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The Mathematics of Plato's Academy: A New Reconstruction

The Mathematics of Plato's Academy: A New Reconstruction


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About the Book

This book presents a radically new interpretation of early Greek mathematics; its central theme is a mathematical and historical exploration of several different ways of characterizing ratio. To set the reconstruction in context, David Fowler describes both how early Greeks wrote and how their writings have then been transmitted to us. This leads to descriptions of taxation and land-measurement in the Greek administration of Egypt, of the development of continued fractions from the seventeenth century, including a recent algorithm for arithmetic with continued fractions, and many other topics.

Table of Contents:
PART ONE: INTERPRETATIONS: The proposal; Anthyphairetic ratio theory; Elements II: The dimension of squares; Plato's mathematics curriculum in Republic VII; Elements IV, X, and XIII: The circumdiameter and side; PART TWO: EVIDENCE: The nature of our evidence; Numbers and fractions; PART THREE: LATER DEVELOPMENTS: Later interpretations; Continued fractions; Bibliography; Indices.

Review :
`He cites an impressive array of evidence ... should be widely read by classicists and mathematicians as well as by historians of mathematics.' Isis `the process of reading his reconstructions is irreversible; you will never again be the naive, innocent reader of ancient mathematics you used to be. His book leaves important questions that must be answered, and many statements that must be either believed or refuted.' Mathematical Reviews `... the explorations and speculations in this fascinating book - with its many stimulating insights and intriguing bypaths - will arouse the interest and command the admiration of any historically minded lover of mathematics ...' Bulletin of the Institute of Mathematics and its Applications '... speculative in the best sense, engages the ancient material on its own terms in setting forth what the Greeks might have thought and done ... represents an important departure in historical research ...' Zentralblatt fur Mathematik 'a book by a real enthusiast, and a real treat ... Fowler is a mathematician, not a classicist, but his grasp of the evidence for the development of Greek mathematics is very impressive.' Richard Wallace, Greece and Rome, Vol. xxxvii, No. 1 Apr '90 'fascinating and thought-provoking book ... All praise to Oxford University Press for publishing this book.' John Fauvel, ATM (an Open University publication) `This book presents a redically new interpretation of early Greek mathematics.' L'Enseignement Mathematiik ` .. a valuable addition to the continuing reconstruction of Greek Mathematics by Knorr, Fowler, and others. A stimulating and attractively presented work.' Mathematika 'shows an admirable refusal to speculate beyond what is consistent with an honest and careful - but highly readable - evaluation of the evidence we have ... full of interest and useful information ... The reader emerges not only with fresh information, but with a renewed sense that alert critical judgment is the really important attribute to be developed in young people.' John Fauvel, New Scientist, 4 January 1992


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Product Details
  • ISBN-13: 9780198539476
  • Publisher: Oxford University Press
  • Publisher Imprint: Clarendon Press
  • Height: 235 mm
  • No of Pages: 432
  • Sub Title: A New Reconstruction
  • Width: 158 mm
  • ISBN-10: 0198539479
  • Publisher Date: 14 Feb 1991
  • Binding: Paperback
  • Language: English
  • Spine Width: 23 mm
  • Weight: 634 gr


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