Comments for The Golden Ratio: Phi, 1.618

Comment on Pi is 3.1446 per “Measuring Pi Squaring Phi” by Harry Lear—Reviewed by Gary B Meisner

Gary B Meisner — Sun, 30 Aug 2026 01:36:04 +0000

In reply to Arthur.

Radians are not the foundation of trigonometry. Trigonometric ratios arise from right triangles, circle geometry, and the Pythagorean theorem. Trigonometry existed long before the radian measure was introduced.

Modern software usually accepts angles in radians because radians provide the natural scale for calculus and arc length, but the results are identical to trigonometry based on dividing a circle by 360 degrees.

The convention of how the circumference of a circle is divided does not establish a chosen value of pi. In fact, sine and cosine can be defined by power series or differential equations without first assuming pi, after which their period independently yields the accepted value of 3.1415926535…, not 4/√φ.

This claim misrepresents the foundational concepts of trigonometry and does nothing to prove an alternate value for pi.

Comment on Pi is 3.1446 per “Measuring Pi Squaring Phi” by Harry Lear—Reviewed by Arthur

Arthur — Sat, 29 Aug 2026 14:00:30 +0000

In reply to Rudyard Quinn Paine.

Radian is related to the actual value of pi.
All trigonometric functions in softwares are related to radian.
Changing the value of pi means changing all trigonometric functions in computers.
Rewrite a lot of software.
A radian is no more 180 / 3.1415926… degrees but 45 * √ɸ.

Maybe find a way to calculate trigonometric functions without pi and radian.
Directly from degree.
CORDIC formulas can do the job.

Comment on Phi and Fibonacci in Kepler and Golden Triangles by Gary B Meisner

Gary B Meisner — Fri, 21 Aug 2026 18:51:57 +0000

In reply to Mark.

The focus on Fibonacci-based triangles is not an attempt to approximate a true Kepler triangle. It’s simply the fact that this site is dedicated to appearances and applications of the golden ratio and the Fibonacci sequence.

You’re absolutely correct that there are many other ways to approximate a Kepler triangle. Actually there are an infinite number of ways. The focus here is simply to share interesting applications of Fibonacci numbers.

Comment on Pi is 3.1446 per “Measuring Pi Squaring Phi” by Harry Lear—Reviewed by Gary B Meisner

Gary B Meisner — Fri, 21 Aug 2026 18:40:10 +0000

In reply to Rudyard Quinn Paine. In my personal observation, this is pattern seeking. If someone was trying to prove a different value for pi would we just assign a different number of degrees to a circle? The value of pi has nothing to do with how many degrees are in a circle. It can be derived independently of that with a variety of methods. Also, what value would 366 degrees provide? It's prime factors are 2x3x61. The value of 360 is that is divisible by some many numbers, with prime factors of 2x2x2x3x3x5. 3.144… is NOT the true value of pi, and seeking other relationships that try to explain it will always fail mathematically.

Comment on Phi and Fibonacci in Kepler and Golden Triangles by Mark

Mark — Fri, 21 Aug 2026 07:11:54 +0000

I still wonder why not just the roots of 3 consecutive Fibonacci-numbers are used to approximate a true Kepler “Phi-angle” and instead b²-a² = (b-a)(b+a) in particular, Mainly because the súm of 2 consecutive F-numbers is another F-number i.e. 3² + 5² = √34² for example with √(34/25), being √(9/25 +25/25) or √(0.618+1) phi-wise , which in contrast, also accounts, in a similar fashion. for two non-consecutive squares, like 25-4=21 or a √4 : √21 : √25. Both are being somewhat negated by pointing out solely the one based on the difference between consecutive Fibonacci-squares. Is there a special reason for that, which I am missing ? It also makes me wonder if √4+√25=√29 has any particular meaning as well. Or what kind of Phi-angle that represent. That one does not (in contrast) converge to a Kepler-triangle, hat’s for sure.
It is a 1 : phi : √phi × √√5 , probably making little to no sense. A √16 : √25 : √41 does however , I believe, with 40/25 being just ‘1’ off, like 25/16 (instead of 25/15) as well. Next would be a √39 : √64 : √103 , both 39 and 103 being 1 off a golden rectangle as well. Converging to a (true) Kepler Phiangle (?)

