Fibonacci Day

What the day is

Fibonacci Day is observed on November 23, because the date written 11/23 gives 1, 1, 2, 3, the opening of the sequence in which each number is the sum of the two before it.

Origin and background

Leonardo of Pisa, later known as Fibonacci, introduced the sequence to European readers in Liber Abaci in 1202, by way of a contrived problem about breeding rabbits.

Two corrections are worth making straight away. First, he did not discover it. The sequence appears centuries earlier in Indian mathematics, in the work of Pingala, Virahanka and Hemachandra, arising from the problem of counting possible arrangements of long and short syllables in Sanskrit verse. Second, the sequence is not what made the book important. Liber Abaci argued for Hindu-Arabic numerals and positional notation over Roman numerals, and its effect on European commerce and accounting dwarfs anything the rabbits contributed.

The ratio between consecutive terms converges on roughly 1.618, the golden ratio. Where this genuinely turns up is in plant growth. The number of spirals in a sunflower head, a pinecone or a pineapple is usually a Fibonacci number, because new growth placed at an angle of about 137.5 degrees from the last packs most efficiently without leaves shading one another. That is a real result with a mechanical explanation behind it.

Most of the rest is not. Claims that the Parthenon, the Great Pyramid and the Mona Lisa were composed on the golden ratio are retrofitted, resting on rectangles drawn after the fact and measurements chosen to fit. The nautilus shell is a logarithmic spiral, but not a golden one. The mathematics is interesting enough without the decoration.

How to take part

• Count the spirals on a pinecone or sunflower head in both directions and check both numbers against the sequence.
• Work out the first twenty terms by hand. It takes a minute and makes the growth rate obvious.
• Divide consecutive terms and watch the result settle toward 1.618.
• Take one famous golden ratio claim and check where the rectangle was actually placed.
• Read what Liber Abaci was really for. The numeral system was the revolution.