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*From*: John Denker <jsd@av8n.com>*Date*: Mon, 14 Jan 2013 16:08:51 -0700

On 01/14/2013 03:25 PM, Larry Smith wrote:

I asked my students where we see the golden ratio and one of them

suggested astronomy. This was news to me so I assigned her to

research it and bring it back to class. Most of the URLs she came up

with were wacko stuff and numerology, but one web site looked a

little more interesting. Mario Livio has more credibility than the

other sites, but I'd still thought I'd ask this list about \phi

showing up in equations for Kerr black holes.

http://www.huffingtonpost.com/mario-livio/the-golden-ratio_b_1818907.html

The golden ratio has been a magnet for mystics, cranks, and pseudo-scientific

numerologists for a long time. A useful fact-based overview can be found

at

http://www.lhup.edu/~dsimanek/pseudo/fibonacc.htm

As for Kerr black holes in particular: A stopped clock is right twice

a day. There are lots of physics formulas involving square roots, and

if you rummage around long enough you will find some that involve the

square root of 5. Note that the result is sensitive to the units used

to measure G and measure spin. If we measured the gravitational coupling

the same way we measured the electromagnetic coupling, the definition

of G would pick up a factor of 4π, and the alleged golden-ratio result

would disappear.

Similarly, the optimal height for the cushion on a billiard table is

proportional to the diameter of the ball. The constant of proportionality

comes out to a magical ratio, namely 7/10. It could have been 1/Φ i.e.

0.61803398875 but actually it is 0.7.

**References**:**[Phys-L] golden ratio in astronomy***From:*Larry Smith <larry.smith@snow.edu>

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