What You Should Be Learning

[Kees Heiden]

From wikipedia (OK, ok, not the most reliable source, but her I think they are correct)

Architecture

Many of the proportions of the Parthenon are alleged to exhibit the golden ratio.

Further information: Mathematics and architecture
The Parthenon's façade as well as elements of its façade and elsewhere are said by some to be circumscribed by golden rectangles.^[25] Other scholars deny that the Greeks had any aesthetic association with golden ratio. For example, Midhat J. Gazalé says, "It was not until Euclid, however, that the golden ratio's mathematical properties were studied. In the Elements (308 BC) the Greek mathematician merely regarded that number as an interesting irrational number, in connection with the middle and extreme ratios. Its occurrence in regular pentagons anddecagons was duly observed, as well as in the dodecahedron (a regular polyhedron whose twelve faces are regular pentagons). It is indeed exemplary that the great Euclid, contrary to generations of mystics who followed, would soberly treat that number for what it is, without attaching to it other than its factual properties."^[26] And Keith Devlin says, "Certainly, the oft repeated assertion that the Parthenon in Athens is based on the golden ratio is not supported by actual measurements. In fact, the entire story about the Greeks and golden ratio seems to be without foundation. The one thing we know for sure is that Euclid, in his famous textbook Elements, written around 300 BC, showed how to calculate its value."^[27] Later sources like Vitruvius exclusively discuss proportions that can be expressed in whole numbers, i.e. commensurate as opposed to irrational proportions.

[george wilson]

Kees: the steps were considered not as part of the aesthetics of the building,but as a pediment that the building sat upon. Just as I made a mahogany base for a bust of Jefferson for the American Embassy in Paris,the important thing was the bust,not what it sat upon.

[Steve Voigt]

I definitely don't see how it is "destroying" anything to write, as Kees did, that "I am not convinced that the golden ratio is any better or worse then for example a 2:3 or 3:4 or 3:5 ratio." As I wrote before, it is a subject of some debate and controversy, and there's no harm in debating it. Further, I think a number of Kees' specific observations are correct. I spent a lot of time working through Euclid's Elements a number of years ago. My memory is a bit fuzzy but I don't remember that he prioritized the golden rectangle over whole number ratios; rather I remember that the latter are pervasive throughout the book. Euclid was influenced by Pythagoras, and a major basis of Pythagoras' cult was was whole number ratios as instantiated in music (2:1 = octave, 3:2 = perfect 5th, etc.). It's also true that much of the evidence for the use of the golden section and the Fibonacci series in antiquity is circumstantial rather than direct.

It might be worth stepping back for a little perspective and asking what people want to design, and how such things have been designed in the past. I assume the majority of people here want to design furniture, and maybe some joinery stuff like doors and windows. A minority of us are toolmakers, instrument makers, boatbuilders, etc. And most people here, as opposed to the power tool forums, are interested in making and designing stuff the way it was done before the 20th c.

Now, there is some evidence that architects before the 20th c. used the golden section or the Fibonacci series in their designs, though again a lot of that evidence is indirect. But I have never seen any evidence that the great and famous furniture makers of the 18th and 19th c, not to mention all the anonymous makers who produced excellent work, used these ratios in any systematic way. On the other hand, I have seen evidence, including in Walker/Tolpin's book, that they used whole number ratios.

A few posts ago, a guy wrote that "the key to eliminating those sorts of surprises is drafting an entire project before you ever touch a piece of wood." If that works for him, fine, but the evidence is that most furniture makers in the hand tool era never did this. They didn't make drawings at all, or if they did, they were the equivalent of napkin sketches. They didn't make detailed measurements, either. What they did was use dividers and a few basic measurements, the latter often with story sticks rather than numerical dimensions. And this again tends to lead to simple whole-number ratios.

I don't think it's bad though, to argue about what ratios to use. Probably for most people who lack design experience, using any ratios, and thinking in any systematic way about how the parts complement the whole, would be a step in the right direction.

[Jim Koepke]

After studying this for a couple of days I am not convinced that the golden ratio is any better or worse then for example a 2:3 or 3:4 or 3:5 ratio.

2:3 and 3:5 are part of the Fibonacci sequence, which is the sequence of the golden ratio.

3:4 is interesting since a right triangle with sides of 3 & 4 will have a hypotenuse of 5.

jtk

[Patrick Chase]

Later,in 1202,Leonardo of Pisa,who was educated in North Africa by Moors,introduced the 10 digit system,with a decimal point and a symbol for zero. He put 2 rabbits in a field where they could not be killed or escape. He studied the numbers at which they reproduced. These numbers were: 1,1,2,3,5,8,13,21,34,55. The ratio after 3 is 1.618,which is the golden ratio.

A very technical nit-pick: The golden ratio is an irrational number, while the Fibonacci sequence consists of integers. As such the ratios of successive Fibonacci terms are inherently rational numbers, and can therefore never be equal to the golden ratio. Instead the ratio of successive terms in the Fibonacci sequence converges to (1 + sqrt(5))/2 as it approaches infinity.

Just using the examples you posted, the ratios (to 5 digits) are:

1.0, 2.0, 1.5, 1.6667, 1.6, 1.625, 1.6154, 1.6190, 1.6176

It oscillates over/under the golden ratio starting with the first ratio, and does so ad infinitum. There's nothing special at all about the ratio "after 3".

