The Nautilus, the Golf Swing, Golden Ratio, Fibonacci seque

We often hear observers say the swing of a good golfer is rhythmic, flowing, and beautiful.

What is it exactly in the good golf swing that stimulates that reaction?

There may be a clue about this in a valuable engineering research report, published September, 2008 online by the American Society of Mechanical Engineers, and authored by Ryan McGinnis called “Engineering a Better Golf Swing.” Ryan’s report resulted from his work with Dr. Stephen Nesbit. Ryan’s report is available at: .

The computer generated image below was created by Ryan from his research findings.

Pic 01 RM Report 01 graph enlarged.jpg

The elegance of the flowing path of this swing image vaguely reminded me of the flowing internal structure of the nautilus shell as seen below and in Wikipedia at

Pic 02 Nautilus.jpg

Some observers debate whether the flowing spiral in the nautilus shell reflects the Golden Spiral, Golden Rectangle, Golden Ratio, Phi, and the Fibonacci sequence that often exist in other natural as well as manmade designs. Examples and discussion may be seen at many sites including these:

Pic 03 Golden Spiral.jpg

Pic 04 Golden Rectangle.jpg

Some examples showing use of the Golden Rectangle in art are exhibited at:

Studying Ryan’s graph and the similarity to the Golden Spiral led me to wonder if the Golden Rectangle might appear there and in real golf swings. I have not looked into this yet with real swings, but an approximation of the Golden Rectangle appears to me in Ryan’s graph. I demonstrate this with markings I imposed on his graph as seen and described below.

Pic 07 RM Graph 01 GoldRect.jpg
The four sides of the rectangle are enclosed by the intersecting pairs of blue, red, green, and black parallel lines. Three of the lines, the blue, red, and green, are formed by projecting them along the golf shaft where the golf shaft is at the top parallel, downswing vertical, and impact vertical. Observers may note the bottom horizontal (black) line of the rectangle may appear arbitrary but it is tangent to the path of the hands as are the red and green sides.

It seems worthwhile to observe that during the first interval (yellow area) from the top of the swing to the tangent of the green line, the shaft position changes 90 degrees, but in the second interval (orange area)from the green line tangent to impact, the shaft position changes 180 degrees, or twice as much. The ratio of 90 degrees to 180 degrees, or 1 to 2, is also a portion of the Fibonacci sequence as seen here in gray: 0, 1, 1, 2, 3, 5, 8… .

[i]Does the word “harmonious” apply to the coincidence of (a) both the path of the hands fitting the Golden Rectangle and (b) the shaft movement ratio of 1:2 fitting inside the Fibonacci sequence?

Does the approximation of the Golden Rectangle appear in other vantage points in the three dimensions of the swing or is this occurrence unique?

Even if this is the only place, why is it here at all?

How can we visualize this spiral path of the hands and club shaft existing in three dimensions that appears here in one plane?

Can someone create a three dimensional physical model or a computer simulation allowing us to change our point of view of the model infinitely?

Would the differences in the hitting and swinging protocols impact the generation of this model?

Are the Golden Spiral, Golden Rectangle, Golden Ratio, Phi, and the Fibonacci sequence, any of these, possibly useful in helping us conceive and develop our hitting or swinging technique?

What do you think?[/i]


Golfers can find additional valuable golf swing research in another inspired report, published online in 2009 by the Journal of Sports Science and Medicine, “Kinematic analyses of the golf swing hub path and its role in golfer/club kinetic Transfers”, by Ryan McGinnis and Steven M. Nesbit available at:


Additional related information and discussion was found at various internet locations such as these:

1teebox, August 21, 2010

This is a most fascinating topic, and I thank you for taking the time to put this together. This is wonderful stuff.

My mother is a fine masterful painter, and I know that she was very aware of “The Golden Mean” which was taught in some of
the more advanced university work on her way to a Masters degree in fine art.

The first question that comes to mind is “The chicken or the Egg” theory. In other words, does the Golden Ratio, Phi, and the Fibonacci sequence reveal itself only once the mastering of technique is in place? Or can we put the pieces together in advance based upon studying the under laying form with such specific intentions?

