Difference between revisions of "Relationship between sine, imaginary number, logarithm, and the golden ratio"
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| − | + | ==Theorem== | |
The following formula holds: | The following formula holds: | ||
$$2\sin(i \log(\varphi))=i,$$ | $$2\sin(i \log(\varphi))=i,$$ | ||
where $\sin$ denotes the [[sine]] function, $i$ denotes the [[imaginary number]], $\log$ denotes the [[logarithm]], and $\varphi$ denotes the [[golden ratio]]. | where $\sin$ denotes the [[sine]] function, $i$ denotes the [[imaginary number]], $\log$ denotes the [[logarithm]], and $\varphi$ denotes the [[golden ratio]]. | ||
| − | === | + | ==Proof== |
| + | |||
| + | ==References== | ||
| + | [http://www.johndcook.com/blog/2014/02/17/imaginary-gold/ "Imaginary gold" by John D. Cook]<br /> | ||
| + | [https://plus.google.com/u/0/+AndrewStacey/posts/Yvki1GcVywF]<br /> | ||
| + | |||
| + | [[Category:Theorem]] | ||
| + | [[Category:Unproven]] | ||
Latest revision as of 23:31, 27 June 2016
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.
