FIBONACCI NUMBERS
AND THE GOLDEN RATIO

WHAT the site is for:
This is the Plus Maths web page, magazine like in style. It is an educational site explaining how maths is useful beyond the school or college curriculum. "It's about the applications of mathematics to life and the real world". [Editor Dr Robert Hunt Director of Studies in Applied Mathematics at Cambridge University].

WHO provides material:
The article on Fibonacci has been compiled by a Plus Maths staff member from material written by Dr. R. Knott and Dr. D. A. Quinney, university lecturers in computing and mathematics respectively. Many academic sites suggest links to Dr. Knott's Fibonacci material (see Fibonacci in Art Architecture & Music below).

HOW author(s) approaches material:
Aimed primarily at people of school or college age and their teachers it is a good introduction. It makes all assertions as if they are accepted mathematical fact. It relies on the reputation of the writers and the pedigree of the publication itself for these assertions.

FEATURES relating to Fibonacci:
The material on Fibonacci has a brief biography and his mathematical pedigree; how the numbers are calculated and the derivation of the ratio. It alludes to the occurrence of the numbers and the golden ratio in geometry, architecture, nature and maths.

DESIGN of web page:
Download performance is somewhat sluggish as this is a long, monolithic article, it has few images but is reasonable attractive in colour and design. Navigation of the single page is provided by the browser arrows only.

WHAT the site is for:
This is one page of the definitive educational site on Fibonacci numbers which is also a portal site to a vast array of other recommended links. These pages are part of a multi award winning web site aimed at young people and their teachers.

WHO provides the material:
Dr. Ron Knott is a highly qualified mathematician and academic. Currently a visiting Fellow of the School of Electrical Engineering, IT and Mathematics at Surrey University, UK. The author has commercial interests in web education & training.

HOW author approaches the material:
The author comments that other pages on his site relate to issues which are scientifically (mathematically) verifiable. This particular section on Art etc. he sees as containing material which is speculative in nature, and even controversial e.g. the idea that the golden section is "the most pleasing shape" could be contested. He warns about elevating the golden section beyond what is scientifically provable - worth remembering when visiting special interest sites such as Fibonacci and Faith below.

FEATURES relating to Fibonacci:
Excellent treatment of all aspects of Fibonacci numbers for school students (and others!) can be reached by clicking on the Fibonacci Home page link at the bottom of Art, Architecture, Music page. Author says site would amount to over 200 printed pages.

DESIGN of web page:
Mostly made up of long, monolithic text pages with few picture, so does download quickly. Has linked contents page at top, uses interpage links and hyperlinks to navigate, with "where to next" navigation provided at bottom of pages. Some background colour and text contrast used.

WHAT the site is for:
This feature is on the same site as Fibonacci: the man and his numbers. This article won the Times Higher Educational Supplement Science Writing Competition in 1999.

WHO provides material:
His resume on the web page states: Dr. Kevin Jones is a Reader in Music at Kingston University in Surrey. He has degrees in Mathematics and Computer Science as well as in Music. He is particularly interested in exploring the underlying relationships between music, science and culture - in his research, and in his work as writer, composer and teacher.

HOW author approaches material:
Dr. Jones makes specific observations on the structure and syncopation of limericks and ragtime music. He puts forward the theory that they possess qualities of modern fractal models and postulates that this can provide insight into the inter-relationships between the arts and sciences. He uses reasoned observations to back up his arguments. He demonstrates the existence of patterns common to nature, mathematics, poetry and music forms, and poses question that these may influence modern day mathematicians to look to these cultural art forms for inspiration.

FEATURES relating to Fibonacci:
Occurrence of Fibonacci type symmetry in various musical and rhythmic forms, including the music of Gershwin, Bartok, Debussy& Scott Joplin. The relationship between natural pattern of Fibonacci symmetry and it's innate attractiveness to the human ear.

DESIGN of web page:
Identical style as mentioned in Fibonacci: the man and his numbers.

WHAT the site is for:
A personal perspective by a dentist on the applications of the golden section in general, and to dentistry in particular. Includes on line purchase order form for his gauge which he claims measures out the golden proportion and can be used in dental work.

WHO provides the material:
Eddy Levin a Harley Street dentist who has 22 years of experience in writing, lecturing and demonstrating the aesthetic appeal and usefulness of the golden proportion in nature and by extension, dental work.

HOW author approaches material:
He sets out occurrence of Fibonacci series and golden proportion in art forms and nature, referencing eminent works and journals on these subjects. He uses photographs and grids to demonstrate the proportional measurement of items using his gauge. He examines the evidence for the aesthetic value of the proportion to the human eye. Includes bibliography of reference works.

FEATURES of Fibonacci:
In addition to Dentistry he looks at the golden proportion in relation to: Art, Nature, Handwriting, Craft and Design, History, Architecture, Medicine and Mathematics. This site provides an understandable general background to his subject matter.

DESIGN of web page:
Text downloads in advance of large number of small images, these are used well to demonstrate themes. Straightforward site with static margin showing menu. Most items are on one page, some of these are long. Navigation provided predominantly by the side menu.

WHAT the site is for:
This is the Evolution of Truth site; a personal attempt by the author to explore (amongst other things) "evidence for the Divine creation and design in the universe". He sees the recurrence of the golden section or proportion throughout the design of the human body and other life forms as evidence of God's creation. He is open about his views and the purpose of his site.

WHO provides the material:
Someone who was a "cynical agnostic" until he had a Christian faith experience which made him re-think his knowledge of science and reason. We know nothing about his scientific credentials except that he expresses an interest in it. He invites people regardless of belief to look at this thought provoking site - which it is, regardless of whether one agrees with his conclusions about the content.

HOW author approaches his material:
His statements concerning mathematical patterns and their occurrence in the natural world are stated as matters of fact with little corroborating evidence or scientific reference. In other words they may be provable or accepted views or they may just be his own, without reference to other studies it is impossible to say.

FEATURES of Fibonacci:
Plenty of material and images on the occurrence of numbers and golden proportion in all realms of nature and anatomy, but must be measured against the caveat of lack of scientific corroboration on this site. The author does try to be reasoned in putting across his particular beliefs.

DESIGN of web page:
Attractive appearance to site. He uses many photographs and images so download is slow. Easy to navigate with clear contents and links to other scientific and Christian web pages.

"If you had algebra on the underground would you end up with a tube of smarties?"
[Quote from the campaign].

A link to the Isaac Newton Institute web site at Cambridge University UK. This compact web page explains the poster campaign to promote mathematics at the start of the new millennium. It has links to sites on Fibonacci and his numbers, together with other suggested useful mathematical links aimed mainly at schools.

The poster images (one per month) will be added as the year progresses. These are excellent although they do take time to download. Bigger versions of each are available to download from the opening page.