## Numbers in Nature

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. Sunflowers can contain the number 89, or even 144. Many other plants, such as succulents, also show the numbers. Some coniferous trees show these numbers in the bumps on their trunks. And palm trees show the numbers in the rings on their trunks. Fibonacci numbers or patterns are found in: Sea Shells, Petals on Flowers, Sunflower seed Heads, Pine Cones, Palms, Pineapple and other Bromeliads, and Plant Growth or leaf/petal arrangements in 90% of plants.Probably most of us have never taken the time to examine very carefully the number or arrangement of petals on a flower. If we were to do so, we would find that the number of petals on a flower, that still has all of its petals intact and has not lost any, for many flowers is a Fibonacci number. Some species are very precise about the number of petals they have – e.g. buttercups, but others have petals that are very near those above, with the average being a Fibonacci number. Some Fibonacci numbers in nature are: Buttercups … 5 Petals Lillies & Irises … 3 Petals Delphiniums … 8 Petals Corn Marigolds … 13 Petals Asters … 21 Petals Daisies … 34 or 55 (or even 89) Petals Some common trees with their Fibonacci leaf arrangement numbers are: 1/2 elm, linden, lime, grasses 1/3 beech, hazel, grasses, blackberry 2/5 oak, cherry, apple, holly, plum, common groundsel 3/8 poplar, rose, pear, willow 5/13 pussy willow, almond Fibonacci numbers can also be seen in the arrangement of seeds on flower heads. The seeds form spirals (patterns that the eyes sees) curving both to the left and the right, counting the spirals gives you 2 Fibonacci numbers Golden spiral – Milky Way, DNA, Whirlpools, rams horns, Tornados, Fingerprints, Shells all exhibit the golden spiral which is a direct derivative of Fibonacci numbers. Mammillaria, Notocactus, Gymnocalycium, Rebutia and Ferocactus all exhibit Fibonacci sequences in their rib count or tubercule arrangement.Pine cones show the Fibonacci Spirals clearly. Why do these arrangements occur?The same happens in many seed and flower heads in nature. The reason seems to be that this arrangement forms an optimal packing of the seeds so that, no matter how large the seed head, they are uniformly packed at any stage, all the seeds being the same size, no crowding in the centre and not too sparse at the edges. 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. When new leaves grow from a plant, they grow in a spiral around the plant’s stem. Nature spaces the leaves in this way so that higher leaves do not shade the lower leaves too much from sunlight. The number of turns in the spiral (from leaf to leaf) and the number of leaves that exist in the pattern in all cases express a Fibonacci fraction and therefore a Fibonacci ratio. The same pattern repeats again and again as the plant grows. In the case of close-packed leaves in cabbages and succulents the correct arrangement may be crucial for availability of space. So nature isn’t trying to use the Fibonacci numbers: they are appearing as a by-product of a deeper physical process. That is why the spirals are imperfect. The plant is responding to physical constraints, not to a mathematical rule:

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A.K.AHi,just checking out the spaces!!: )

September 1, 2005 at 12:04 pm

JayI actually read your blog re plant, fiboacci numbers etc…..To me it just doesn\’t \’add up\’?! :o)[walks out to garden…. picks daisy……….."she loves me, she loves me not…she love……."]

September 1, 2005 at 7:51 pm