisher description.