Golden Ratio

[Jerry Thompson]

I have no math background. The Web sites that allow one to plug in a number and come up with numbers mean nothing to me. If I were to construct a box 4' long what would be the width? If I wanted it to also be 2' tall how would that fit in?
If anyone answers this please do not use mathematical signs other than divide add, etc.
Basically I want t find out what would be pleasing proportions of a box 2'hX16''wx4'l. I' not sure I have even presented the question in a rational manner.

[Dave Richards]

So a rectangle that is 48" long (wide) would be about 29-11/16" high. If you built box whose front dimensions are those and wanted to maintain the ratio on the end, the box would be about 18-5/8" deep. If the math doesn't help, do you use SketchUp? You can easily draw rectangles with golden proportions if you want and get a graphic look at it.

[Jerry Thompson]

Thanks Dave. No I don't use SketchUp. How did you achieve the numbers? Be gentle.

[Mel Fulks]

Palladio gave three different rules for figuring how tall a room with a vaulted ceiling should be . I think I have found examples of all rectilinear forms that apply them, too. The simplest one is definately used often ,it is : length times width divided by two equals "proper" height. These things are interesting and fun ,but not the only way to get a good design.

[Dave Richards]

Jerry, I did use SketchUp and drew a rectangle that was exactly 48 in. long and then dragged it out until I got the indication I had a golden rectangle. I then looked at the dimension that SketchUp reported and round to the nearest 16th of an inch. I repeated for the depth using the height of the first rectangle as the limit.

If you want to do it with a calculator you can multiply or divide the known number by 1.6. (it's usually consider 1.618 but it won't hurt to simplify it.) So if you know the long dimensions, divide it by 1.6 and you'll get the other dimension. If you know the short dimension, multiply it by 1.6 to get the long one.

I like the graphical output from SketchUp so I don't need to worry about the math.

[Jerry Thompson]

Thanks Mel. The problem I have with your explanation is that I have no idea what divided by two equals "proper" height means. Dave, I understand what you say and can do it.
Thanks.

[Dave Richards]

Good. I was hoping to keep it simple. Keep in mind that you can round the result to something you can measure and cut in the shop without any problem.

[Mel Fulks]

Proper according to Palladio! Those renaissance guys all had their own ideas of how to improve on the work of the ancients. I'm not saying it works for the table, I just thought you wanted to make the whole project by a system.

[Michael Mahan]

OK , I'm sorta lost here , what's a "Golden Ratio" in woodworking terms ?

[Dave Richards]

It just refers to a method of creating pleasing proportions between elements. That could be for a piece of furniture or a building or whatever.

[Myk Rian]

Leonardo Fibonacci. Google it.

[Michael Mahan]

It just refers to a method of creating pleasing proportions between elements. That could be for a piece of furniture or a building or whatever.

OK gotcha , I gotta start working with SketchUp , I'm dyslexic I'm lost when I get numbers throw at me but I can plan in my mind in 3D very well .
I visualize out a idea in my head keep it there & finish a whole comlex project without a drawing

[Bill Edwards(2)]

Simple example:

Height / width

1.6 / 1

If height is 48" then width is 48 X .625 = 30 (width = 30")

Width is 30" then height is 1.6 X 30 = 48 (height = 48")

:confused:

[mike holden]

Jerry,
Here is a no math method: Start with the narrow side, draw a square, set dividers or trammel points to the diagonal of the square, this is the length of the long side of a golden ratio.
Mike

[Jason Roehl]

Jerry,
Here is a no math method: Start with the narrow side, draw a square, set dividers or trammel points to the diagonal of the square, this is the length of the long side of a golden ratio.
Mike

Sorry, but it's not. The diagonal of a square is a side times the square root of 2, which is about 1.414:1. The Golden Ratio is one plus the square root of five, all divided by 2, which is about 1.618, as someone stated above.

In non-numerical terms, the Golden Ratio is this: Think of a rectangle with side of length a, and the other side length a+b. The ratio of a+b to a will be the same as the ratio of a to b.

http://www.sawmillcreek.org/showthread.php?211749-Golden-Ratio

[Pat Barry]

Golden ratio is a made up thing and the whole idea of the proportions being 1.618 to 1 is a load of hooey, er humbug (Thanks for the correction Bill!). The thought that daVinci used the modern formula to calculate the proportions of the Mona Lisa is ludicrous. Find something in his autobiography to change my mind but it doesn't exist. The fact is, whatever you like for proportions are just fine. Don't worry about the math because its secondary. Merry Christmas.

[Bill Edwards(2)]

Golden ratio is a made up thing and the whole idea of the proportions being 1.618 to 1 is a load of hooey. The thought that daVinci used the modern formula to calculate the proportions of the Mona Lisa is ludicrous. Find something in his autobiography to change my mind but it doesn't exist. The fact is, whatever you like for proportions are just fine. Don't worry about the math because its secondary. Merry Christmas.

Hooey and Merry Christmas in the same paragraph? (shouldn't that be hum bug and Merry Christmas?):D

[phil harold]

multiply the short dimension by 1.618 to get the long side

or

multiply the long dimension by 0.618 to get the short side

[Mel Fulks]

I made a mistake in the formula example I gave yesterday . Should have been length PLUS width ,NOT times width. Apology to anyone who made anything wayyy too tall....

[Frank Drew]

Every time I sketched out a piece using the Golden Mean for proportions I didn't like how it looked, so I never used that formula.

