# The golden ratio



## grumpy749 (Nov 22, 2011)

AS most woodworkers are aware, the golden ratio is a proportionate formula. It refers to lengths, widths and depths and there relationships to one another. If closely adhered to, the subject, namely furniture, will appear more esthetically pleasing. The ratio formula is fairly long but if rounded up it is 1.6. this ratio formula should be used when designing furniture in 2 or 3 dimensions. I have viewed many beautiful pieces of work on display here with little regard for this key design rule. why is that. It's so simple. For further clarification on this there is a great article in woodworkers Journal about 10 years ago. Go to there archives or simply google it.


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## Bogeyguy (Sep 26, 2012)

Since you brought it up, why don't you post a link?


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## CharlesA (Jun 24, 2013)

Part of it is that the golden ratio has been oversold-not all the examples from the ancient world, for example, actually fit it. It is a nice way to design something, but it isn't sacrosanct. There's lots of examples of great design that don't fit it.

Here's a good quotation from Theodore Cook (1922) included in an interesting web posting on the subject: "There is no short cut to the beautiful, no formula for the creation of the perfect." The analysis of the ratios in an Aston Martin is illustrative. That being said, it is a good start for a lot of conventional furniture.


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## lwllms (Jun 1, 2009)

Historically, people were aware of the golden mean as a mathematical construct but I'm aware of no documented evidence it was used in architectural or furniture design before the 20th Century. Can you provide any documented evidence the golden mean was used in design before the 20th Century?


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## jumbojack (Mar 20, 2011)

golden ratio parthenon

https://www.google.com/search?q=golden+ratio+parthenon&espv=210&es_sm=93&tbm=isch&source=iu&imgil=yjeYPqkMWbyjuM%253A%253Bhttps%253A%252F%252Fencrypted-tbn0.gstatic.com%252Fimages%253Fq%253Dtbn%253AANd9GcT291okovZfJqPIKBIGjOGjVbJ-g1fz5AUwUm4efHFPPQCLt7v3FQ%253B800%253B498%253Bz_Oy_Ii_zVs56M%253Bhttp%25253A%25252F%25252Fbritton.disted.camosun.bc.ca%25252Fgoldslide%25252Fjbgoldslide.htm&sa=X&ei=8e7EUrnFBoj1oASs_IKABA&ved=0CC4Q9QEwAA&biw=1440&bih=784#facrc=_&imgdii=_&imgrc=yjeYPqkMWbyjuM%3A%3Bz_Oy_Ii_zVs56M%3Bhttp%253A%252F%252Fbritton.disted.camosun.bc.ca%252Fgoldslide%252Fgold08.jpg%3Bhttp%253A%252F%252Fbritton.disted.camosun.bc.ca%252Fgoldslide%252Fjbgoldslide.htm%3B800%3B498


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## CharlesA (Jun 24, 2013)

Maybe. Read this posting that raises questions about the golden ratio and the Parthenon. http://www.lhup.edu/~dsimanek/pseudo/fibonacc.htm


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## TopamaxSurvivor (May 2, 2008)

Livio raises a lot of issues, the Parthenon included.


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## Wildwood (Jul 22, 2012)

Did not know there are rules of design! Design does not go beyond concept. Design comes from an old Latin word, look it up.

I am more aware of design elements & principles that makes art more pleasing to the eye. Hard to use all elements & principles of design in whatever you build.

http://do-it-yourselfdesign.blogspot.com/2010/02/elements-and-principles-of-design.html

If you go looking for rules of design to today might find something like these to follow.

http://speckyboy.com/2012/07/10/the-10-golden-rules-of-simple-clean-design/

If really want to design and build furniture just go read a book on designing furniture or furniture design.

If want to discuss rules of proportion, bring in your formulas. If go into study of proportion will find a formula for every line you put on paper in today's world of design. Today's designers go beyond golden mean with there formulas.


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## Sylvain (Jul 23, 2011)

another blog about it :
design matters


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## JustJoe (Oct 26, 2012)

When those radio talkshow guys hyped up the price of gold to $1800 I couldn't afford the golden ratio anymore. I had to get by with the Silver Quotient. Then the price of silver went through the roof and I was stuck using the Copper Relationship. It worked OK, although a few of my projects seem a little lopsided or maybe a bit too skinny. 
Now that the price of gold is dropping again I hope to be able to afford the golden ratio in time for my next big project.


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## Finn (May 26, 2010)

I make my many many boxes with a 1.4 to one ratio, simply because it appeals to me more than the 1.6 to 1 ratio. Others like this ratio enough to buy hundreds of boxes each year from me. I sell few square boxes.