Comment on The Human Face and the Golden Ratio by CodeTrendy

CodeTrendy — Thu, 06 Aug 2026 19:48:43 +0000

The tooth ratio is the one that stopped me. Width of center tooth to second tooth, filed right alongside the eyes and the chin. I went in expecting the face rectangle and came out at dentistry. That page has been collecting comments since 2012, so a real question: which objection keeps coming back? CodeTrendy is a directory of sites worth a look, and you can add goldennumber.net yourself, free:

https://codetrendy.com/submit

Comment on Donald Duck visits the Parthenon in “Mathmagic Land” by Mark

Mark — Fri, 31 Jul 2026 12:11:03 +0000

I kind of agree with R.Eastaway however; that the dimensions of a creditcard being esthetically pleasing is not the strongest let alone sole argument, for why the credit card has a fairly (undisputable) golden ratio of round about 2717.. There might be other less ‘profound’ reasons, that for instance make it ergonomically ‘handy’. Form and function are often not that far apart. Design may not be Eastaway’s field of expertise, but nor serms mathematics, or logic reasoning, by practically arguing that the ratio is randomly just not golden enough. I guess that’s why he hád to dispute my finding of ending up with a dimension of √5 √10 when taking of a square of twice (a la Fibonacci in reverse,with an accuracy of 8 digits (2.236 : 3.612) in total. Just because it still makes no sense to him. Maybe somewhere along the way, there actually wás some covert mathematician who tried to leave his mark on the world, of credit cards and far beyond.. Seems not some far fetched theory or even conspiracy, to me at least Maybe he is just too modest to take the credit for his own more public contributions to the world of mathematics . Denying himself the prestigeous field medal. He really shouldn’t and stick it up somewhere where the sun actually shines. Like his revere.

Comment on Meisner Beauty Guide for Golden Ratio Facial Analysis by Nuco Z

Nuco Z — Thu, 30 Jul 2026 12:18:50 +0000

This is a helpful explanation of why the golden ratio keeps appearing in facial-aesthetics discussions. I think it is important to treat phi as one reference among several rather than a universal beauty threshold: facial thirds, symmetry, feature relationships, expression, and cultural context all affect how a face is perceived. For anyone measuring a selfie, consistent camera distance, head position, lighting, and lens choice matter because perspective can shift the ratios more than people expect. A useful tool should explain those limitations and turn measurements into practical styling guidance, not just a single score. I am exploring that approach with a browser-based face analysis tool at https://lookblueprint.com/

Comment on Human Heartbeat and Fibonacci Patterns by elizabeth schiemer

elizabeth schiemer — Tue, 14 Jul 2026 08:52:59 +0000

On the Facebook page of the Australian Labyrinth Network a number of the new posts relate to the golden ratio and theta state ,elicited by the walk in a labyrinth ……There are research articles about labyrinth and neuroscience, psychology, art and spiritual, physical health and wellbeing. …… The ancient labyrinth, was mentioned in Sanskrit, Greek, Hopi Indian and Celtic mythology and built into floors of medieval Cathedrals designed to the golden ratio like Chartres , but recent interest and research indicates the ‘labyrinth effect’ is the theta state for problem solving. ……. You are welcome to scroll through and share what serves you well, Ronald Esquivel ” Labyrinth Design and the Energy of its Geometry” is a book with labyrinth designs to the Golden ratio.

Comment on Pi is 3.1446 per “Measuring Pi Squaring Phi” by Harry Lear—Reviewed by Rudyard Quinn Paine

Rudyard Quinn Paine — Sun, 24 May 2026 19:58:12 +0000

I am probably thinking about this backwards, because I know Pi is a ratio…
Still, its a curiosity to me, has anyone tried this Pi = 3.144… and relating it to a circle divided into 366 degrees?
I am aware Pi is about Radians, just if someone could demonstrate on a known circle, if this is in anyway ‘lined up’ with this other basis for the circle delimitation.

consider 180/pi as 3.1415… vs 183/pi as 3.144…
and vice-versa. I am only curious, perhaps there is something here that has been lost to translation.
Again, maybe I am ‘grasping at straw’, still 366 vs 360 is a small difference, as is 3.141 vs 3.144…

If there is something to this, I would be interested in collaborating on an academic paper. If not, then we can chalk it up to the pattern seeking primate brain.