There is a lot to go into here, and I would think a proper understanding of mechanical engineering, architecture, as well as the visual arts would all have there place in understanding and application. I have heard of musicians or composers applying these concepts in their work… from Stravinsky to modern experimental composers such as Eno, Fripp, and Roach.

I´ve seen this “form” applied to a golf swing before - i just cant remember where it was. But it was a rather old picture.
Just because somebody defined what an “optimum” for a certain motion is, that doesnt mean we can easily reproduce it. Just as Lag does with his program you would have to develop certain steps/building blocks you had to master, to come close to such a motion. The motion alone doesnt help us. Just cuz we know that our swing should look like a Nautilus, doesnt mean we can reproduce it. Otherwise we could just watch Ernie Els or Sam Snead hitting balls all over again and all of a sudden we would master the motion.

I doubt it. I have read so many discussion by people who try to seperate between swingers and hitters - but they never seem to come to a real conclusion. Why, because it just looks so very similar, and how would you want to generate these motions into a model if the human eye isnt capable of picking out differences at the first place. Be it a hitter or a swinger or something in between, when it comes down to the key positions they look all very much the same. And everything in between is just blur that has to happen since we have to move from position A to B and cant just skip ahead.

Although I am quite familiar with the golden mean and fib ratios, I have no idea how they might relate to the golf swing. I do find this rather interesting…

Under the Rules of Golf, a golf ball weighs no more than 1.620 oz

and this change COULD NOT have been a good idea
I say it could not have been a good idea because it screws up the natural harmony of perfection in size…

Until 1990, it was permissible to use balls of no less than 1.62 inches in diameter in tournaments under the jurisdiction of the R&A


In the case of 1.620 ounces… was there some preference in the historical analysis to yards, pounds, ounces… compared to metric? … which might be easier to see the ratios mathematically… ?


Holy cow!! That is one heck of a comprehensive deep thought provoking post. Gonna have to ponder that for a long while.

But at first glance, I would have to bet that the better golfers will be found to have swings that comply with these ratios…either in space or time …or both. The ratios may even be boundaries, or invisible controls that can or should be sought and utilized. Didn’t Sam Snead advise listening to a certain kind of music on the way to the course, as a way to create a good rhythm to his swing.

I’m also sure I saw a golf website that was using this as it’s platform. Seems like they were selling some “num chuck” looking device to validate the Golden Ration and the Fib sequence. It was very interesting but I never bit the bullet and signed up. I’ll look back in my files and see if I can dig it up.


very interesting, I wonder will Dan Brown write a golf book next?!! :laughing:


You might want to have a look at

Taylor Spalding’s Golden Barefoot Golf

and more specifically at

What is Golden? - The aesthetic dimension

[i]Taylor Spalding is the pen name of J.J. Moore. He has been posting his thoughts on golf at

Golden Barefoot Golf ( was established in 1996 as a web portal for speculative golf philosophy. The site is the self publishing effort of J.J. Moore, who writes from the perspective of literary invention Taylor Spalding, a recovering goof.[/i]

Because I suspect there are qualified people who can contribute meaningful information on this topic, the main purpose of introducing it was to ask some questions in the context of the posted and linked material and work that other people have already done.

Like robbo and kafka01, I also remember a fellow on the web several years ago who wrote about golf and the golden rectangle and, and if I remember rightly, the Fibonacci sequence.

This fellow came to my mind again after I began to think about this topic on seeing Ryan’s graph. This fellow, I don’t mean Ryan now, also showed his artwork on the web. At least some of his artwork was about a connection between golf and the golden rectangle and the golf swing being like a tornado, hurricane, and spiral. I looked hard at his stuff and made notes on my computer at the time. He had put a lot of thought into his project. I regret I do not remember his name. The hard drive I had the notes on died several years ago along with the link to his web site. So far, I have not found a new connection to him on the web.

