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In science, the ratio of two quantities is the value of the first quantity divided by the value of the second one. For example, the ratio of 10m to 5m is 2.
The value of a ratio - of two numbers - is the value of the first divided by the second.
The value of the Golden Ratio is (1 + sqrt(5))/2. It is visually appealing because it is!
As for example 15 and 9 can be reduced to a ratio of 5 and 3
Golden ratio can be traced back to as early as 2500 BC. The Great Pyramid of Giza is an example of the golden ratio. the side is 612.01. and the half of the base is 377.9. 612.01/ 377.9= 1.61950... its approximately the measurement of the golden ratio. Another example is the Parthenon.