# The Golden Mean



## ClintSearl (Dec 8, 2011)

The Greeks(?) derived the ratio of 1:1.618… which came to be known as the Golden Mean for its perfect proportions in the layout of a rectangle. I have used the Golden Mean to divide a sequence of drawers into a linear progression such that the first and last drawers are in the 1:1.618 ratio, whether it's a horizontal row or a vertical stack. To determine the correct dimensions of all the drawere, I constructed an Excel spreadsheet that takes the ratio and total dimension to be divided as inputs and returns the sequence of individual dimensions for any number of divisions up to ten as the output. The program is not limited to just the Golden Mean, but will accept any ratio between the first and last. An example is my interpretation of a G&G inspired credenza that has a horizontal row of drawers and a vertical stack of drawers proportioned as described. PM me if interested in getting a copy of the spreadsheet.


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## tierraverde (Dec 1, 2009)

Now thats cool.
Thanks


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## lysdexic (Mar 21, 2011)

I have employed the golden mean in many ways for the past 2 decades. I believe this ratio permeates our lives. That said, have you made one of these golden ration calipers?


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## Kentuk55 (Sep 21, 2010)

Looks like it works


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## madts (Dec 30, 2011)

Any time something looks good the golden ratio is in there somehow.


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## ClintSearl (Dec 8, 2011)

The calipers are clever, but the calculator is easier and doesn't have any length restrictions.


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## waho6o9 (May 6, 2011)

http://www.leevalley.com/en/wood/page.aspx?p=57625&cat=1,43513









Great topic, the golden ratio rulers work best for me and the set is well worth the money.
Although, the computer generating one as no limit as mentioned by Clint and could come in handy.


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## MrRon (Jul 9, 2009)

Interesting. People that build live steam ride-on locomotives build to a ratio of 1:1.6. Thats pretty close to the golden mean. I wonder if there is a connection.


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## Dark_Lightning (Nov 20, 2009)

The "Golden Ratio" is but one of many log-periodic ratios in use. TV antennas (the old ones that got put on the roof) also are log-periodic. Mario Livio wrote a book about this, and I tend to agree with his assessment- "The Golden Ratio is a product of humanly invented geometry". We are a product of our surroundings, having adapted to it to survive. I think that the mathematics made us, and we discover it as we learn more…maybe we "co-evolved".


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## 280305 (Sep 28, 2008)

This number appears all over the place. It has this fun property:
G - 1/G = 1

You can try this in a calculator:
G = 1.6180339887498948482045868343656
1/G = 0.6180339887498948482045868343656

I think of the ratio like this. Divide a line segment into two pieces so that the ratio of the whole line to the larger piece is the same as the ratio of the larger piece to the smaller piece.

There is plenty of information online. Here is the Wikipedia entry:
http://en.wikipedia.org/wiki/Golden_ratio


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## Wildwood (Jul 22, 2012)

When talking about proportions can begin with known proven design standards like golden mean or rule. Those proportion do change when studying different periods and styles of furniture. Proportion ratio do change depending on piece of furniture too; end tables, entertainment centers, dining tables, and chairs for example. 
Other design elements and principles of design cannot be overlooked if want to move your furniture into works of art.

Elements are the build blocks of design: color, line, shape or form, space, and texture. 
Principles of design, which often overlap: Balance, proportion, rhythm, emphasis, and unity.

Of course, none of this is important if furniture fails function and aesthetics buyers want. Alternatively, if there is total lack of craftsmanship forget everything said here.

Love the piece shown by OP!


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## Bonka (Apr 13, 2012)

I have no and I mean no math background besides add, subtract, multipyl and divide. The a's, b, and x's mean nothing to me. If I had a box with a 12'' long front what should the side be.?


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## lysdexic (Mar 21, 2011)

7.4"


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## a1Jim (Aug 9, 2008)

I know this works for many folks but I trust my eye as to proper proportions . I guess we all do what works for us.


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## richgreer (Dec 25, 2009)

Just as an FYI - Some people may not realize this.

If you have a golden rectangle and you draw a line across it that divides the rectangle into a square and what is left over, what is left over is also a golden rectangle, albeit smaller.


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## JGM0658 (Aug 16, 2011)

hmmm..ok maybe I will get flamed for this, but the golden mean is not always golden…the top row just does not work for me. I would have made 2 equal length drawers with a short one in the middle. There is just something strange about the progressive series on the top row.

