Beautiful irrational number.

Number Theory Level 2

S = 1 + 1 1 + 1 1 + 1 1 + 1 1 + . . . S=1+\frac{1}{1+\frac{1}{1+\frac{1}{1+\frac{1}{1+...}}}}

S is one of the most important irrational constants in the history of mathematic. What is S?

2 \sqrt{2} half of p i pi where p i pi is the ratio of a circumference of a circle to its diameter p h i phi (golden ratio) 3 \sqrt{3}

Lee Young Kyu by Lee Young Kyu , 25, Hong Kong

This section requires Javascript.
You are seeing this because something didn't load right. We suggest you, (a) try refreshing the page, (b) enabling javascript if it is disabled on your browser and, finally, (c) loading the non-javascript version of this page . We're sorry about the hassle.

1 solution

Lee Young Kyu
Aug 17, 2014

S − 1 = 1 S S-1=\frac{1}{S}

S 2 − S − 1 = 0 S^{2}-S-1=0

S = 5 + 1 2 S=\frac{\sqrt{5}+1}{2} because obviously S is a positive real number.

Thus S is phi, the golden ratio.

2 Helpful 0 Interesting 0 Brilliant 0 Confused

0 pending reports

×

Problem Loading...

Note Loading...

Set Loading...