The golden ration can occur anywhere. The golden proportion is the ratio of the shorter length to the longer length which equals the ratio of the longer length to the sum of both lengths. The golden ratio is a term used to describe proportioning in a piece. In a work of art or architecture, if one maintained a ratio of small elements to larger elements that was the same as the ratio of larger elements to the whole, the end result was pleasing to the eye. The ratio for length to width of rectangles is 1.61803398874989484820. The numeric value is called "phi". The Golden Ratio is also known as the golden rectangle. The Golden Rectangle has the property that when a square is removed a smaller rectangle of the same shape remains, a smaller square can be removed and so on, resulting in a spiral pattern. The Golden Rectangle is a unique and important shape in mathematics. The Golden Rectangle appears in nature, music, and is often used in art and architecture. Some thing special about the golden rectangle is that the length to the width equals approximately 1.618

Golden Ration = Length = 1.6
Width

The golden rectangle has been discovered and used since ancient times. Our human eye perceives the golden rectangle as a beautiful geometric form. The symbol for the Golden Ratio is the Greek letter Phi.

The Fibonacci Series was discovered around 1200 A.D. Leonardo Fibonacci discovered the unusual properties of the numeric series, that's how it was named. It is not proven that Fibonacci even noticed the connection between the Golden Ratio meaning and Phi. The Renaissance used the Golden Mean and Phi in their sculptures and paintings to achieve vast amounts balance and beauty.

The Golden Ratio in Architecture and Art
Throughout the centuries, artists have used the golden ratio in their own creations. An example is "post" by Picasso. When using a golden mean gauge you can see that the lines are spaced to the Golden...

...rederick smith
The GoldenRatio
March 31 2011
1. The introduction:
Hello my name is Frederick Smith, I will be speaking you about a fascinating thing that is in everything, it’s a part of you, it created you & its not just in you, its all around you. Its also in all plants and in all animals. Take for example an octopus has eight tentacles hence the name “octo’~pus, each one of its tentacles has the exact number of suckers on it and each tentacle is the same...

...Golden Patterns
It is a common misconception to believe that mathematics is only found in books, written on paper, expressed as variables, functions, shapes and alphanumerical characters or as a real world application of a mathematical problem found in real life now worded and written into text. As a student progresses through grade school a student can’t help but feel no connection between the world’s nature and mathematical work, this concept however could not be further...

...The GoldenRatio
Body, art, music, architecture, nature – all connected by a simple irrational number – the GoldenRatio. According to Posamentier & Lehmann in their work The
(Fabulous) Fibonacci Numbers, there is reason to believe that the letter φ (phi) was
used because it is the first letter of the name of the celebrated Greek sculptor Phidias (490-430 BCE). He produced the famous statue of Zeus in the Temple of Olympia...

...calculate the rest of the terms the same way:
F0 | F1 | F2 | F3 | F4 | F5 | F6 | F7 |
0 | 1 | 1 | 2 | 3 | 5 | 8 | 13 |
Segment 2: The Goldenratio
In order to define the goldenratio we need to examine the following sketch:
The line above is divided into two segments in such a way that ABAP=APPB
The ratio described above is called the goldenratio.
If we assume that AP=x units...

...The GoldenRatio
The theory of the Italian mathematician Leonardo Pisano is extremely present today. While he was trying to sort out the number of rabbits that mated in a year, he discovered a series of numbers, that are profoundly consistent in man, nature & animals. This discovery was extraordinary, but he also found that the ratio always resulted in 1.618. Although it is called...

...The History of Algebra and
The GoldenRatio in Nature
By: Lauren Pressley
Introduction to Statistics
Throughout history algebra has changed in words through etymology. Etymology is an account of the history of a particular word or elements of a word. The word “algebra” is derived from Arabic writers. Algebra is a method for finding solutions of equations to the simplest possible form. Different cultures...

...Secret of golden mean ratio:
1.618~(or its inverse 0.681~): number of goldenratio is a mystery of ka`aba. Unbelievely, the closer a ratio to this number in an object or a system of objects ,the more beautifull it is manisfied.
Phi constant: 1.681~; superior design number of mathematics, is a repairing decimal , which never ends. This formula is b/a.
The creator has always used the very same number in numerous events in...

...THE GOLDENRATIO IN THE HUMAN BODY
GABRIELLE NAHAS
IBDP MATH STUDIES
THURSDAY, FEBRUARY 23rd 2012
WORD COUNT: 2,839
INTRODUCTION:
The GoldenRatio, also known as The Divine Proportion, The Golden Mean, or Phi, is a constant that can be seen all throughout the mathematical world. This irrational number, Phi (Φ) is equal to 1.618 when rounded. It is described as "dividing a line in the extreme and...

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