fibonacci spiral

Logarithmic Spirals of the Nautilus Shell.

The spiral is a common element of Sacred Geometry as well as to all natural development. Spirals in nature tend to follow the Golden Ratio (Phi) or Fibonacci Sequence in their rates of expansion. The key to Sacred Geometry is the relationship between the progression of growth and proportion. Harmonic proportion and progression are the essence of the created universe and is consistent with nature around us. The natural progression follows a series that is popularized in the West as the “Fibonacci Series” where the first two numbers in the series are added to create the third number for a series of number that begins 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377, 610, 987…and goes on ad infinitum. The ratio of the numbers gains great importance as the series continues. By dividing one number by the previous number, the answers result in or come closer to phi: 3/5 = 1.6666, 13/8 = 1.6250, 233/144 = 1.6180. These numbers can be demonstrated with the spiral of the Nautilus. 

The Golden Ratio (phi) is the unique ratio such that the ratio of the whole to the larger portion is the same as the ratio of the larger portion to the smaller portion. The ratio links each chamber of the nautilus to the new growth and symbolically, each new generation to its ancestors, preserving the continuity of relationship as the means for retracing its lineage. This geometry of the Nautilus can be found in the spiral patterns of cauliflower, the placement of the leaves on most plants, the arrangement of pattern on a pine cone. The ratios can be retrieved from the shape of our DNA and the measurement of distant galaxies as the Sacred Geometry demonstrates the blueprint of the sacred foundation of all things and the interconnectedness of all the various parts of the whole. 

Fibonacci Series.

The Fibonacci series covers the simplest golden section sequence which can be expressed in whole-numbers (the golden section of 89 being 55, and that of 55 being 34, etc.):

2, 3, 5, 8, 13, 21, 34, 55, 89 …

In it each number equals the sum of the two preceding numbers (that is, 2+3 =5, 3+5=8, 5+8=13, etc.).

The sequence approaches nearer and nearer the proportion of the geometrical golden section i.e. the irrational key-number of the geometric mean: the square of every number is equal to the product of the numbers preceding and following it - with the difference of plus or minus 1.

The Fibonacci series embodies the low of natural growth. In the fir-cone starting from the centre, a system of spirals runs in the right and left directions, in which the number of spirals always result in the values of the Fibonacci sequence: 3, 5, 8 and 13 spirals.

A similar setting can be seen on the sunflower, pineapple, chamomile, dandelion, marguerite, cactus, likewise in the arrangement of leaves on the stem and in the horns of some ruminating animals.