Friends of the Wild Flower Garden

Spirals in nature

by Gary Bebeau

When Leonardo of Pisa (1180-1250), important Italian mathematician, wanted to know how fast rabbits multiply he derived a sequence of numbers that unlocked in later years some secrets in the plant kingdom.

You may have noticed that many plants exhibit arrangement of parts in an increasing sequence of numbers such as leaves around a stem, number of petals or number of florets in the disc of aster family plants. Many of these parts are arranged in spirals, frequently two sets of spirals, winding in opposite directions.

Leonardo of Pisa was known as Fibonacci (”son of Bonaccio”) thus his sequence is known as the Fibonacci Sequence and it goes 0,1,1,2,3,5,8,13,21,34,55,89 etc and is arrived at by adding the two previous numbers to get the next number. The number of spirals in the disc of a coneflower or a sunflower is usually a Fibonacci number as are the number of florets in each spiral for those who like to count such things.

Gray-headed coneflower

You can see the counter twining spirals in the photos of the coneflower, the spruce cone and the vervain. This all has to do with spacing - so that each element gets the amount of exposure needed. Other examples from plants are a sequence of species with ever-increasing number of petals. Lilies have 3 petals, most buttercups have 5, delphiniums eight, and so it goes.

Incidentally, the rabbit question posed in his book, Liber Abaci, was “How many pairs of rabbits will be produced in a year, beginning with a single pair, if in every month each pair bears a new pair, one male and one female, which become productive from the second month on and none die during the year?”

The answer is 144 pairs❖

Hoary Vervain flowers Norway Spruce Cone


Gary Bebeau is a Fiends member and director.