The use of Golden number in wood turning

[La truciolara]

The golden ratio, usually denoted <v:shape id="_x0000_i1025" style=" 9pt; 10.5pt;" alt="\varphi" type="#_x0000_t75"><v:imagedata o:href="http://upload.wikimedia.org/math/3/5/3/3538eb9c84efdcbd130c4c953781cfdb.png" src="file:///C:&#37;5CDOCUME%7E1%5CUser%5CIMPOST%7E1%5CTemp%5Cmsohtml1%5C01%5Cclip_image001.gif"></v:imagedata></v:shape>('phi'), expresses the relationship that the sum of two quantities is to the larger quantity as the larger is to the smaller. The golden ratio is the following algebraic irrational number with its numerical approximation:<o></o>
http://img118.imageshack.us/img118/6083/orue7.png<o></o>
<o></o>
This number is still quite frequently used by architects, designers, artists to obtain closet o perfect proportions. <o></o>
A friend of mine, Jacques Portal, Turned this bowl in strict observance of the golden ratio.
http://www.aftab-asso.com/html/forum/userpix/25_waIMG_8525_1.jpg<o></o>

<o>
</o>
http://www.aftab-asso.com/html/forum/userpix/25_wIMG_8529a_1.jpg<o></o>

<o></o>
For diameters:
370/140 = 2.618 (square of 1.618)

From which you can deduct:<o></o>
370 / (115 + 115) = 1.618<o></o>
(115 + 115) / 140 = 1.618

For eighth:
75 / 46 = 1.618<o></o>
<o></o>
We can add than the depth of the bowl is 370 dived by the square of the square of 1.618. But let’s not exaggerate, we can be satisfied to commonly utile 1.618, it’s square or it’s square root. We are not that fussy or anal compulsive. Are we? :U :U <o></o>

[Jim Carroll]

So what you are saying is that you work in 1/3rds

diameter divided by 3 will give you the base dimension.

height divided by 3 will give you transition between the side and going down to the base.

So it would be fair to say that most shapes will be 2/3 and 1/3. As a general rule of thumb:2tsup:

[Cliff Rogers]

That is roughly how I do it too Jim.
1/3 & 2/3 but I do it by eye, not by the ruler.

What I would do different to the piece above is the shape of the side profile.
I'd make the foot lower & put the transition in the wall profile 1/3 from the top, not 1/3 from the bottom.
It looks far more elegent.

[Hickory]

IMHO (although Bourbon is involved with my concerns at this time) You should take the Golden Rule and toss it out with the rest of the chips an saw dust. Some nose in the air snobery fellow (or the college of smart thinkers) came up with that thought to stiffle creativity. I know there are those out there who will say I am a drunk old kook and blabbering, as the gods of design have spoken these great words about proportions, but I am here to tell you that design is not to be limited to a ratio or standard. What you will find is that over time, through observation, pieces that have been deemed attractive have demonstrated certain ratios to thickness, depth, width, or other measurements. That does not limit your piece to being bad or good if or not it is within certain ratios or limitations.

The figuring in your piece overshadows any design shape and ratio considerations. Who will look at the ratios of design when the Spalt marking you have are so distinct. A chunk squared and quartered would have been as impressive but your use of the wood is excellant.

I Like it!!!:2tsup:

[Jackson]

I'm going to disagree with you Hickory and agree with Cliff.

You are correct, I think, when you say that pieces that people generally agree are attractive have demonstrated certain ratios to thickness, depth, width, or other measurements. But more often than not, the ratio will be 3 to 1 or thereabouts.

It's interesting how often people will look at a piece and agree it's proportions are pleasing. Similarly it is also interesting how often people will look at the same piece and think the "shape" or "proportions" - or something - is just not right. Beauty may be in the eye of the beholder but it is surprising how consistent all our eyes are. People can't put a finger on why they think similarly. It seems to me however that the golden mean (as I understood the term) works to provide proportions which seem to provide pleasing shapes. This can be the ratio between height and width, or other comparison which meets the eye together.

