All of these numbers observed in the flower petals-3, 5, 8, 13, 21, 34, 55, 89-appear in the Fibonacci series. There are exceptions and variations in these patterns, but they are comparatively few. Some flowers have 3 petals others have 5 petals still others have 8 petals and others have 13, 21, 34, 55, or 89 petals. Tim Entwisle is the director and chief executive of Royal Botanic Gardens Victoria.įor more about design, architecture, food, travel and fashion, subscribe to the Blueprint for Living podcast on iTunes, the ABC Radio app or your favourite podcasting app.For example, although there are thousands of kinds of flowers, there are relatively few consistent sets of numbers of petals on flowers. In our human world we might see them where they don't exist, but when they do, we seem to like it. In nature these numbers are common, probably reflecting the practicalities of life.

Whether we are attracted to golden ratio and Fibonacci sequence by the mystic of the mathematics or by the aesthetic they produce is uncertain. Some gardeners will group together plants with heights that also correspond to this sequence, for example, 5-metre-tall plants next to 8-metre-tall ones. In gardening, unless we want a particularly formal design, we avoid planting an even number of any particular species, considering odd numbered groupings as more pleasing to the eye.īut adherence to the Fibonacci sequence - which only includes the even numbers 8 and 34 in its early parts - is another approach. The number of petals in a flower is said to be a Fibonacci sequence number, but there are plenty of (and I think too many) exceptions. Renaissance and later buildings, and sometimes their gardens, also seem to include this apparently attractive and important measurement.īut sometimes we see patterns where they don't exist.

Leonardo de Vinci's Vitruvian Man stretches within a circle and square that may or may not have a 'golden' relationship. For example, the Parthenon may or may not represent, let alone be designed to accentuate, the golden ratio. The golden ratio is much loved by artists and architects, although it is sometimes wishfully induced, particularly in historical buildings.

Shapes based on it are, apparently, pleasing to humans. (and so on it's a number that continues on for an infinite number of decimal places, an irrational number). The bigger the sequential numbers in the sequence, the closer their ratio is to phi: 1.6180339887498948420. If you divide one of its numbers by the one before it you get an increasingly good approximation of the golden ratio. In mathematics it is now known by the Greek letter Φ (phi, mostly pronounced 'fi' today, or 'fee' in Greek).Īt first the Fibonacci sequence was the practical answer to an apparently pressing question of the time: how many pairs of rabbits result from a single pair of breeding rabbits over a particular period of time?įibonacci's sequence has a few other surprises.

While his achievements and influence were considerable - including an early adoption of the decimal system in Europe - Fibonacci is best known today for a peculiar sequence of numbers and its connection to an 'irrational number' first defined by the ancient Greeks.Ī few centuries after Fibonacci, this number was called the divine proportion, and then in the 1800s, the golden ratio. Leonardo of Pisa (1170-1240), nicknamed Fibonacci, was perhaps the greatest mathematician in Europe during the Middle Ages. They show up not only in plants themselves, but also in the way we design gardens. What does interest me is the pervasiveness of these numbers in nature and whether that is anything more than a happy happenstance. I wasn't attracted to Dan Brown's 2003 bestseller The Da Vinci Code, but I gather that to decode 'the code' you need a passing knowledge of the golden ratio and its mathematical mate the Fibonacci sequence.

Fibonacci sequence in nature pinecone