The Fibonacci Number Sequence Leonardo Fibonacci Math and Art The Fibonacci Number Sequence

Fibonacci patterns are numerical sequences that fascinated the Italian mathematician Leonardo Fibonacci in the early 1200s. Each entry of the sequence is obtained by adding the two previous numbers together: 0, 1,1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144....

The patterns have been noted to frequently appear in biological settings, like the spiral arrangement in flowers, seeds, sepals and scales on such plants as pinecones, pineapples and sunflowers.

For instance, people may find two sets of lines connecting the centers of each segment of the pinecone, 13 in clockwise and 8 in counterclockwise.

In terms of sunflower spirals, the combinations can be in 21 by 34, 34 by 55 until 89 by 144

Here is a spiral drawn in the squares, a quarter of a circle in each square.. Such spirals are seen in the shape of shells of snails and sea shells and, as we see later, in the arrangement of seeds on flowering plants too. The spiral-in-the-squares makes a line from the centre of the spiral increase by a factor of the golden number in each square. So points on the spiral are 1.618 times as far from the centre after a quarter-turn. In a whole turn the points on a radius out from the center are 1.6184 = 6.854 times further out than when the curve last crossed the same radial line.

Nautilus

Golden spiral is seen in Milky Way, DNA, Whirlpools, rams horns, Tornados, Fingerprints, Shells all exhibit the golden spiral which is a direct derivative of Fibonacci numbers.

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 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.

Why do these arrangements occur? 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.

Coneflower

Simple Fibonacci Examples Simple examples for you to shoot in an original way with concentration on lighting. IN FOCUS Unusual views

0, 1,1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144....

Euporbia with two petals 0, 1,1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144....

Trillium with 3 petals 0, 1,1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144....

0, 1,1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144.... Columbine with 5 petals

0, 1,1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144.... Bloodroot with 8 petals

Black-eyed Susan with 13 petals 0, 1,1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144....

Shasta daisy with 21 petals 0, 1,1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144....

The Fibonacci Sequence is everywhere Shoot it 1. In focus 2.With a creative twist or Unusual view 3. Explain In PP