I also understand the golden mean was not soemthing some design guru came up with. If I'm wrong here no doubt there'll be a million posts pointing out my error, but I believe the golden mean was recognised by by builders in ancient times.

Apart from that - a great piece Claude. The spalting looks terrific.

[Toolin Around]

I guess the pic, in some ways, proves what hickory has said. Personally I think the bowl is at best average in shape and style - but still a great exercise.

[rsser]

A rule of thumb is not a rule Hickory, it's a starting point.

[ozwinner]

Ive used the Fibonacci rule of 1.62 in the past and it does seem to make things look ok.

Its not the be all, and end all of measurements, but you will find a lot of things seem to work better proportionally if you use the Fibonacci or golden rule.

Al :-

[rhancock]

If I remember my high school art and woodwork teacher, the fibonacci sequence, which is the basis of the Golden Mean, is a natural sequence demonstrated in spiral patterns such as the layout of seeds in a sunflower head and many others, so although, yes the ancient greeks used the golden mean in their classical buildings, I think its even older than that!

[ozwinner]

Sorry.
The bowls foot need to be 186mm to be within the golden rule.

115mm x 1.62 is 186.
Only the height works for the golden rule.

Al :doh:

[powderpost]

Sometime back I posted some findings I had observed 20 odd years ago. When trying to get a handle on proportion, I turned a dozen goblets of varying sizes and proportions. They were placed on a bench in no specific order. Each person that unwittingly wandered into my workshop was asked to place them in an order from bad to good. After six months of recording the outcomes, a pattern did emerge. Hardly a scientific process but the result was fairly definite. What I would like to see is for someone to do the same, just to compare the results. The bowls also produced a definable result. Base equals about half the diameter, height divide into about thirds. Again this is only a starting point and not intended to infer that these ideas are definitive and there shall be no variation. Sometimes we look at a turning and can't quite work out why it doesn't appeal, but then we all have different perceptions, don't we?
Jim
p.s. I have deliberately not mentioned the results of the goblet exercise.
Jim

[derekcohen]

It can be easier than maths. Here is a Fibonacci gauge I made recently...

... Tasmanian Oak .. such wondeful chattoyance ...

http://i13.photobucket.com/albums/a262/Derek50/Marking%20and%20Measuring/FibonacciGauge2.jpg

... and handmade brass rivets ...

http://i13.photobucket.com/albums/a262/Derek50/Marking%20and%20Measuring/FibonacciGaugerivets1.jpg

Regards from Perth

Derek

[joe greiner]

As said, it's a good starting point. But slavish adherence doesn't guarantee success. Also note that perception is altered by wood grain pattern, incidental features, etc. Such alteration is the basis of many optical illusions, after all. Study other successful works that adhere to it, as well as others that violate it but still look good, for added insight.

Joe

[ToolRest]

While I agree that phi has some uses in design, I think we need to be careful about how and where we apply it.

It might work very well for the profile of a vase, setting the height/width ratio, and maybe even determing the placement of the widest part. But how many people will ever view the profile of a bowl like this?

For all the math involved with this bowl, I'm afraid that the profile doesn't appeal to my aesthetic at all. I don't like the noticeable transition from wall to bottom, much prefering a smooth curve from rim to foot and a very definite transition around the foot, which I would prefer to be much lower.

The other problem with the application of phi to the height is that it is difficult to know exactly where the transition point is. It seems to have been chosen pretty much at random to me, and the marked position could have been either a little higher or a little lower and thrown the math right off.

[La truciolara]

Sorry.
The bowls foot need to be 186mm to be within the golden rule.

115mm x 1.62 is 186.
Only the height works for the golden rule.

Al :doh:
:U :U :U
you forgot part of the calculation
370 / (115 + 115) = 1.618<O></O>
(115 + 115) / 140 = 1.618

[Wayne Blanch]

Thanks for the information,:2tsup: I think that for me as a relative beginner it will give me a better guide than the "Lets have a look" process I have been using till now. I have been aware of and have been using one third as a guide but this process will certainly help me.

