Golden ratio
$20
In mathematics, two quantities are in the golden ratio if their ratio is the same as the ratio of their sum to the larger of the two quantities. Expressed algebraically, for quantities a and b with a > b > 0,
- a + b a = a b = def φ {displaystyle {frac {a+b}{a}}={frac {a}{b}} {stackrel {text{def}}{=}} varphi }
where the Greek letter phi ( φ {displaystyle varphi } or ϕ {displaystyle phi } ) represents the golden ratio. It is an irrational number that is a solution to the quadratic equation x 2 − x − 1 = 0 {displaystyle x^{2}-x-1=0} , with a value of:
φ = 1 + 5 2 = 1.618033 … {displaystyle varphi ={frac {1+{sqrt {5}}}{2}}=1.618033ldots }
