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Other titles in the Sources and Studies in the History of Mathematics and Physic series:
A Remarkable Collection of Babylonian Mathematical Texts: Manuscripts in the Sch??yen Collection: Cuneiform Texts I (Sources and Studies in the History of Mathematics and Physic)by Joran Friberg
Synopses & Reviews
The book analyzes the mathematical tablets which are in the possession of a private collector, Martin Schoyen. This collection contains all sorts of tablets, some similar to classical ones but also others with fascinating new material. Here the author translates their mathematical content, compares it with previous known material, then evaluates the period of the tablet and its purpose. This allows the author to provide new insights into the interpretation of some classical tablets, as for example Plimpton 322 which has an exclusive appendix.
What makes this book so unique is the light being shed on Babylonian mathematics. For instance, new evidence of Babylonian familiarity with sophisticated mathematical objects is provided, including the knowledge of the three dimensional Pythagorean equation and the familiarity with the geometry of the icosahedron is new and unexpected. The author is a master of analysis of the errors found in the tablets. It is well known that computational errors in the tablets are revealing of the algorithms employed in the computations. The author exploits with mastery this clever technique to gain new insight in the mathematical reasoning behind the content of the tablets. From the analysis it becomes increasingly clear that Babylonians were outstanding calculators, probably only comparable in modern times with exhibition genius calculators. For example, it appears that schoolboys were familiar with the multiplication tables at least up to 25!. He also gives numerous geometrical possible explanations and interpretations of the tablets. Another very important finding is the use of the zero notation in novel contexts and periods.
The book is verycarefully written and organized, the tablets are classified according to their mathematical content and purpose, while useful drawings and pictures are provided for the most interesting tablets. The author makes a great effort to make the material accessible to both assyriologists and mathematicians. There is an introduction with basic background on babylonian mathematics and on numerous occasions the author reviews basic mathematical material
This new text from Jöran Friberg, the leading expert on Babylonian mathematics, presents 130 previously unpublished mathematical clay tablets from the Norwegian Schøyen collection, and provides a synthesis of the author's most important work. Through a close study of these tablets, Friberg has made numerous amazing discoveries, including the first known examples of pre-Classical labyrinths and mazes, a new understanding of the famous table text Plimpton 322, and new evidence of Babylonian familiarity with sophisticated mathematical ideas and objects, such as the three-dimensional Pythagorean equation and the icosahedron. In order to make the text accessible to the largest possible audience, the author has included an introductory chapter entitled, "How to get a better understanding of mathematical cuneiform texts." Throughout the text he avoids anachronisms and makes every effort to teach the reader to do the same. The approach in this book is inherently pedagogical, as Friberg illustrates all the steps of the process of interpretation and clearly explains the mathematical ideas, including terminology, metrological systems, and methods of calculation. Drawings and color photos of a large selection of tablets are also included. Particularly beautiful hand copies of the most complicated texts were made by Farouk Al-Rawi, professor of Ancient Languages and Archaeology at Baghdad University. While the book is reader-friendly, it remains as detailed and exhaustive as possible. It is the most comprehensive treatment of a set of Babylonian mathematical texts ever published and will open up this subject to a new generation of students, mathematicians, and historians of science. Jöran Friberg is Professor Emeritus of Mathematics at Chalmers University of Technology, Sweden. He has recently published the book Unexpected Links Between Egyptian and Babylonian Mathematics (World Scientific 2005), and its sequel Amazing Traces of a Babylonian Origin in Greek Mathematics (World Scientific 2007).
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.
Table of Contents
Acknowledgements.- Introduction.- Documentation of Provenance.- Abbreviations.- How to Get a Better Understanding of Mathematical Cuneiform Texts.- Old Babylonian Arithmetical Hand Tablets.- Old Babylonian Arithmetical Table Texts.- Old Babylonian Metrological Table Texts.- Mesopotamian Weight Stones.- Neo-Sumerian Field Maps (Ur III).- An Old Sumerian Metro-Mathematical Table Text (Early Dynastic IIIa).- Old Babylonian Hand Tablets with Practical Mathematics.- Old Babylonian Hand Tablets with Geometric Exercises.- The Beginning and the End of the Sumerian King List.- Three Old Babylonian Mathematical Problem Texts from Uruk.- Three Problem Texts Not Belonging to Any Known Group of Texts.- App. 1. Subtractive Notations for Numbers in Mathematical Cuneiform Texts.- App. 2. The Old Babylonian Combined Multiplication Table.- App. 3. An Old Babylonian Combined Arithmetical Algorithm.- App. 4. Cuneiform Systems of Notations for Numbers and Measures.- App. 5. Old Babylonian Complete Metrological Tables.- App. 6. Metro-Mathematical Cuneiform Texts from the Third Millennium BC.- App. 7. CUNES 50-08-001. A Combined Metro-Mathematical Table Text (ED IIIb).- App. 8. Plimpton 322, a Table of Parameters for igi-igi.bi Problems.- App. 9. Many-Place Squares of Squares in Late Babylonian Mathematical Texts.- App. 10. Color Photos of Selected Texts.- Vocabulary for the MS Texts.- Index of Subjects.- Index of Texts.- References.
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