I am one person who likes to have some process to follow but that doesn't mean that you have to be slavishly bound to the process. I agree that there are many times that the wood itself wont lend itself to this formula.
However I have found when I come close to these proportions in less decorative (should that be more boring??) timber the results are generally pleasing to the eye.

Once again thanks I finally get it! Must be a little (Lot??) slow with some things:? . The formula makes it easier for me:D
Greenie on the way!

[rsser]

Wayne,

You may also find it useful to sketch out some profiles that will fit your blank (or a modded blank).

I use 1cm graph paper to full or half scale, draw the blank size in ink and then play around with shapes in pencil.

Once you've got a profile you like you can use a divider to transfer transition points to the blank.

For printable graph papers see http://www.woodworkforums.ubeaut.com.au/showthread.php?t=39245

[Wayne Blanch]

Wayne,

You may also find it useful to sketch out some profiles that will fit your blank (or a modded blank).

I use 1cm graph paper to full or half scale, draw the blank size in ink and then play around with shapes in pencil.

Once you've got a profile you like you can use a divider to transfer transition points to the blank.

For printable graph papers see http://www.woodworkforums.ubeaut.com.au/showthread.php?t=39245

Thanks Ern:2tsup: , Yet another good idea, why didnt I think of that:doh: , and thanks for the link to the graph paper. I'll start using it.

I think I am getting the hang of the Munro Hollower, last night I was really creating some shavings - Problem was I was making a hollow form and now I have largish bracelets. Woops:C

Thanks again

[hughie]

[ , Yet another good idea, why didn't I think of that:doh: , and thanks for the link to the graph paper. I'll start using it.

I


Wayne,
I nearly always sketch out the shape on paper, generally a half bowl is all I do.
In fact, after I have roughed out the bowl I sketch the shape on the rough out. This gives me a record for later use. I do this as it is often many months later when I pick up the bowl again and I quite often have 15-20 on the shelf drying out at any one time.

[joe greiner]

Here's a couple screenshots for construction of the Fibonacci gauge. In the spreadsheet, b = a * 0.618, c = a * 0.618 * 0.618. Original dimensions were Imperial, but the computer doesn't need to know that. Value of 0.618 calculated same as Claude's derivation. [Curious thing about phi, is that 1/phi = phi - 1.]

Joe

[Hickory]

"A rule of thumb is not a rule Hickory, it's a starting point.":doh: I think I said that.... I agree that proportions that are appealing to look at generally fall within certain ratios... It is the attitude that "Oh My God...Its numbers are 0.1(?)2 mm off so it is crap" attitude that blows up my skirt. :~

Been off a couple of days and couldn't speak back as an Ice storm blew through here Tuesday, downed powerlines , etc. I lost power for a few days and spent time in a motel. Zero (F) temps Lost the top half of a 30 years old Grande Floria Magnolia Tree (Southern Magnolia with sweet smelling lovely giant blooms from May through September) :( Will have to find an Arborist to save it.

[Rookie]

If I remember my high school art and woodwork teacher, the fibonacci sequence, which is the basis of the Golden Mean, is a natural sequence demonstrated in spiral patterns such as the layout of seeds in a sunflower head and many others, so although, yes the ancient greeks used the golden mean in their classical buildings, I think its even older than that!

Yes. Fibonacci developed the series when he was analyzing all things natural, such as the seeds mentioned, the ratio between the sizes of leaves on branches, the distance between those leaves as you measure along the branch, the distance between branches measuring up the tree, the ratios between various parts of birds, and animals, all manner of things. His measurements kept coming up with the same ratios time and time again, and concluded that this ratio was why so many things in nature were pleasing to the eye. It was then suggested at some point, don't know if it was by him or not, that this ratio could be used to make the shape of man made things look as pleasing to the eye as the shape of natural things.

[rsser]

Seems the ratio was known to the Greeks.

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

[Rookie]

Yep. My oops. Didn't research enough. Fibonacci didn't develop the series, he used it as an example in his writings. It was known about as far back as 400BC, according to wiki.