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The Mathematics of Plato's Academy : A New Reconstruction - D. H. Fowler

The Mathematics of Plato's Academy

A New Reconstruction

Paperback

Published: 14th February 1991
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Ancient sources tell us of Plato's zeal for mathematics, but the problem of interpreting many of the mathematical references in his "Dialogues" has perplexed later commentators. Part 1 of this book presents several interpretations of the ideas of ratio in early Greek mathematics, and illustrates them in detailed discussions of several texts. Principally, it looks at the advanced mathematics curriculum described by Plato in "Republic VII" as part of the training of future guardians of the state. Part 2 discusses three questions: what do we know of Plato's Academy during his lifetime?; from where do we get our text of Euclid's "Elements"?; and what do we know of early Greek numerical practice? Part 3 contrasts some of the evidence from early and late antiquity and then gives a historical account, starting in the 17th century, of the theory of continued fractions - today's version of the mathematics underlying the reconstruction.

`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

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.

ISBN: 9780198539476
ISBN-10: 0198539479
Series: Oxford Science Publications
Audience: Professional
Format: Paperback
Language: English
Number Of Pages: 422
Published: 14th February 1991
Publisher: Oxford University Press
Country of Publication: GB
Dimensions (cm): 23.5 x 15.8  x 2.3
Weight (kg): 0.67