A Mathematical History of the Golden Number: Herz-Fischler

A Mathematical History of the Golden Number

Golden Number
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In A Mathematical History of the Golden Number, Roger Herz-Fischler traces the historical development of the Golden Number, also known as the divine proportion, or Division in Extreme and Mean Ratio, DEMR. Unlike other writings on the early history of DEMR, Herz-Fischler provides an in-depth study of the role of the “golden number” in “The Euclidean Text,” the Elements. With help from qualified linguists, he gifts the reader with proper translations of primary sources, mathematical texts, and literature which had previously addressed the concepts but were in inaccessible languages (e.g. Greek, Latin, Sumerian, Arabic, etc.).

The book is mathematically “self-contained and internally comprehensible from a strictly mathematical viewpoint,” accessible not only to mathematicians but also to even the most casual math student. For starters, the “Guide for Readers” and “Introduction” and the two Appendices are filled with tremendously helpful dates, definitions, cross-references, bibliographical details, abbreviations, and symbols, etc.

The pages referencing Fibonacci are remarkably detailed, for Herz-Fischler explains connections between Fibonacci’s mathematical predecessors and his own computational approaches thoroughly, with detailed evidence rather than conjecture.

There is no one person or book which is utterly provident in enumerating all of the properties of DEMR. Having maintained an intense, precise approach towards the topic, Herz-Fischler concludes by admitting his limitations and agrees with Luca Pacioli (1447-1517), who said in Divina proportione, “It does not seem to be appropriate to me to continue further on its infinite effects because the paper would not be sufficient for the ink to express them all …” (Pacioli, 1509, Chap. XXIII). Nevertheless, A Mathematical History of the Golden Number, fully documented through careful citations, exhaustive explanations, and meticulous bibliographical features, certainly comes nearer accomplishing the task than most.

I found this book enjoyable to read because it is not written like a textbook; it is a history book with narrative filled with countless references not only to mathematicians but also to a host of influential political, science, art, and literary figures. Therefore, historians of science, classicists, archaeologists, and art historians will find this book worth having as well.

About the Roger Herz-Fischler

Roger Herz-Fischler was born in 1940. In addition to numerous books, textbooks, research, and scholarly publications, he co-authored material in French covering art, literature, and language with his wife, Eliane Herz-Fischler. His home page contains strictly educational and computational material, with links to a Research Home Page containing more educational, computer-related, and cultural material, as well as writings concerning Judaica. His books include: Shape of the Great Pyramid (2000); Adolph Zeising, 1810-1876: The Life and Work of a German Intellectual (2005); and A Mathematical History of Division in Extreme and Mean Ratio (1987).

Herz-Fischler, Roger. A Mathematical History of the Golden Number (Dover Books on Mathematics). Dover Publications; Unabridged edition, 1998.

Series: Dover Books on Mathematics; ISBN-10: 0486400077; ISBN-13: 978-0486400075

About the author

Shelley Allen is a writer, editor, poet, and mother of four. She is the author of Master Fibonacci: The Man Who Changed Math. Allen holds a Bachelor of Arts degree in English and a Master’s Degree in Secondary Education from Southern Methodist University. A former teacher and bookstore owner, Allen is a bibliophile with broad literary interests. She works professionally as a freelance writer from her home in Dallas, Texas. Her website is RuthlessRedPen.com.


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Paperback: 128 pages
Author: Shelley Allen, M.A.Ed.
Publisher: Fibonacci Inc.; 1st edition (2019)
Language: English