Pi and the Golden Ratio

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

Baez is also the author of this interesting paper:

Physics, Topology, Logic and Computation: A Rosetta Stone

http://math.ucr.edu/home/baez/rosetta.pdf

Example of his books (unfortunately the only one I have read...so far)

Permutation City: People can run simulations of themselves or entirely migrate their consciousness into computer programs, but existence is often limited to the amount of computation that you can afford, leading to slow existences that stretch time into fractions of realtime. That premise had me hooked, but the book has fantastic thought provoking plot points throughout. Highly recommended.

I feel in love with his novel Diaspora before I knew anything about Egan the mathematician.

Then in my grad school work, I randomly ran across his name and have subsequently read most of his books.

Diaspora, however, remains my all time favorite novel.

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?

Probably related to what some call "flow".

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...

Decimal is so mainstream

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.

But... why? If you wanted to express their equation in terms of tau (that is, 2pi), you could just set the first term of the right hand side to 10/phi instead of 5/phi. In fact, throughout their derivation there are points where a tau-based version would be a bit cleaner (though of course there are other points where tau might be a bit messier).

i can't tell you how many failed trig tests happen as a direct result of a non-intuitive unit circle defined in terms of Pi [1].

Pi is fundamentally wrong. A circle is defined by a point and a radius. Diameter is just something that has always been easier to measure, so now we're stuck with it :( The fact that Tau makes some formulas less "elegant" is irrelevant.

[1] http://www.shelovesmath.com/wp-content/uploads/2012/11/Unit-...