Fibonacci Numbers In Nature

The Fibonacci numbers are Nature's numbering system. They appear everywhere in Nature.

The sequence, in which each number is the sum of the two preceding numbers is known as the Fibonacci series: 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377, 610, 987, 1597, 2584, 4181, ...

Fibonacci was known in his time and is still recognized today as the "greatest European mathematician of the middle ages."

He was born in the 1170's and died in the 1240's.He was one of the first people to introduce the Hindu-Arabic number system into Europe.

Fibonacci and Nature

Plants do not know about this sequence - they just grow in the most efficient ways. Many plants show the Fibonacci numbers in the arrangement of the leaves around the stem. Some pine cones and fir cones also show the numbers, as do daisies and sunflowers.

Why do these arrangements occur? In the case of leaf arrangement, or phyllotaxis, some of the cases may be related to maximizing the space for each leaf, or the average amount of light falling on each one. Even a tiny advantage would come to dominate, over many generations. In the case of close-packed leaves in cabbages and succulents the correct arrangement may be crucial for availability of space.


Petals on flowers

On many plants, the number of petals is a Fibonacci number:
buttercups have 5 petals; lilies and iris have 3 petals; some delphiniums have 8; corn marigolds have 13 petals; some asters have 21 whereas daisies can be found with 34, 55 or even 89 petals.

• 3 petals: lily, iris
• 5 petals: buttercup, wild rose, larkspur, columbine (aquilegia)
• 8 petals: delphiniums
• 13 petals: ragwort, corn marigold, cineraria,
• 21 petals: aster, black-eyed susan, chicory
• 34 petals: plantain, pyrethrum
• 55, 89 petals: michaelmas daisies, the asteraceae family

  

  
  

Here is a passion flower (passiflora incarnata) from the back and front:

Back view

the 3 sepals that protected the bud are outermost,
then 5 outer green petals followed by an inner layer of 5 more paler green petals

Front view

the two sets of 5 green petals are outermost, with an array of purple-and-white stamens (how many?);in the centre are 5 greenish stamens (T-shaped) and uppermost in the centre are 3 deep brown carpels and style branches)


Vegetables and Fruit

Here is a picture of an ordinary cauliflower. Note how it is almost a pentagon in outline. Looking carefully, you can see a centre point, where the florets are smallest. Look again, and you will see the florets are organized in spirals around this centre in both directions.

Human Hand

Every human has two hands, each one of these has five fingers, each finger has three parts which are separated by two knuckles. All of these numbers fit into the sequence.

However keep in mind, this could simply be coincidence.