# The Fibonacci Sequence

**The Fibonacci Sequence**

The Fibonacci sequence is a series of numbers where a number is found by adding up the two numbers before it. Starting with 0 and 1, the sequence goes 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, and so forth. Written as a rule, the expression is xn = xn-1 + xn-2.

**Fibonacci In Nature**

Fibonacci numbers do actually appear in nature, from sunflowers to hurricanes to galaxies. Sunflowers seeds, for example, are arranged in a Fibonacci spiral, keeping the seeds uniformly distributed no matter how large the seed head may be.

**The Golden Triangle**

The spiral and resulting rectangle are known as the Golden Rectangle. - A rectangle with sides in the ratio of 1 : φ is known as a Golden Rectangle, and many artists and architects throughout history (dating back to ancient Egypt and Greece, but particularly popular in the Renaissance art of Leonardo da Vinci and his contemporaries) have proportioned their works approximately using the Golden Ratio and Golden Rectangles, which are widely considered to be innately aesthetically pleasing.

**The Golden Spiral**

An arc connecting opposite points of ever smaller nested Golden Rectangles forms a logarithmic spiral, known as a Golden Spiral. The Golden Ratio and Golden Spiral can also be found in a surprising number of instances in Nature, from shells to flowers to animal horns to human bodies to storm systems to complete galaxies.

**The Golden Ratio**

A Fibonacci spiral is a series of connected quarter-circles drawn inside an array of squares with Fibonacci numbers for dimensions. The squares fit perfectly together because of the nature of the sequence, where the next number is equal to the sum of the two before it. Any two successive Fibonacci numbers have a ratio very close to the Golden Ratio, which is roughly 1 : 1.6180339887 (it is actually an irrational number equal to (1 + √5)⁄2 which has since been which has since been calculated to thousands of decimal places) . The larger the pair of Fibonacci numbers, the closer the approximation.

The Golden Ratio value is also known as the Golden Mean, Golden Section, Divine Proportion, etc, and is usually denoted by the Greek letter phi φ (or sometimes the capital letter Phi Φ).

Essentially, two quantities are in the Golden Ratio if the ratio of the sum of the quantities to the larger quantity is equal to the ratio of the larger quantity to the smaller one. The Golden Ratio itself has many unique properties, such as 1⁄φ = φ - 1 (0.618...) and φ2 = φ + 1 (2.618...), and there are countless examples of it to be found both in nature and in the human world.

**An Intra Dimensional Doorway**

The vibrational quality of the Golden Mean gives it very strong communication properties, which facilitate resonance with higher realms in prayer. We live in the 3rd dimension, or the 'Plane of Manifestation'. The Golden Mean is an intra-dimensional doorway though which matter emerges into manifest 3-D reality. For example, when a star is born it follows specific number sequences or universal rules, the same rules of life in the expansion process. Then we see the light! Thus the Golden Mean is the "fingerprint" of creation. When we re-create this moving and always expanding sequence, we have in effect - 'the exact movement of creation in the expansion process'.

**Leonardo of Pisa **

The Fibonacci Sequence is named after the 13th Century Italian Leonardo of Pisa, better known by his nickname Fibonacci, was perhaps the most talented Western mathematician of the Middle Ages. Little is known of his life except that he was the son of a customs official and, as a child, he traveled around North Africa with his father, where he learned about Arabic mathematics. On his return to Italy, he helped to disseminate this knowledge throughout Europe, thus setting in motion a rejuvenation in European mathematics, which had lain largely dormant for centuries during the Dark Ages.

**Fibonacci Sequence Patterns And Mathematical Properties **

A closer inspection of the numbers making up the Fibonacci sequence brings to light all sorts of fascinating patterns and mathematical properties. Fibonacci himself makes no mention of these patterns in his book, but many patterns have been brought to light over years of examination of the numbers in the sequence. For more detailed information I suggest checking out a Thesis by Anna Grigas

**Michael J Robey
Psychic Medium | Psychic Investigator
Psychic.gr
www.psychicgr.com**

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