
Incidentally, in Halifax, Nova Scotia, there are 4 noncable TV channels and they are numbered 3, 5, 8 and 13! Karl Dilcher reported this coincidence at the Eighth International Conference on Fibonacci Numbers and their Applications in summer 1998.

A M B  1x  x The line AB is divided at point M so that the ratio of the two parts, the smaller to the larger (AM and MB), is the same as the ratio of the larger part (MB) to the whole AB.
If AB is of length 1 unit, and we let MB have length x, then the definition (in bold) above becomesPacioli's work influenced Leonardo da Vinci (14521519) and Albrecht Durer (14711528) and is seen in some of the work of Georges Seurat, Paul Signac and Mondrian, for instance.
the ratio of 1x to x is the same as the ratio of x to 1 or, in symbols:1  x = x which simplifies to 1x = x^{2 } x 1This gives two values for x, (15)/2 and (51)/2.
The first is negative, so does not apply here. The second is just phi (which has the same value as 1/Phi and as Phi1).
Many books on oil painting and water colour in your local library will point out that it is better to position objects not in the centre of the picture but to one side or "about onethird" of the way across, and to use lines which divide the picture into thirds. This seems to make the picture design more pleasing to the eye and relies again on the idea of the golden section being "ideal".
Top9.com's
List of the top art sources on the web is an excellent place for links
to good art sources on the web. Highly recommended!
The Metropolitan
Museum of Art in New York houses more than 2 million works of art.
The Fine
Arts Museums of San Francisco site has an Image base of 65,000 works
of art. It includes art from Ancient to Modern, from paintings to ceramics
and textiles, from all over the world as well as America.
A
Guide to Art Collections in the UK
Michelangelo
is famous for his paintings (such as the ceiling in the Sistine Chapel)
and his sculptures (for instance David). This site has links to
several sources and images of his works and some links to sites on the
golden section.
Using the picture of his David sculpture, measure it and see
if he has used Phi  eg is the navel ("belly button") 0·618 of the
David's height?
Why not visit
the Leonardo Museum in the
town of Vinci (Italy) itself from which town Leonardo is named, of
course.
There are many sketches and paintings of Leonardo's at The
WebMuseum, Paris too.


Various composers have used the Fibonacci numbers when composing music  more details in Garland's book.
Baginsky's method of constructing violins is also based on golden sections.
The Mathematics Magazine Vol 68 No. 4, pages 275282, October 1995 has an article by Putz on Mozart and the Golden section in his music.
There is a
very useful set of mathematical links to Art
and Music web resources from Mathematics
Archives that is worth looking at.
1·61803 39887 49894
84820 45868 34365 63811 77203 09179 80576 ..More..
So this page has lots of speculative material on it and would make a good Project for a Science Fair perhaps, investigating if the golden section does account for some major design features in important works of art, whether architecture, paintings, sculpture, music or poetry. It's over to you on this one!
Key:  

a book  
an article in a magazine or
a paper in an academic journal 

a website 
 Fascinating Fibonaccis by Trudi Hammel Garland,
 Dale Seymours publications, 1987 is an excellent introduction to the Fibonacci series with lots of useful ideas for the classroom. Includes a section on Music.
 An example of Fibonacci Numbers used to Generate Rhythmic Values in Modern Music
 in Fibonacci Quarterly Vol 9, part 4, 1971, pages 423426;
Other music
 Gamelan
 is the percussion oriented music of Indonesia.
 New music
 from David Canright of the Maths Dept at the Naval Postgraduate School in Monterey, USA; combining the Fibonacci series with Indonesian Gamelan musical forms.
 Some CDs
 on Gamelan music of Central Java (the country not the software!).
Art
 The Fibonacci Sequence
 is the name of a classical music ensemble of internationally famous soloists, who are the musicians in residence at Kingston University (KingstonuponThames, Surrey, UK). Based in the London (UK) area, their current programme of events is on the Web site link above.
 A Mathematical History of the Golden Section ISBN 0486400077.
 Education through Art (3rd edition) H Read,
 Pantheon books,1956, pages 1422;
 The New Landscape in Art and Science G Kepes
 P Theobald and Co, 1956, pages 329 and 294;
 H E Huntley's, The Divine Proportion: A study in mathematical beauty,
 ISBN 0486222543 is a 1970 Dover reprint of an old classic.
 C. F. Linn, The Golden Mean: Mathematics and the Fine Arts,
 Doubleday 1974.
 Gyorgy Doczi, The Power of Limits: Proportional Harmonies in Nature, Art, and Architecture
 Shambala Press, (new edition 1994).
 M. Boles, The Golden Relationship: Art, Math, Nature, 2nd ed.,
 Pythagorean Press 1987.
 The "Golden Cut" or beauty and design using the golden section, through the eyes of a florist.
Who was Fibonacci?  Fibonacci
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