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Topic: [HM] Calendars and the Golden Number
Replies: 19   Last Post: Apr 19, 2002 7:35 PM

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David Fowler

Posts: 241
Registered: 12/3/04
Re: [HM] Calendars and the Golden Number
Posted: Apr 17, 2002 3:53 PM
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At 4:55 am -0400 16/4/02, Peter Flor wrote:

<< How old is the term "Golden section"? Jeff Miller's web page on
the earliest occurrences of mathematical terms has a rather definite
reference to a textbook in German by Ohm, of 1835, where the term
"Goldener Schnitt" is used; he has another quotation: a certain
Baravalle claimed that sectio aurea was used by Leonardo da Vinci. >>

There's a long discussion of the situation at the end of

Roger Herz-Fischler, A Mathematical History of Division in Extreme
and Mean Ratio, Waterloo: Laurier: 1987,
reprinted by Dover under the different title
A Mathematical History of the Golden Section [alas!], date?

(I have copies of both, but cannot now find either of them.)
An opening section of an article of mine also discusses the issue:

A generalisation of the golden section, Fibonacci Quarterly 20 (1982), 146-158.

The situation, at least in 1987, was what Peter Flor says: the first
*known* use of 'golden section' was in Ohm's book of 1835. (That is
Martin Ohm, the younger brother of Georg Ohm of Ohm's Law.) But Ohm's
use of it is so easy and straightforward that it is not impossible
that it had been used elsewhere, though nothing more was known about
that in 1987. The first use in English seems to be in Chrystal,
Introduction to Algebra, 1890.

On the other hand, I am sceptical that Leonardo used 'sectio aurea'.
I can't remember what R H-F says, but I knew of nothing *in Latin*
before D'Arcy Thompson, On Growth and Form, 1st ed (only) 1917!

The story is quite complicated - indeed as is the history of the
construction itself - and I can best recommend Roger H-F's book to
you, for this and 1000 other things about the construction.

David Fowler

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