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How do the lengths of line segments define the golden ratio?

User Ibm
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Answer:


(a+b)/(a)=(a)/(b)

Explanation:

The golden ratio is a special number favored by the Greeks. Its ratio roughly equals 1.618. The ratio is formed by taking a line segment and dividing it into two parts labeled a and b. The golden ratio is formed when this proportion is true
(a+b)/(a)=(a)/(b).

When you add a and b then divide by a, it will be the same as a divided by b. This will hold true only for specific lengths of a and b. This means you must divide the line segment in such a way that a and b meet this requirement.

Example:

If the line segment is 50 cm long. Split the segment into parts a and b where a = 30.9 and b = 19.1. Substitute the values into the proportion
(a+b)/(a)=(a)/(b).


(30.9+19.1)/(30.9)=(30.9)/(19.1)


(50)/(30.9)=(30.9)/(19.1)

1.618 = 1.618

This is the golden ratio.

User Tahj
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