Friday, July 04, 2008

Begonias, Fibonacci and fame

click photo to enlarge
In 1202 Leonardo of Pisa (known as Fibonacci) wrote Liber Abaci, also known as The Book of the Abacus and The Book of Calculation. It was not the first book to introduce Arabic numerals to Europeans, but the wide audience that it found greatly increased their popularity and persuaded people of their superiority. Arithmetic, conversions, calculations, measurements, mathematical problems, formulas, types of numbers, approximations, geometric proofs and simultaneous linear equations all feature in Fibonacci's book. However, posterity remembers him for a section that describes a succession of numbers that we now call the Fibonacci Sequence.

This sequence starts with 0. The second number is 1. Each subsequent number is the sum of the previous two numbers. So, it begins, 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, and continues infinitely. This sequence found application in visual art (architecture and painting particularly) where it was used to determine harmonious relationships in formal elements. Musicians have made use of it in tunings and intervals. Even financial markets have used the Fibonacci sequence in trading algorithms and strategies. My introduction to the sequence was through the link between mathematics and the natural world. The branching of trees, the arrangement of florets in the centre of a sunflower head, and the arrangement of the parts of a pine cone can all be shown to relate to the Fibonacci sequence. Some have said that the growth of ammonite whorls, or in fact any spiral sea shell, is related to the sequence, and the Fibonacci Spiral shows how this happens.

When I saw this begonia leaf (a type related to the aptly named Escargot variety) I immediately thought of the medieval Italian. It is said that living organisms evolved to grow in this way because it allows an increase in size at a constant rate without a change in shape. Whatever the truth of the matter, this spiral shape is a visually satisfying form, and a suitable subject for a photograph!

Incidentally, it seems that Indian mathematicians discovered this sequence before Fibonacci, but as is often the case, the person who placed the information before the public was the one whose name became attached to the idea, and became famous.

photograph & text (c) T. Boughen

Camera: Olympus E510
Mode: Aperture Priority
Focal Length: 35mm macro (70mm/35mm equiv.)
F No: f16
Shutter Speed: 1/8
ISO: 100
Exposure Compensation: -0.3 EV
Image Stabilisation: Off