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What is the golden ratio?

To describe it in simple terms, consider any two quantities where each quantity is greater than zero. Let us say the two quantities have the ratio m:n. Now calculate the sum of the two aforementioned quantities and find the ratio of that sum to any larger quantity of the two, let us call it ratio x:y. If it turns out that ratios m:n and x:y are same, then the two quantities are described as being in a golden ratio.

Algebraically, for quantities b and a where a>b>0, it is expressed as;

((a+b)/a)=def a/b=phi where phi denotes the golden ratio.

Using the above descriptions, if you were to take a perfect square with sides a and place it adjacent to a rectangle that matches its “height” (“height” of the square) but with at least half of the square’s breadth b, then two will form a similar golden rectangle with the longer side of the golden triangle being a+b and the shorter side being a. Therefore, a is to b as a+b is to a. the golden ratio has a decimal approximation of 1.6180339887…

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