Though I suspect the mental connection between the golf swing and tornados, hurricanes, spirals, and possibly a connection with the golden rectangle have been around much of the time golf has existed, this fellow may have been the first person to put his thoughts and his art about it in that context on the web. He is the only person I recall that addressed golf in that context on the web. But I could have missed things by other folks. There was a lot of his thinking that I did not grasp in part because of the unique system of words he devised and the way he used them to define things.

Even though I did not remember his name, it might have been good to cite his work though the citation would have been anonymous. I say “might have been good” because I am not sure how many other folks out there would believe I meant them and not the one person I remember. If I could have remembered his name, citing him would have been the right thing to do. I hope he finds this topic and will post his thoughts.

As I reviewed this before posting it, I saw that mandrin identified the fellow, J.J. More. Thank you mandrin.

This is a very interesting topic- nice work, 1teebox, I always enjoy when you get your ideas out here as they’re always well thought out and thought provoking.
It hits home to me regarding an idea about how the game is perceived that has been forming in my mind for a good while, that being the difference between swinging a golf club and moving a golf ball. I think they’re two different things, different art forms with different ends. It has repercussions in modern culture, I think, or modern culture has had repercussions on it, more specifically. It’s about aesthetics, and form vs function. The bottom line, in my view, is that the pretty golf swings tend not to work very well. The ‘ugly’ ones, by and large, are the ones that seem to be better equipped to control the ball- Trevino, Nelson, Doyle, Chi Chi, etc. etc. all valued function over form. This may well be the swinging/hitting question.
In our modern consumer based culture, where advertising and physical ‘beauty’ rule the day, where video swing analysis is the answer to all problems in golf(and sells lessons!) What the swing looks like as opposed to what it actually does, seems to be what’s valuable. If it looks a certain way, then it’s supposed to work. I’ve talked a little about this before, but we seem to trust that how we do it, or how it looks, will create the results we want, as opposed to having the creation of a ball flight or how we strike it, form the shape of the action. As an aside, clearly Lag is tackling the form vs. function topic very well- when I say ‘we’ I mean modern golf.
I’ve heard more times than I care to remember, and I’ve regrettably said it myself, that Lee Trevino has an ugly golf swing. Yet he was arguably the best ball striker ever- how could that be? (A topic I’ve been thinking of posting is Hogan vs. Trevino- who struck it better?)
This is an idea that’s been forming in my mind for a while, and I haven’t yet gotten to the bottom of it, but this post seems to be connected to it on some level. This stuff is obviously a pretty large generalization, but I think specific things show up slowly but in dramatic ways. Cultural shifts happen gradually, but when they do happen, they tend to impact most things. Looking around us today, it’s clear that the heart and soul are being ripped out of the world and in their place there’s an image of something that doesn’t actually exist. So why wouldn’t this be the case with the golf swing? Or the whole game? Or popular music? Or economies? etc. etc. etc.
I’m not saying that humans haven’t always been interested in beauty, or that beauty itself isn’t real or valuable, but we seem to be creating it unnaturally more and more often in modern times, or looking in the wrong places for it, or even just completely making it up based on creating a perception or an image.
A bit heavy for a sunday morning? I need more coffee. Or less. :slight_smile:

Back in '65 or '66 a Physical Ed instructor, in Junior College, for my virgin try at golf, handed me a beat up 9 iron with a dried out slippery grip to hit some balls.
He moved away to tend other students.
After the first few attempts, the balls were flying surprisingly far and reasonably straight without instruction.
I was stoked and probably already innocently hooked.
From nowhere he popped up and grabbed the club from my hands and said I was doing it all wrong, “Do it this way!”
His intensity and tone was actually, “YOU ARE AN ATHLETIC MORON! DO IT THIS WAY!”.
Classic grunt PE coaching finesse for the time.
Mentally, before his inspirational critique, I was already a part time 19 year old basket case, now I was totally screwed. Groovy.
I wish he’d left me the bleep alone.
Trying to hit the pretty way his swing looked just messed me up.
Fortune Cookie Conclusion: Seeking beauty can be a slippery slope and the outcome can be ironic both in golf and the other life.

