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I continued to do arithmetic with my father, passing proudly through fractions to decimals. I eventually arrived at the point where so many cows ate so much grass, and tanks filled with water in so many hours. I found it quite enthralling.
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Review of A Remarkable Collection of Babylonian Mathematical Texts
A Remarkable Collection of Babylonian Mathematical Texts: Manuscripts in the Schøyen Collection of Cuneiform Texts I (Sources and Studies in the History of Mathematics and Physical Sciences), Jöran Friberg, 2007, xx +534 pp, 259 illustrations including 70 color plates, hardback $120, ISBN-13: 978-0-387-34543-7, Springer Science + Business Media, Spring Street, New York NY 10013.
Early in my quest to better understand the history of mathematics, I came to the conclusion that the European development of mathematics emerged more from the computational techniques of Ancient Mesopotamia rather than arithmetica-directed speculations of Greek philosophers. Granted the intellectual exuberance of the Renaissance exalted in the accomplishments of Ancient Greece and passed this heritage of admiration down to us, but modern scholarship and research has matured and broadened our understandings of the development of mathematics. In past years, my quest for information on Babylonian mathematics was limited to a very few sources, particularly Neugebauer’s and Sachs’ Mathematical Cuneiform Texts (1945). However, now a wonderful new resource book on Babylonian mathematics has appeared, Jöran Friberg’s A Remarkable Collection of Babylonian Mathematical Texts. Indeed, the Collection is “remarkable” in presenting and discussing 130 previously unknown (to a popular reading audience) Old Babylonian cuneiform texts. Friberg, an applied mathematician, a well respected scholar in the field of Babylonian mathematics, and a teacher, has chosen the majority of his subject tablets from the Schøyen Collection of rare texts and documents.
The book consists of twelve chapters and ten appendices. A wealth of fascinating information is offered to the reader. The style and form of the presentation is reader-friendly. This is a book that can be consulted by a wide reading audience. Chapters are laid out in a systematic fashion, first presenting basic information from the mechanics of numeration and Babylonian arithmetic to the construction and employ of multiplication tables. Consideration is then given to Babylonian metrological systems and the types and forms of weight stones. The remaining chapters discuss the content of specific mathematical texts involving a variety of problems from land measurement and the distribution of resources to purely geometric situations. Some surprising results appear, such as the Babylonian interest in mazes and maze problems and scribes’ use of fine grids of construction lines to accomplish linear design motifs and the clarity of inscribed geometric diagrams. A text from a circa 14th century BCE tablet describes a gaming piece with sides formed by 20 equilateral triangles (an icosahedral die?). The author’s scholarly experience is evident in his identification of the caliber of the scribe and the work being performed from novice practice problems to master inscriptions. All translations and comments are supported by drawings and diagrams. A striking set of color plates enriches the presentation and the extensive sets of appendices reinforce and further extend the discussions of the text. One of my favorite problems was the asking of a scribe to find the area enclosed between two equilateral triangles, one inscribed in the other. The scribe drew the diagram and then, to my chagrin, divided the desired area into a chain of three congruent trapezoids, for which he then (it seems certain that all scribes were male) computed the area. To me, it certainly appeared more efficient to compute the areas of the individual triangles and subtract one from the other.
To anyone interested in the history of Babylonian mathematics and mathematical communication, this is a marvelous resource. A copy should be in every university library and this book should be referenced in all history of mathematics courses.
Swetz, Frank J., "Review of A Remarkable Collection of Babylonian Mathematical Texts," Loci (December 2012), DOI: 10.4169/loci003952