Difference between revisions of "Golden ratio"

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(Properties)
(Properties)
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=Properties=
 
=Properties=
 
[[Relationship between sine, imaginary number, logarithm, and the golden ratio]]
 
[[Relationship between sine, imaginary number, logarithm, and the golden ratio]]
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[[Relationship between cosine, imaginary number, logarithm, and the golden ratio]]
<strong>Theorem:</strong> 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]].
 
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<strong>Proof:</strong>  █
 
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=Videos=
 
=Videos=

Revision as of 09:20, 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 Relationship between cosine, imaginary number, logarithm, and the golden ratio

Videos

The Golden Ratio & Fibonacci Numbers: Fact versus Fiction

References

[1]
[2]