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

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

Postby 1teebox » Sat Aug 21, 2010 12:16 pm

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:
http://www.asme.org/NewsPublicPolicy/Newsletters/METoday/Articles/Better_Golf_Swing.cfm .

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

Pic 01 RM Report 01 graph enlarged.jpg
Pic 01 RM Report 01 graph enlarged.jpg (38.01 KiB) Viewed 16864 times


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
http://en.wikipedia.org/wiki/File:NautilusCutawayLogarithmicSpiral.jpg.

Pic 02 Nautilus.jpg
This Wikipedia and Wikimedia Commons image is from the user Chris 73 and is freely available at http://commons.wikimedia.org/wiki/File:NautilusCutawayLogarithmicSpiral.jpg under the creative commons cc-by-sa 2.5 license.
Pic 02 Nautilus.jpg (48.79 KiB) Viewed 16854 times


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
Golden Spiral (Approximation)
Pic 03 Golden Spiral.jpg (20.96 KiB) Viewed 16826 times

http://en.wikipedia.org/wiki/Golden_spiral


Pic 04 Golden Rectangle.jpg
Golden Rectangle
Pic 04 Golden Rectangle.jpg (38.66 KiB) Viewed 16822 times

http://en.wikipedia.org/wiki/Golden_Rectangle

Some examples showing use of the Golden Rectangle in art are exhibited at:
http://www.world-mysteries.com/sci_17.htm
http://en.wikipedia.org/wiki/List_of_works_designed_with_golden_ratio
http://photoinf.com/General/Robert_Berdan/Composition_and_the_Elements_of_Visual_Design.htm

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
Pic 07 RM Graph 01 GoldRect.jpg (73.22 KiB) Viewed 16844 times

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… .

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?


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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:

http://jssm.org/vol8/n2/11/v8n2-11pdf.pdf

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

http://en.wikipedia.org/wiki/File:Golden_ratio_line.svg
http://en.wikipedia.org/wiki/Phi
http://www.sound-physics.com/Music-Physics/Fibonacci-Sequence
http://www.maths.surrey.ac.uk/hosted-sites/R.Knott/Fibonacci/fibnat.html#spiral
http://www.vashti.net/mceinc/rgphigra.htm
http://www.vashti.net/mceinc/unfold7.htm
http://education.uncc.edu/cmste/summer%20ventures/2010%20History%20of%20Math/Fibonaccifinal.pdf

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1teebox, August 21, 2010
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Re: The Nautilus and the Golf Swing

Postby lagpressure » Sat Aug 21, 2010 12:50 pm

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.
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Re: The Nautilus, the Golf Swing, Golden Ratio, Fibonacci seque

Postby kafka01 » Sat Aug 21, 2010 1:35 pm

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?


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.

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

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.
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Re: The Nautilus, the Golf Swing, Golden Ratio, Fibonacci seque

Postby bentshaft » Sat Aug 21, 2010 3:42 pm

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

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

Postby lagpressure » Sat Aug 21, 2010 4:08 pm

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.. ?
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Re: The Nautilus, the Golf Swing, Golden Ratio, Fibonacci seque

Postby eagle » Sat Aug 21, 2010 5:19 pm

Tee,

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.
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Re: The Nautilus, the Golf Swing, Golden Ratio, Fibonacci seque

Postby robbo » Sat Aug 21, 2010 6:11 pm

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.

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

Postby Styles » Sun Aug 22, 2010 2:07 am

very interesting, I wonder will Dan Brown write a golf book next?!! :lol:
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Re: The Nautilus, the Golf Swing, Golden Ratio, Fibonacci seque

Postby mandrin » Sun Aug 22, 2010 7:35 am

1teebox,

You might want to have a look at

Taylor Spalding's Golden Barefoot Golf

and more specifically at

What is Golden? - The aesthetic dimension

Taylor Spalding is the pen name of J.J. Moore. He has been posting his thoughts on golf at http://www.goldengolf.com since 1996. He also posts videos at http://www.youtube.com/goldengolf.

Golden Barefoot Golf (goldengolf.com) 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.
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Re: The Nautilus, the Golf Swing, Golden Ratio, Fibonacci seque

Postby 1teebox » Sun Aug 22, 2010 7:49 am

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.
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