[george wilson]

The ratio of the golden mean is well documented in use throughout history I wish some of you would Google around more,truly.

I am not trying to force anyone to se the golden mean rectangle,the root 2,or any of the other classical rectangles. I offer them only as a suggested aid to those who may want help in designing things.

As I mentioned in the first post(I think),I haven't used them myself. But,I seem to have a natural ability to design. The Master Cabinet Maker,Mack Headley used the golden mean all the time in his design work. He studied Chippendale's book a lot. On a daily basis,as far as I could tell. Every time I saw him,he had that book(when he was in the shop).

I don't make much furniture,and the things I make do not usually involve rectangles anyway. I don't know how I'd work the golden mean into the bronze drill,for example.

Take the information I have made available and run with it,or ignore it. You are free to choose. I tire of arguing with those who discount it. It exists,and was and is used,period.

[Kees Heiden]

I did google quite a bunch, but of course it depends on your search criteria what you are going to find.

There were three important points in history where something was written about the golden ratio. Euclid, we allredy discussed. He was probably the guy who invented the ratio, and gave it the unromatic name "mean and extreme ratio". BTW, he lived about 100 years later then the build of the Parthenon.

Then we have the book Divina Proportiona from 1509. Written by Pacioli and brilliantly illustrated by Leonardo Davinci. It's about geometrics, not aesthetics. The second part of the book about architecture is following the traditional whole number ratio system from the Roman architect Vitruvius. This part of the book really is not much more then his view on the famous book from Vitruvius, De Architectura, the book every architect and artist from the Renaissance knew by heart (probably).

Finally we have Adolf Zeising (1810-1876) who thought the golden ratio was operating as a universal law. He studied the branching of leaves from the stems of trees and similar the branching of skeletical parts, geometry of chemicals and crustals and thought everything was according to the golden ratio. The name "golden ratio" is from this time. He really kicked of the whole golden ratio thing.

I am certainly not saying that golden ratios can't be used with good effect, leading to good designs. It's just not the only way to design and it certainly has been hyped up a bit.

[george wilson]

That's daVinci. I've said my piece.

[Joe Leigh]

"......I tire of arguing with those who discount it. It exists,and was and is used,period."

This is really the point I was making. The minute there's a dissenting opinion, you start using words like "attacking" and "destroying" and "arguing". Kees is certainly not arguing, he is simply and respectfully presenting a different opinion.
98% of the posters in this thread have agreed with you. Does everyone have to agree?

You said you were 75 years old, is this the way you act when someone disagrees or sees things differently?
I hope not. Seems like a long time spent making sure everyone sees things your way.

Other than that it's an interesting thread and I've enjoyed reading it.

[Jim Koepke]

Dang, I spent a bit of time on a response and it disappeared.

What happened to the auto save feature?

jtk

[David Carroll]

Back in Art School, (1978) in our intro to drawing and design class, the instructor asked each of us in the class to draw a rectangle in which the long sides were six inches in length. The short sides could be whatever yielded a rectangle of pleasing proportions to the one who did the drawing. Once the 12 or 15 of us did this, the instructor measured each and took an average of the lengths of the short sides all of us had come up with. He drew a rectangle using this average and compared it to the "Golden Rectangle" and it was remarkably close.

We talked about it quite a bit, it's history and use. During the discussion we debated whether we thought that the sense of proportion was hard wired into us (nature) or whether we all have been exposed the to use of the golden mean so much that our idea of correct proportion was influenced by its ubiquity (Nurture). I find it a fascinating subject and I am thrilled that George and everybody are discussing it.

The folks who were on the side of Nature pointed out the natural occurrences of (approximate) golden ratios, (cell division and embryonic growth patterns) and the Nurture camp pointed out that even in the classroom example, our rectangle was not exactly the golden section, it was off a bit (more square) and could've been influence by a rectangle we (in those days) were intimately familiar with, TV screens.

We were shown the same examples posted here, and adherence to the golden mean is most always approximate, but if you were to change the proportions of the Parthenon much, it would look wrong, in terms of pleasing proportions.

It's a great starting point in design work, practical concerns will often necessitate deviation from the golden mean, but it's a solid base to start upon to find pleasing proportions. It's discussion and debate is a great way to fill time while one waits for stain to dry enough to apply a finish (What I'm doing).

Thanks to all for the discussion!

[Paul McGaha]

Thank you George, for taking the time to post here and sharing your thoughts and experience.

It really is very nice of you.

PHM

[Pat Barry]

Enough has been said about the golden ratio / proportion / rectangle, both factual and fictional, and everyone is never going to agree about it. Lets just drop it before tempers get too high and agree to disagree and move on.

[george wilson]

Well,Joe,if you have computed that 98% of members agree with me,then perhaps I have reached more than a few. I hadn't done the math. We do seem to be stuck on the golden mean rectangle,and I too,would be glad to move on to other things that designers and woodworkers might find useful to know. I have said my piece about it.

Does anyone have suggestions as to what other things those would be that should be learned? I'm opening this up to creative suggestions.

[steven c newman]

Maybe how to not only read a wood's grain, but the best way to make use of the grain. How to make a few boards seem to flow together?