A Mathematical History of the Golden Number (Dover Books on Mathematics) by Roger Herz-Fischler (PDF)

Description

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.

User’s Reviews

Reviews from Amazon users which were colected at the time this book was published on the website:

⭐Its approach is very geometrical and incredibly historical. The bibliography is humongous.

⭐Great

⭐The truth is out there!

⭐Recommend! Shipped fast

⭐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.

⭐AM happy

⭐Este libro es esencialmente un compendio histórico matemático de gran valor científico, aunque es algocomplicado en hilvanar sus reseñas sobre lo dicho por autores antiguos acerca del origen del Númerode Oro, asociado éste a la figura geométrica de un pentágono regular. Y, se echa algo de menos suindudable relación y conexión con la figura del rectángulo áureo, y Fi ( Nº Aureo, 1,618… ), con su espiraláurea de Durero representada tantas veces en el Arte y la ciencia de la Naturaleza ( Leonardo da Vinci,Nautilus Emperador, respectivámente ). Desde el punto de vista matemático es altamente recomendable.

⭐Difficile; segue molto “Elementi” di Euclide che non è certo per principianti.Non fa nulla per semplificarlo. Libro per esperti

⭐

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