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A Mathematical History of the Golden Number (Dover Books on Mathematics), by Roger Herz-Fischler
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The first complete, in-depth study of the origins of division in extreme and mean ratio (DEMR)-"the Golden Number"-this text charts every aspect of this important mathematical concept's historic development, from its first unequivocal appearance in Euclid's Elements through the 18th century.
Readers will find a detailed analysis of the role of DEMR in the Elements and of its historical implications. This is followed by a discussion of other mathematical topics and of proposals by modern commentators concerning the relationship of these concepts to DEMR. Following chapters discuss the Pythagoreans, examples of the pentagram before 400 H.C., and the writings of pre-Euclidean mathematicians. The author then presents his own controversial views on the genesis, early development and chronology of DEMR. The second half of the book traces DEMR's post-Euclidean development through the later Greek period, the Arabic world, India, and into Europe. The coherent but rigorous presentation places mathematicians' work within the context of their time and dearly explains the historical transmission of their results. Numerous figures help clarify the discussions, a helpful guide explains abbreviations and symbols, and a detailed appendix defines terminology for DEMR through the ages.
This work will be of interest not only to mathematicians but also to classicists, archaeologists, historians of science and anyone interested in the transmission of mathematical ideas. Preface to the Dover Edition. Foreword. A Guide for Readers. Introduction. Appendixes. Corrections and Additions. Bibliography.
- Sales Rank: #1087682 in eBooks
- Published on: 2013-12-31
- Released on: 2013-12-31
- Format: Kindle eBook
About the Author
Roger Herz-Fischler teaches mathematics at Carleton University.
Most helpful customer reviews
5 of 6 people found the following review helpful.
How did this brilliant gem go so long without applause and acclaim? Pure Gold without equal
By VeritasluxMea
Brilliantly researched, well thought out, magnificent references; this book about the golden ratio, i.e. the Platonic logo(logos!)rithmic section (republic 509d-511) is a genuine supreme masterwork.
To prospective amazon buyers of this book, it must be said that there is absolutely no question that you will aught but love this book and it is impossible that you will regret the purchase of this book.
This book contains research on greek arithmetic's that you absolutely cannot find in ANY other book on the topic; I say this with certainty since I own every book ever published on said topic. An absolute must must own book.
0 of 0 people found the following review helpful.
A tour through Euclid
By Jordan Bell
The right way to think about the golden ratio is not as the decimal expansion 1.618... or even as the positive solution of x^2-x-1=0, but as a particular way of cutting a line AB, "division in extreme and mean ratio" (DEMR): cut a line AB at a point C such that AB:AC = AC:CB. The original title of the book was "A Mathematical History of Division in Extreme and Mean Ratio". The first part of this book lays out the propositions in Euclid that have to do with DEMR. What is especially useful about the book is listing for each proposition what propositions it uses and what propositions it is used for. DEMR is not a small topic in the Elements, and following this path is a nice way to go through the Elements without having to digest the whole work.
1 of 2 people found the following review helpful.
Four Stars
By George A. Huttlin
Its approach is very geometrical and incredibly historical. The bibliography is humongous.
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