Wolfram Math World has a few things to add: http://mathworld.wolfram.com/GoldenRatio.html I personally like my ratios to be in the range (0,1]. In fact I once wrote some code that made extensive use of "phi", where I was treating it as the smaller ratio. When I realized I was using the opposite of the more common convention, I was annoyed, but just replaced the name "phi" with "rphi" (reciprocal of phi) and called it a day. Tom James Buddenhagen writes:
Coxeter called (1+sqrt(5))/2 tau.
On Wed, Jul 15, 2015 at 1:53 PM, James Propp <jamespropp@gmail.com> wrote:
There is ambiguity in the mathematical literature as to whether the term "golden ratio" refers to 1.618... or 0.618...
I think it's been suggested that one of these quantities be called tau and the other phi, but I can't remember which is which.
Jim Propp
On Wednesday, July 15, 2015, Dan Asimov <asimov@msri.org> wrote:
I don't agree. There is a real mathematical difference between positive and negative reals among complex numbers: Positive reals are the reals having their square roots among the reals; negatives don't. So tau is the positive root of 1/x = x-1.
There is no mathematical difference between +i and -i. (They are distinct complex numbers, but they have the same properties.)
—Dan
On Jul 15, 2015, at 11:29 AM, Veit Elser <ve10@cornell.edu <javascript:;>> wrote:
I’m guessing they are using the less popular “conjugate" definition tau = (1-sqrt(5))/2. Calling that an “error" is the same as taking issue with systematic replacement of i with -i in the equations of quantum mechanics.
Curious that it was caught when the museum turned 34.
-Veit
On Jul 15, 2015, at 2:17 PM, James Propp <jamespropp@gmail.com <javascript:;>> wrote:
Does anyone know anything about this?
http://www.dailymail.co.uk/news/article-3152858/Teen-catches-math-error-gold...
The press release (sounding more political than mathematical) asserts
that
the way the Museum presents the Golden Ratio in its exhibit "is in fact the less common - but no less accurate - way to present it".
So, what was the "mistake" in the Eames exhibit, and was it in fact a mistake?
The newspaper story doesn't give details.
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