According to Wikipedia, the Golden Ratio expresses the relationship that the sum of two quantities is to the larger quantity as the larger is to the smaller. It is usually denoted as the Greek letter 'phi' (φ). However, it is more accurately represented by (√5+1)/2. It is also known as, or closely related to, the golden section, the golden number, and divine proportion.
The Golden Ratio is approximated as 1.6180339887... Therefore, it is considered an irrational number. Phi has the value √5 + 1 /2 and phi is √5 – 1 /2.
It is the only number, which, when diminished by unity, becomes its own reciprocal:
Φ – 1/Φ = 1 i.e., φ² - φ – 1 = 0
The golden ratio of a straight line can be viewed at the following site:
http://plus.maths.org/issue22/features/golden/
Here is an explanation of a line cut in Golden Ratio (as seen in the above link):
It is the only number, which, when diminished by unity, becomes its own reciprocal:
Φ – 1/Φ = 1 i.e., φ² - φ – 1 = 0
The golden ratio of a straight line can be viewed at the following site:
http://plus.maths.org/issue22/features/golden/
Here is an explanation of a line cut in Golden Ratio (as seen in the above link):
If line AB is longer than the segment AC, the segment AC is longer than CB. If the ratio of the length of AC to that of CB is the same as the ratio of AB to AC, then the line has been cut in extreme and mean ratio, or in a Golden Ratio.
The Golden Ratio cannot be expressed as a fraction; in other words, the ratio of the two lengths AC and CB cannot be expressed as a fraction. For example, we cannot find some common measure that is contained, for instance, 31 times in AC and 19 times in CB. Two such lengths that have no common measure are called ‘incommensurable’.
Here is a link to show the calculation of the golden ratio:
http://en.wikipedia.org/wiki/Golden_ratio#Calculation
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