Difference between revisions of "Golden ratio"
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| − | [http://www.johndcook.com/blog/2014/02/17/imaginary-gold/] | + | [http://www.johndcook.com/blog/2014/02/17/imaginary-gold/]<br /> |
| + | [https://plus.google.com/u/0/+AndrewStacey/posts/Yvki1GcVywF] | ||
Revision as of 04:51, 11 April 2015
The golden ratio is $\varphi = \dfrac{1+\sqrt{5}}{2}.$
Properties
Theorem: The following formula holds: $$2\sin(i \log(\varphi))=i,$$ where $\sin$ denotes the sine function, $i$ denotes the imaginary number, $\log$ denotes the logarithm, and $\varphi$ denotes the golden ratio.
Proof: █
