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

Accepted Solution

Answer:[tex]\frac{a+b}{a}=\frac{a}{b}[/tex]Step-by-step 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 [tex]\frac{a+b}{a}=\frac{a}{b}[/tex].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 [tex]\frac{a+b}{a}=\frac{a}{b}[/tex].[tex]\frac{30.9+19.1}{30.9}=\frac{30.9}{19.1}[/tex][tex]\frac{50}{30.9}=\frac{30.9}{19.1}[/tex]1.618 = 1.618This is the golden ratio.