There are several different ways to express the golden ratio. 4 different ways are listed below.

 

\(\displaystyle \text{Golden Ratio } \displaystyle\phi = \frac{1+\sqrt{5}}{2}\)

 

\(\displaystyle \text{Golden Ratio } \displaystyle\phi = 1+\frac{1}{1+\frac{1}{1+\frac{1}{1+…\frac{1}{1+\frac{1}{1+…}}}}}\)

 

\(\displaystyle \text{Golden Ratio } \displaystyle\phi = \frac{a}{b} \text{ such that } \frac{a+b}{a}=\frac{a}{b}\)

 

\(\displaystyle \text{Golden Ratio } \displaystyle\phi \approx 1.61803398875 \)

 

See Related Pages\(\)

\(\bullet\text{ Fibonacci Sequence}\)
\(\,\,\,\,\,\,\,\,0,1,1,2,3,5,8,13,21…\)

\(\bullet\text{ Golden Ratio}\)
\(\,\,\,\,\,\,\,\,1.61803398875…\)

\(\bullet\text{ Pascal’s Triangle}\)
\(\,\,\,\,\,\,\,\,\)

\(\bullet\text{ Binomial Theorem}\)
\(\,\,\,\,\,\,\,\,\displaystyle\frac{n!}{(n-(k-1))!(k-1)!}a^{(n-(k-1)))b^{k-1}}\)

\(\bullet\text{ Andymath Homepage}\)