Did I miss ‘something’? You seem to state that I had…& U went on then to say the same thing: it is an INFINATE NUMBER! THAT was not my point! I was encouraging others to “investigate” & involve themselves. So; just sit back in your easy chair & awaite tour Super Computer to Print-Out a copy. Just remember man(kind) need only use the Tooles Available and not trumpet your knowledge (wisdom?) of the simple fact that we all accept/know about WHO is in knowledge of that “Number” & most of us spend time with “Him” every week-end.
… ..that’s all.

If you want the true, complete number the golden ratio is calculated as (√5+1)/2. This is an irrational number with an infinite number of random digits, so sharing it “in full” would not only take an infinite amount of time and energy, but would also be a colossal waste of time. In the physical world, real life applications of any mathematical concept or measure rarely require more that 4 to 6 decimal places of accuracy. If you’d like more though see my page at https://www.goldennumber.net/phi-million-places where I list not just the first 500 digits of the golden ratio but rather the first 20,000. If you want to see how it is applied, click on the section headers at the top of any page of this site and explore the articles in the Design/Art, Beauty/Face, Markets/Gaming and other sections. If you’d like to go beyond the hundred plus articles on this site, see the applications listed on my PhiMatrix software site at https://www.phimatrix.com/applications/. There no tease or hold back here. Just dig a little deeper.

Okay. If you are so excited about the “Golden mean”; aka the Golden Ratio… then give me the FULL Number! Do not tease about your “discovery”! We all deserve you giving us the FULL STORY… The COMPLETE STORY AND the true/complete number! And! They’ll us how to find it and where we may see it Applied. Let us not be left with a fragment of one of The Most Important Numbers known time ManKind! Don’t be selfish: SHARE! Share it in Full!
Okay, I dare you to tell us the first numbers after the decimal point… and show At Least the First (let’s say) 500! Ok?

Consider this quote then from Dr. Stephen Marquart:

“All life is biology.
All biology is physiology.
All physiology is chemistry.
All chemistry is physics.
All physics is math.”

I respect that the golden ratio is sometimes used in music, but Lateralus is one obscure song, and Vi Hart is one relatively unknown “mathemusician” so I do not believe these two appearances together comprise “popularity”. Furthermore Lateralus is good, but its not exactly amazing (as seen in the fact that it is little known outside its links to the golden ratio) so this is not proof that ratio is somehow aesthetically pleasing in music

Consider looking at Asian (especially Japanese gardens and interiors) as they work with this in approaching it from their special appreciation of innate balance and the comfort of balance as they have experienced it for thousands of years. Perhaps they have a certain mathematical relationship – but the final “adjustments” are from a personal-human level; even superhuman, level. It is certainly “comfortable” and does appear to conform to the “Western” mathematical schemas [including: 1+1 = 2+1 = 3+2 = 5+3 = 8…. Fibonacci Progression!]. As in the layout of formal gardens, the “final” adujstment of a stone’s location is made in consideration of where the viewer is positioned, the size, shape and color of that stone – as well as the time of day and the location of the solar source of light – either sun or moon – as relating to the view AND – perhaps – a PARTICULAR EVENT. So much for “Pure” mathematical analysis!

wrong number. she got greedy when it should have been $1.61