On the piece itself the quality of your craftsmanship is flawless. Although I applaud the intention of not just copying the G&G style the doors for me are just too busy, too many accent plugs. And those hinges….For the next one I recommend you look at the Soss hidden hinges.

The choice of wood for the pulls as well as the face of the drawers takes away some of the beauty of your craftsmanship, the pulls are beautiful but they get lost on the face of the drawers. I would have used a contrasting wood with no figure so that the face of the drawers look more impressive.

As I stated, overall you clearly have the craftsmanship, but the devil is in the details and the piece is just too busy for me. Something the G&G brothers tried to avoid at all costs.


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## Zinderin (Jul 24, 2012)

JGM0658 …

I sort of thought the same thing when I looked at it. But like anything else, this is art that this point. Granted, its functional art, but its art just the same. So it becomes a matter of taste and opinion.

Looking at it as art, I can appreciate that is gorgeous, the amount of work and time that was put into it's creation, and hopefully it will be out there providing "oooohs" and "Ahhhhs" long after all of us are worm food.

Clint, that -is- absolutely gorgeous. Not to my tastes, but from what we can see, just stellar work, and as art it really is gorgeous! Thank you for sharing it with us.

Now I will spend the next couple of weeks in my shop playing with this "golden ratio" crap …. like I don't have enough to do already damn it!!!!!


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## JGM0658 (Aug 16, 2011)

Zinderin, I agree with you, but many times people post a project and all they get are "oohh" "ahhh" beautiful…blah, blah, blah.

If I post a project I will take the pats in the back, but I also want to hear differing opinions and maybe improvements. If you look at my posts I rarely ever make a critique. But I thought Clint's piece could use a differing opinion. Here is a guy who is already past the square table A&C stuff, craftsmanship is outstanding, maybe some of my critique might give him food for thought, maybe not and completely dismiss it. The idea is that we help each other improve through communicating our opinions.

Bear in mind that my comments are not "negative", nor was my intention to take away any merit from his work. But on the other hand I don't understand why everybody in LJ is so afraid to post an honest critique and say, "I don't like it and here is why"..... I can tell you that in my personal work I have learnt more from those who said "I don't like it" than from my mom and wife who think everything I make is awesome…


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## Wildwood (Jul 22, 2012)

Gerald, not sure anyone can answer your question until know what kind of box you are talking about. Boxes can be square or rectangle. Knowing the box is 12" longs tell us nothing.

Really, need height to coo-coo-late. Try 12" height divided by 1.618 think will come up with 7.42" since 0.42 less than half round down to 7" or 7 3/8" for sides.

Folks that came up with golden mean, rectangle, and rule were mathematicians of their day. That early ratio- proportion formulas used for viewing art and architecture not understood by all craftsman then or now. Yes, all industries today still use proportion ratio formulas in their designs whatever the product.

Furniture/cabinet industry done most of the calculations for us and given us average lengths, widths, and heights as standards. Yes, there are size exceptions especially for things like jewelry boxes which can be small or large. Also kid vice adult furniture, lets not forget doll house furniture. If study period and different style furniture might notice slight difference in dimensions too.


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## lwllms (Jun 1, 2009)

Actually the Greeks were aware of the golden ratio as a mathematical construct but never used it for design. It's use in design is a late 19th Century concept. There's even nonsense about the Greeks using the letter Φ (phi) to represent the golden ratio but this actually was first suggested by American mathematician Mark Barr around 1910. If you want to understand proportions and how they were used, I suggest you investigate the sector which was used from Galileo's time and was called the "proportional rule" in Europe. You can learn about the sector on the web but a reprint of John Robertson's 1775 3rd edition of _A Treatise of Mathematical Instruments is available. It has a great section on how to delineate the Classical Orders with the sector.


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## ClintSearl (Dec 8, 2011)

Different strokes for different folks.

The idea was to extrapolate the design motif they employed in a drop front desk for the Tichenor house into a matching credenza. The desk was also the only piece they ever executed in ash. Was I successful in capturing the essence of the detail?


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## waho6o9 (May 6, 2011)

http://www.orbitals.com/books/tmi/index.html


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## ClintSearl (Dec 8, 2011)




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## Wildwood (Jul 22, 2012)

Clint, shown side by side your credenza and period drop front desk (Fall Hall Desk) comparing apples to oranges.

http://www.gamblehouse.org/nnb/object/411.html

I like both pieces for different reason.


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## ClintSearl (Dec 8, 2011)

Bill….I don't know what you mean


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