
Pi and the Golden Ratio - signa11
https://johncarlosbaez.wordpress.com/2017/03/07/pi-and-the-golden-ratio/
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adrianratnapala
I wanted to make in intelligent comment about this. But that comment turned
out be: "Well holly crap, I didn't expect that".

Then again John Baez is the dude who very nearly explained General Relativity
to my satisfaction, long after I got my PhD in physics.

    
    
        http://math.ucr.edu/home/baez/einstein/
    

So I am no longer surprised by what he (and apparently Greg Egan) can do.

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HappyTypist
That link was hard for me to copy on mobile. Here it is, unformatted:
[http://math.ucr.edu/home/baez/einstein/](http://math.ucr.edu/home/baez/einstein/)

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shas3
In case you missed it, John Baez's collaborator in that post is Greg Egan, who
is well known for his brilliant and visionary science fiction.
[http://www.gregegan.net/](http://www.gregegan.net/)

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andyjohnson0
I always thought that Egan was primarily a SF writer who happened to be a
proficient mathematician. Have I got that the wrong way around?

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pavel_lishin
If you read The Clockwork Rocket, it becomes very, very obvious that Egan is a
mathematician who will go to any length - including writing excellent fiction
- to attempt to cram knowledge into your head.

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pavel_lishin
> _Greg Egan and I came up with this formula last weekend._

He says with the same sort of casual tone that I would refer to my wife and I
rearranging the living room last weekend.

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andyjohnson0
> Greg Egan and I came up with this formula last weekend.

I always wonder what it _feels like_ to be able to do that. Even if, as Baez
says, the formula wasn't actually "new", to be able to dive down and come back
up with new to you must be very satisfying.

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j7ake
Probably related to what some call "flow".

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gefh
So the key here is that cos(pi/5) = phi/2\. From there, you could relate pi
and phi in many ways. The proof of cos(pi/5) is quite simple, neatly done
here:
[http://faculty.wwu.edu/curgus/Courses/125/Pentagon.pdf](http://faculty.wwu.edu/curgus/Courses/125/Pentagon.pdf)

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mtreis86
I have always disliked pi. Well, the 3.14 version. Ever since learning other
number bases...
[http://turner.faculty.swau.edu/mathematics/materialslibrary/...](http://turner.faculty.swau.edu/mathematics/materialslibrary/pi/pibases.html)

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kej
One advantage to the hexadecimal version is that you can compute [1] an
arbitrary digit without finding all the digits before it.

[1]
[https://en.wikipedia.org/wiki/Bailey%E2%80%93Borwein%E2%80%9...](https://en.wikipedia.org/wiki/Bailey%E2%80%93Borwein%E2%80%93Plouffe_formula)

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mtreis86
I had not seen that before. I wonder if any other interesting numbers are
better calculated in alternate bases. Thanks

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onychomys
Those people who want to ditch pi in favor of 2pi should read this article to
learn why they're wrong.

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aradhakrishnan
I'm not sure I follow. Multiplying through by two to get tau would simply move
the nested square roots from the denominator to the numerator in the relation
with the golden ratio (as is explained in the link).

I certainly don't see any step in the outlined derivation that gains or loses
the ability to be intuited simply due to a factor of two.

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samstave
I haven't read this article yet - but I just wantedto point out an interesting
trivia tidbit about the golden ratio...

If you draw a typical star, the one you likely first learned to draw, each
line is intersected by 1 to 1.618

