Difference between revisions of "Golden ratio"
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Revision as of 09:15, 5 June 2016
The golden ratio $\varphi$ is the irrational algebraic number $$\varphi = \dfrac{1+\sqrt{5}}{2}.$$
Properties
Relationship between sine, imaginary number, logarithm, and the golden ratio
Theorem: The following formula holds: $$2\cos(i \log(1+\varphi))=3,$$ where $\cos$ denotes the cosine function, $i$ denotes the imaginary number, $\log$ denotes the logarithm, and $\varphi$ denotes the golden ratio.
Proof: █
Videos
The Golden Ratio & Fibonacci Numbers: Fact versus Fiction