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## mojapitt (Dec 31, 2011)

Most of the items I build are to the size that the customer ordered. I doubt if they look at the formula.


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## lwllms (Jun 1, 2009)

The Golden Ratio, almost always expressed out to three decimal points (thousandths), is pretty precise but seems amazingly variable when people claim to find or use it. Even its demarcation points can apparently be arbitrary. Some time actually check some of these authors' images, you'll find the illustrated isn't even 1.618/1. Some claim the Greeks used the letter phi (Φ) to represent the Golden Ratio but it was American mathematician Mark Barr who first made that association around 1910.

18th or 19th Century drafting sets typically include a mathematical instrument called a sector. Sectors, known as "proportional rules" in Europe, have been around since Galileo and have several scales for different calculations and the scale called the line of lines is for calculating proportions. I've yet to see one or even read of one that has a mark indicating the Golden Ratio. This scale is labeled "L." Here's a sector by Thomas Jones, the leading scientific instrument maker of his time and it's from around 1800. Can you find anything on it that represents the Golden Ratio?


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## LeeBarker (Aug 6, 2010)

Good discussion. To be slavishly stuck with the GR would be like doing all your drilling with one size bit.

That said, I find it a helpful tool when I have the freedom in a piece to create, say, door sizes.

I think of Mr. Fibonacci whenever I look at one of my wife's sunflower heads. It is humbling.

Kindly,

Lee


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## mnguy (Feb 4, 2009)

Just because something that looks good doesn't follow the ratio doesn't mean the ratio isn't extremely valuable. I think the Golden Ratio is a good starting point in design, or when one gets 'stuck'.


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## oldnovice (Mar 7, 2009)

Beauty has always been and always will be in the eye of the beholder.

What is beautiful to one may not be to anyone else …..... 
........ otherwise would we all not b married to identical women/men would we all not buy the same car etc.?


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## pintodeluxe (Sep 12, 2010)

I think the take home message is that slightly rectangular shapes often are more interesting than square shapes. I don't ever calculate for the golden ratio, but many of the shapes I use are pretty close.


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## ClintSearl (Dec 8, 2011)

I designed this credenza such that the GM is used in the drawer dimensions. The top right drawer is about 1.6 times the width of the top left one, and in the vertical stack the bottom drawer is about 1.6 times the height of the top one. The intermediate drawers are proportioned in an arithmetic progression between the first and last.


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## Jim Jakosh (Nov 24, 2009)

A Fibonacci gauge lets you layout your projects to the golden rectangle ratio automatically!
Here is the one I made: http://lumberjocks.com/projects/50436

..............Jim


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## Wildwood (Jul 22, 2012)

Agree with what George R. Walker had to say in "Golden Rectangle Different Point of View," article. Sylvain thanks for providing that article.

People will not know if you used golden mean, Fibonacci sequence designing your piece, unless they measure your work. Yes, there are many points of views on applying proportion ratios to your design.

Indeed whether making contemporary or whimsical furniture or other items out of wood, need to start with an idea. Whether that item is pleasing to the eye or merely functional up to you the designer and craft person.

Whether you use one or complex ratio sequences, some elements or principles of design, nobody cares about your journey. Acceptances about is good as it gets!

Anyone remember the Ford Edsel?


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## Woodbum (Jan 3, 2010)

It is a good starting point, but certainly not the be all - end all of design. I too am fascinated by Fibonacci numbers and how they relate to most things in life. I use a Fibbonacci sequence when sizing stacking drawers in a cabinet or tools chest. I have 2 Fibonacci/Golden Mean rules and a Woodpeckers Fibbonacci/Golden Mean guuge that takes the math out of the design. Often though, a variation of the Golden Mean adjusted to visual appeal like the 1:4 to 1 version mentioned above is better than a straight Golden Mean layout.


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## Sylvain (Jul 23, 2011)

SQRT [2] =1.414213…...
this is the ratio used in the "A" (standard ISO 216) paper format.
The interesting property is that when you cut a paper in two, the resulting two papers have their length and width in the same proportion as the starting paper.

Except in a few countries where the iso paper format is not used for letters, most people in the world are familiar with this proportion and I guess, as a consequence of this, will find it pleasant. At least you will not be shocked by something you see every day.
The force of habit…

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


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## crank49 (Apr 7, 2010)

Golden mean/ratio or what ever; I hate to see a really well made and finished project that just looks clunky or spindly because someone did not pay any attention to correct proportions. Just sayin.


