Decoding Da Vinci: Finance, Functions and Art

by Tim Johnson

Dan Brown in his book, The Da Vinci Code, talks about the "divine proportion", an irrational number given the Greek symbol , as having a "fundamental role in nature". Brown’s ideas are not completely without foundation. The proportion crops up in the mathematics used to describe the formation of natural structures like snail’s shells and plants, and even in Alan Turing’s work on animal coats.

But Dan Brown does not talk about mathematics, he talks about a number, . What is so special about this number?

From rabbits to ratios

The divine proportion appears in Fibonacci's 1202 book on financial mathematics, the Liber Abaci. The Liber is a series of increasingly difficult problems (with solutions) that generations of apprentice merchants used to learn their trade in the middle ages. It was the textbook that taught Copernicus, who wrote about money before he wrote about planets, and Simon Stevin(1548 – 1620), who made mathematics useful and helped free the Netherlands from Spain.

One of the simpler problems Fibonacci used was on the business of breeding rabbits. Given that one pair of rabbits produces one other pair of rabbits a month, how many rabbits will there be after a year, assuming that we start with one pair?

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