Classic! I think I remember being promoted to full time at this job for a while myself- I was very talented.
Your story reminds me of IOZ getting his ‘lesson’ to help him get out of this crappy action…

As an aside re: the spirals… was it RR who posted something a while ago about them that was pretty cool?.. or maybe it was Eagle? I’m pretty sure it was one of them…

Interesting stuff. However, regardless of rhythmic, flowing or beautiful…I’m fostering a swing that keeps the rectangles (golden or otherwise) off my scorecard! :wink:

Captain Chaos

Very well said. I believe this may have originited from the way we percieve a golf swing in realtime, as we normally see them in person or on TV. Because the player is swinging fast, we can really only see the backswing, maybe a little of the start down, then its a big blur until the finish swivel. However, the part of the swing that the golf ball cares about is in the blur…3rd parallel to 4th parallel or even up to vertical. Combine this with the fact that muscle exertions are obscured by clothing and applied forces are unseen because they are reacted with the ground or the golf club and you wind up with people teaching the parts of the swing they easily observe…fixing the top of the backswing and the grip at setup. A highly functional swing may involve asymmetry, sudden motion, and a generally non-relaxed look that is easily percieved as ugly. Somewhere along the line the golfing world developed a love with “effortless power”. I believe that’s why so many people love Hogan’s motion… he was able to take the functional, “ugly”, aspects of the swing and make them look asthaetically pleasing. Knudsen too. That’s why people get so confused trying to mimic Hogan. I no longer believe it was effortless. Not with how much I’ve sweated in ABS.

Much like a duck on the water… it looks graceful, yet it is really working hard with it’s feet under the water to give that
graceful looking glide.

Here are some diagrams sent over by Saul Berstein who is one of my favorite artists.

Saul is an enormously accomplished fine artist, and I have invited him over here to add into this discussion if he would be so kind as to contribute.

phi 1.jpg


Bom:…that side-by-side of Hogan and the other guy is still the most fascinating photo I’ve seen in a long time.

It looks like he is a field hockey player…I know nothing about that endeavor, do you happen to know by way of the picture what type of shot he is playing…how is it executed…and how might it be different from other field hockey shots. Is the photo capturing just a “basic” shot that any field hockey player should be proficient with.

Is it a shot with loft? A lot of questions, I know, but it’s such a wonderful comparison. :slight_smile: RR

It’s interesting to make note of the five divisions…

Without consciously knowing this… we move the golf swing to PV5.

I very much feel five distinct feelings in the golf swing if I break them down.

  1. The initial movement away from the ball
  2. The move through transition into the slot
  3. The firing into impact from P3
  4. The post impact pivot acceleration (second stage rocket firing)
  5. Preservation of impact alignments (PV5 intention)

It’s interesting to note the five appendages coming off the torso, then to 5 fingers. Five openings on the face, and five senses.

Reviewing module 7, I talk about the 5 points of connection pressure centers in the body.

Certainly fascinating stuff.

That photo is a bit of a mind blower for sure. As far as I know, and IOZ would be better equipped to answer, it’s a standard enough shot where the ball leaves the ground- how high, I’m not sure. In the small world thread there are full sequences from that shot as well as more of a drag type shot where I’m pretty sure the ball stays close to the ground. The stick itself has no loft, and that’s a give away in itself.
I’m sure that the length of arm swing going back, or lack thereof, is what forces that ‘position’ coming down as the body creates force in a short enough period of time. Both Hogan and that hockey player have fairly limited arms swing going back. As an aside, I also think the forward/downward action is actually what elongates, or completes the shoulder turn, but again, it’s in the name of creating power that it happens. I’m not aware of any other sport that recommends an active shoulder turn other than golf- If any body knows one let me know. As a general rule, the appearance of delay in the parts of the body out to the thing that’s being thrown/used etc., happens in the forward/downward action- a baseball pitcher, for example. Nelson had a pretty limited backswing shoulder turn, instead going back together- Trevino too imo. Obviously, the shoulders turn, and the bits above always turn more than the bits below, but I do think that the separation is as a result of acceleration in the direction you’re looking to go. This is probably for a different thread- sorry for the hijack, 1T…
Thanks for posting those diagrams… very interesting stuff.