Difference between revisions of "Relationship between sine, imaginary number, logarithm, and the golden ratio"
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(Created page with "===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 [...") |
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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== | |
Revision as of 09:18, 5 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.