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## CharlesA (Jun 24, 2013)

"correct" proportions . . .


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## 49er (Jan 3, 2014)

The golden ratio,PHI, is also used in the ElliotWave Theory to track and predict the markets. It works sometimes!


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## CharlesA (Jun 24, 2013)

On markets and phi. http://caps.fool.com/Blogs/is-the-elliott-wave-theory/213366


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## oldnovice (Mar 7, 2009)

*Sylvain*, I like your comment about paper but I have to disagree with "most people know that"! Most people see the relationship but do not and/or don't know that little fact it is based on √2!

*Crank49* this is so true. You see a beautifully crafted, finished piece and something doesn't "feel right" when you look at it and that is because the proportions are out of kilter. I know since I am guilty and those projects are never mentioned around here!


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## TopamaxSurvivor (May 2, 2008)

Gary Brumfield, Gunsmith of Williamsburg fame, told us in at a workshop in the 70s the grand masters in the Golden Age of the Kentucky Long-rifle use 3:5 proportion.


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## grumpy749 (Nov 22, 2011)

your right crank, 100 % that was the point I was maken


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## CharlesA (Jun 24, 2013)

But that's just the point. There is no such thing as "correct" proportions.

Edit for elaboration:

IMHO the bottom line is that in the West many find a rectangle about 1.5/1 to be a pleasing shape in many instances. But the use of Phi as a magic design (or even worse, a stock market predictor) is just not substantiated by facts. Even if you go the GR route, you really only need to get in the neighborhood-1.4-1.7. Moreover, many, many really interesting and innovative designs completely ignore phi. So, it can be helpful, but it is hardly "correct."


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## jumbojack (Mar 20, 2011)

topamax; Now you funny too. 3:5 is the golden ratio.


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## Sylvain (Jul 23, 2011)

Oldnovice
I didn't say : "most people know it is √2".

What I mean is 
"most people are (visually) familiar with this proportion" 
parenthesis added for clarity

8/5< phi < 5/3 or 1.6 < 1.618033988….< 1.6666666….... 
as visually shown in the blog design matters


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## TopamaxSurvivor (May 2, 2008)

jumbojack, just wondered if anyone was paying attention ;-))


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## oldnovice (Mar 7, 2009)

*Sylvain*, you said "I didn't say : "most people know it is √2"." and I believe I said the same thing about the √2 but I think that most people see the size relationship; i.e. 8-1/2" x 11", 17" x 11", 17" x 22" ............

*If I did not say it, I meant the same!*


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## wormil (Nov 19, 2011)

Many times the Mean is rounded off to thirds which is also pleasing. Fibonacci numbers work best in pieces with different elements sized in relation to one another; not necessarily as a shape unto itself. For example people often say a rectangle with a 1:1.618 ratio is most pleasing but it doesn't suit my tastes; however a wardrobe laid out with Fibonacci ratios does look pleasing.


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## TopamaxSurvivor (May 2, 2008)

It is very hard for me to see the difference between 1:1.618, 3:5 and 5:8 unless they are side by side.


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## lwllms (Jun 1, 2009)

The difference Top is that the whole number ratios are very easy to work with compared to 1/1.618. 1/1.618 is pretty specific, it either is or it isn't the golden ratio. If it's not, why not just use the whole number ratios and skip all the mystique and nonsense surrounding the golden ratio?


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## TopamaxSurvivor (May 2, 2008)

I think the mystique surrounding the golden ratio is more in all the mathematical relationships that have been discovered than the proportional differences of a few decimal points in a design.


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## lwllms (Jun 1, 2009)

Bob, it's often pushed as a magic formula-the key to good design. It's not, it's a barrier or a dead end. A woodworker is much better off with a sketch pad than any knowledge of the golden ratio. I think my business partner nailed it when he called it the "golden meaningless."


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## TopamaxSurvivor (May 2, 2008)

I can't say I disagree with that ;-)) It is not the Holy Grail of design, that is for sure. Have you read Livio's Book?


