There are two main areas where the ratio is used and they are for different reasons.
One reason is that the human mind finds the Golden ratio aesthetically pleasing. It is, therefore, used in art and architecture.
The second reason is directly related to its mathematical properties (the ratio of the whole to the larger part is the same as the ratio of the larger to the smaller parts). This is used in designing paper sizes like the A and B series. Divide an A3 sheet in half and you will get two A4 sheets which have the same aspect ratio as the A3. Repeat and you get two A5s with the same property and so on.
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The Fibonacci sequence can be used to determine the golden ratio. If you divide a term in the sequence by its predecessor, at suitably high values, it approaches the golden ratio.
In italy, the Pantheon, however has the golden ratio. Its pillars below the roof is a rectangle, the golden rectangle, on the roof (top part) is a triangle, the golden triangle.
The golden ratio is a pure number and so has no dimensions.The golden ratio is a pure number and so has no dimensions.The golden ratio is a pure number and so has no dimensions.The golden ratio is a pure number and so has no dimensions.
they used it tot work out things like propotions!
It is pleasing to the human eye.