[Roy Harding]

The number you're looking for is "phi" - which is roughly equal to 1.618 (like "pi" is roughly equal to 3.14). It is called the "Golden Ratio" for a variety of reasons - the Greeks derived it by observing natural ratios - if you google "phi", you can get all kinds of graphic representations of how the ratio is discovered in the spiral of a snail's shell, the layout of the petals of flowers, etcetera, etcetera. The Greeks (and Romans) used it when constructing buildings - because they felt that as it was so pleasing in nature, it would also be pleasing in architecture - and in the opinion of many, they were for the most part right.

However, as someone else has pointed out, using it doesn't always give a pleasing result - but it's not a bad place to start.

[Mel Fulks]

I see golden rectangles as more of a statement of the knowledge of the unique qualities of the math than an assertion that they are the most beautiful rectangle. Don't know how many times in books , auction catalogs ,and antique advertisements I've seen photos of chests with drawers graduated with that formula referred to as "beautifully graduated
drawers". That implies that the writers think the work is due to to the cabinetmakers' superb judgement. It really just means he was a schooled tradesman and not a guy slapping something together. What makes the formulaic result instantly subliminally recognized is that any two drawers immediately adjacent are 1 to 1.273 proportion ,and drawer one to drawer three ( and so on ) 1 to 1.618 in proportion. That double proportion ,even with a hundred drawers ,assures that they don't get bigger too slowly or become a symbol for an out of control problem. And it makes the cabinetmaker a genius , posthumously.

[Larry Edgerton]

I use Phi in almost everything that I do, it just makes it easier to come up with a pleasing design. I start with the known dimensions that have to be, and work both ways to numbers that are as large and as small as I will likely need, and then pick my numbers out of this list. I generate these lists before I ever start to draw a piece. It is not mandatory that you use the next number in sequence, and you certainly can create something beautiful without it, but for me it is a tool that helps me figure out sizes of parts that relate to the whole.

For example one of the uses I like the most is determining the size of a moulding that will fit the piece. Another that I used today was using it as a guide to come up with diminishing rail sizes from bottom to top on my own kitchen cabinets. I also picked my style sizes out of the same list. I even picked the size of the bead off of that list of numbers. For me it works out most often and in the end I get a product that has a certian something that is hard for me to quite put a finger on. I do get a lot of compliments on my work however, and they may not know what it is that they like, but they are pleased, and I get paid.

I wish I was better at computer stuff because I would like to have a "Phi generator" on my desktop. Now I do it with a calculator, a bit slower than I like.

Larry

[Dave Sheldrake]

Hi Roy,

There are many claimed visualisations of the GR such as the Parthenon that in reality aren't made to that ratio at all, leaves on a tree are a good example of a real use (non repeating pattern) as are silencing rooms / hearing test rooms but many of the other things attributed to the GR (such as printed picture sizes etc) have no basis in fact.

Larry,

You want an app that does the numbers for you? if so my programming skills are just about good enough the scribble one up if required :)

cheers

Dave

[Roy Harding]

...

I wish I was better at computer stuff because I would like to have a "Phi generator" on my desktop. Now I do it with a calculator, a bit slower than I like.

Larry

Try this http://www.radovleugel.com/golden-ratio-calculator or this http://www.evenfallstudios.com/metrology/golden_ratio_calculator.html or here http://www.calculator.com/calcs/calc_golden.html

OR here's an interesting tool (I don't have one) http://www.woodpeck.com/fibonacci.html

[Roy Harding]

Hi Roy,

There are many claimed visualisations of the GR such as the Parthenon that in reality aren't made to that ratio at all, leaves on a tree are a good example of a real use (non repeating pattern) as are silencing rooms / hearing test rooms but many of the other things attributed to the GR (such as printed picture sizes etc) have no basis in fact.
...

Dave

Isn't that interesting - this is what was taught to me in high school math (LONG before the internet and its' attendant inaccuracies). And I recall calculating the proportions - of course we were only calculating width:height.

[Dave Sheldrake]

http://skeptoid.com/episodes/4325

Brian did quite a bit of work on this subject. The Math behind it is great but it's claimed implementation is often flawed.(that said in Nature non repeating values are quite often seen)

cheers

Dave

[Larry Edgerton]

Try this http://www.radovleugel.com/golden-ratio-calculator or this http://www.evenfallstudios.com/metrology/golden_ratio_calculator.html or here http://www.calculator.com/calcs/calc_golden.html

OR here's an interesting tool (I don't have one) http://www.woodpeck.com/fibonacci.html

Yea, kind of like that Roy. The first one will only input full numbers, no good for me.

The second one is perfect except it will not generate a list, just the next number in sequence. I need to go all the way to about 1/4" usually. I tried it and I can do it faster with a calculator.

Not sure about the third one.

I made one of those Fibbinachi thingys years ago,, but found it to be a pain in the tush as it was clumsy and did not generate numbers I could take to the tools.

[Mel Fulks]

The true or untrue thing is just part of all architecture . Everyone has a belief system and finds a way to prove it . Some of the ancient buildings when measured by renaissance architects were different sizes.. When Jefferson sent his drawings for for the Va Capitol building he defended it by saying if changes were made to the design it would not be like the ancient building he was copying. But he wasn't copying it anyway! There have been fierce ongoing debates about whether the Greek or Roman works provided the better standard. But only the modern guys proclaim buildings with leaky roofs, and buildings falling apart and buildings the people who commissioned them didn't like. To be works of genius. Just weeks ago a bunch of professionals were arguing over which of two buildings was taller when the height of both are known...one of those "if you call a tail a leg ,how many legs does a dog have " things.