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## littlecope (Oct 23, 2008)

Reading this, all I can hear in my head
is Gilda Radner (as Emily Litella) saying…

*"What is all this I keep hearing, about Older Radios?!"*


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## grumpy749 (Nov 22, 2011)

Iwllms Using a sketch pad is most certainly the starting point when formulating a design idea. This stage has nothing to do with proportions, size, dimensions etc. Once one graduates to the drafting table or of course the computer using sketch up, then proportions begin to matter. To disregard the golden ratio at this point would result in a disproportionate piece of work as we know it. That being said, now if you are drawing artwork of some sort then design principals know no bounders. Its a free for all, whatever looks good to you. Denis


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## lwllms (Jun 1, 2009)

Denis,

I disagree. Every project I've ever done began with a specific space it had to fit in and a specific task that it had to fulfill. Take for example a dining table or a desk. Both have a very narrow range of functional heights so one dimension is set. Building to the golden ration would mean other dimensions are rigid as well. So all desks and dining tables would be the same dimensions or be a "disproportionate piece of work as we know it?" I don't think so, I've seen well proportioned tables and desks in a huge range of sizes.


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## CharlesA (Jun 24, 2013)

For those of,you who believe in the GR, how does it apply to designs like these? http://www.thegardenerseden.com/?s=david+holzapfel


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## TravisH (Feb 6, 2013)

Well when I take my Fibonacci gauge and place start to "measure" things on the Holzapfel tables I find a lot of apparent "GR" aspects. Now I am sure it is a little off but it would appear for example top table: Width of table top to table height, the side shot the far right opening to the left opening, bottom opening to remaining height….

While it isn't dead on and maybe I am willing to accept to much error to make it "fit" I find like most things I encounter they often fall into this range. Is it a must for an eye pleasing design of course not.


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## BJODay (Jan 29, 2013)

I used to work in the printing trade. We used "Picas" as a base for measuring. One Pica = 1/6 of an inch.

I always thought this was archaic and just a throw back but it had a purpose. It was used because it makes inches divisible by 3. Good page layout and design is done in thirds. A page looks better if is divided this way instead of by halves or quarters. Newspapers were often 12 column pages. They would then lay out photos or ads over 4 or 8 columns, ( 1/3 or 2/3) and text over the rest. Landscape gardening uses the same principle.

I now pay attention to printed ads and publications. The pleasing ones are designed in thirds. The others are uglier, less pleasing and less likely to be read. Print is 2 dimensional, furniture is 3 dimensions. I'm not sure if it relates to the GR or not.

BJ


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## 280305 (Sep 28, 2008)

Like many things, the GR is a guideline that can be used in some circumstances - certainly not all.

If I found that some of my body parts were not related by the GR as some sources claim, I would hesitate to make any modifications to improve the fit!


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## CharlesA (Jun 24, 2013)

Ok, so what are some examples of fine furniture where proportions are off bc of ignoring GR?


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## TopamaxSurvivor (May 2, 2008)

Close to GR is eye pleasing, but does not have to be precisely correct dimensions.

*Using a sketch pad is most certainly the starting point when formulating a design idea. This stage has nothing to do with proportions, size, dimensions*

I certainly disagree with that statement. My minds eye sees a project in proportions before it ever gets on a scratch pad. I doubt if I would bother to sketch or start if it were butt ugly at that point.

*For those of,you who believe in the GR, how does it apply to designs like these?* http://www.thegardenerseden.com/?s=david+holzapfel

It is close; dimensions are 15×23. GR is 14.215×23


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## CharlesA (Jun 24, 2013)

There are all kinds of "ratios" on that page. That second table is 36×37. Looks pretty dang good to me.


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## TopamaxSurvivor (May 2, 2008)

Everything that isn't close to GR doesn't have to look bad. Most round or square tables are are not close to GR ;-))


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## basswood (Dec 18, 2013)

The bookcase I am building now is the shape of the state of Minnesota. It will be a pleasing design to the owner, because of their affection for a state, the lines are obviously not prescribed by anything other than odd twists of history and surveying, including a rather famous mistake called the "Northwest Angle". That little mistake makes the shape of the state more interesting and endears some people to it, actually.

Sometimes the same can be true in woodworking. What are your favorite mistakes?


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## CharlesA (Jun 24, 2013)

That's the point-its not a square or an acceptable rectangle. It is just beautiful.


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## CharlesA (Jun 24, 2013)

Nakashima, one of the 2or 3 most influential furniture designers of the last 50 years, said he tried to "find beauty in the irregular." If you do a google image search for george nakashima and behold the beauty of the irregular.


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## wormil (Nov 19, 2011)

Honestly some of those Holzapfel pieces have terrible proportions, specifically the Newlyweds table, 2nd down, previously mentioned. Likewise the Tutuila with leaf petal legs is hideous, the top is way too small. The Katzman table is okay, better than the previous two. The Miller and Prohibited Where Void are both beautiful.


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## CharlesA (Jun 24, 2013)

I think newlywed table is stunning.


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