THOUGHTS FROM CAMP ABOUT THE GOLDEN RATIO,(PHI=1.618)

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We arrived at our camp and are just goofin off. Im reading some home carpentry pamphlets and have decided to build a chest of drawers for a gift for a nice member of the family. I want to use the "golden mean" which, as those of you whho are Fibonacci nuts , will recognize as the ultimate ratio of fibonacci number series.

However, for cabinetry , I want to calculate this graphically. I want to create a chest wherein the lowest drawer is some fixed depth, then each higher drawer will be slightly smqaller in depth by a ratio of 1/1.618. I know that there is a method thaT the old time carpenters would use to calculate the drawer depths of a multi drawered unit , like a Highboy.
I know that this is a bit arcane , but hell, you guys always come through.

Ill owe ya big time. This is gonna bug me till I find the answer and the cabinet shops up here in Washington County , only seem to be interested in ship gear.

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Ah, farmerman. Don't leave out the golden spiral please. Sorry that Letty isn't a better math person. Razz

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well the golden spiral is also a subject that interests designers of the decreasing radius stairways like those of the shakers at Hancock Mass

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farmerman, the only thing that I know is that Fibonacci was the only person to interpret beauty geometrically; the curl of the wave; the architect's translation into the structures that still awe the modern world; the fetus. And if I remember correctly, he was considered well below the average intellect.

I'm sorry that I can't give you advice on how to create your carpentry. I just get carried away with the sense of how one man can finally define beauty using math.

Sorry to invade your thread, my friend.

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What'cha do here, is take the diagonal of the face of the smallest (top) drawer. That becomes the heigth of the next drawer. Measure the diagonal of the second drawer, and that becomes the height of the next, and so on.

Now, I've evaded the question, I think, but this will look quite balanced, and is the way real (non-scientific) people do it.

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Actually, one can create a "golden spiral" by creating a series of rectangles having the "golden mean" as the proportion of the sides. Each rectangle is nested in the next larger one, and by squaring the end of each rectangle, and finding the center of the square, you establish a series of points through which a curved line will establish such a spiral.

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roger, work with me here. From where, to where is the diagonal taken?. is there a specific right triangle that works? if i create a fibonacci series based on the simplest side, like 1,2,3. Whhich side is 1 and 2? No I remember a simple drawing trick that used a compass and a rule,
Dammit set, now ive gotta go look up golden spiral construction.

PS set, was there a referendum on Creation in ohio at the primary?

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The practical and the romantic:

Oliver Wendell Holmes (1809-1894)

The Chambered Nautilus

1This is the ship of pearl, which, poets feign,
2 Sails the unshadowed main, --
3 The venturous bark that flings
4On the sweet summer wind its purpled wings
5In gulfs enchanted, where the Siren sings,
6 And coral reefs lie bare,
7Where the cold sea-maids rise to sun their streaming hair.

8Its webs of living gauze no more unfurl;
9 Wrecked is the ship of pearl!
10 And every chambered cell,
11Where its dim dreaming life was wont to dwell,
12As the frail tenant shaped his growing shell,
13 Before thee lies revealed, --
14Its irised ceiling rent, its sunless crypt unsealed!

15Year after year beheld the silent toil
16 That spread his lustrous coil;
17 Still, as the spiral grew,
18He left the past year's dwelling for the new,
19Stole with soft step its shining archway through,
20 Built up its idle door,
21Stretched in his last-found home, and knew the old no more.

22Thanks for the heavenly message brought by thee,
23 Child of the wandering sea,
24 Cast from her lap, forlorn!
25From thy dead lips a clearer note is born
26Than ever Triton blew from wreathèd horn!
27 While on mine ear it rings,
28Through the deep caves of thought I hear a voice that sings: --

29Build thee more stately mansions, O my soul,
30 As the swift seasons roll!
31 Leave thy low-vaulted past!
32Let each new temple, nobler than the last,
33Shut thee from heaven with a dome more vast,
34 Till thou at length art free,
35Leaving thine outgrown shell by life's unresting sea!

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That is a neat poem Letty, too bad Holmes had to put those numbers in front of each line, it spoils the tempo when ya read it out loud

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No referendum, FM, it's still in the hands of the Board of Education, i'll try to remember to go check that out for you.

For constructing that spiral. A rectangle, one unit in height, and 2 units at the base, is squared at the left end to a one by one square. Two diangonals find the center point. From this, a rectangle two units by three units is constructed, at a right angle, i.e., the height is three units and the base is two units. Square the end, two by two, etc., connect the center points by a straight line. Form another rectangle at a right angle to the second, three units by five units, square the right-hand end, find the center point, connect that to the second square. Form a rectangle at a right angle to that, five units by eight units . . . etc., etc.

A curved line drawn with a compass, situated on a line formed from dropping a perpendicular forom a base line formed by the line connecting the center of each square will produce the "golden spiral." I'm sure this is all as clear as mud. I also know a trick to draw a "circle" (optical illusion) using nothing but straight lines. The only math or science in which i excelled was geometry, largely because if i could draw it, i could conceive of it properly. For that reason, i didn't do bad in chemistry, as long as i could imagine and correctly draw the bonds of the atoms in a molecule.

It is interesting that the Greeks conceived of the "golden mean" long before Fibonacci the Idiot formulated the mathmatical expression. I believe it is safe to say that builders ever since have constructed windows, doors and rectangular floor plans, where possible, on the basis of that ratio.

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Cool Topic... I've been admiring your project and wondering about it too, Mr.P being a carpenter and I, a carpenter's wife. We're always in the midst of many projects. Here's something I found by googling Golden Ratio Furniture. There is a surprising amount... is this diagram close to the drawer sequence you were considering?

The Golden Section in Furniture Design

Quote:

The practice
How do we actually use this golden section? Let's use it for what it is, a ratio. When we design a new piece, first of all we need to decide its dimensions. Normally, some of them are defined by its use or by standards. For instance, in Italy most dishwashers are 85 cm high, 60 cm wide, and 57 cm deep. If you are designing a cabinet to be placed on the side of the dishwasher, you must use the same high and depth. But for the remaining dimensions you have some freedom. For the piece above, the width can be set as you please, but not wider than the space you have available between the dishwasher and the next object (a wall, another cabinet). For other dimensions, you might have almost complete freedom. If the cabinet is actually a chest of drawers, you can set the high of each drawer freely.
Let's develop this example further, and compare two easy styles. We design a four drawer chest for our kitchen. We could set the hight to 82 cm, and width 42 cm. while the depth is not important for this example (see figure). The total hight of the drawers is 71 cm......

http://members.fortunecity.com/petemullard/casset1b.gif

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farmerman, I put the numbers there just in case you read from right to left instead of from left to right. Razz

Just wanted to show how the chambered nautilus is a good example of the golden spiral in nature.

Set, that is perfectly clear to me.

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Bookmarking - cool thread!

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aha. The spiral works set. cool. and Piffka, that is a good ref, it led me to others. We have a cable modem here at camp and we dont have that at home so I got a site with a compilation of carpentry tricks for constructing a nest of drawers where the next levelsw down grow by the mean. It was almost in a manner that set descried the spiral. Roger was close but there were some things missing

As Ive read it, you take the bottom drawer measurements . It could be 4 ft long on the face and i ft wide on the face. You create a square on paper scaled to 1ftX 1 ft. Then you take an ARC on the diagonal(you are making an arc out of the hypotenuse of the triangle described by the diagonal.
Using a compass, swing the arc so it intersects a line drawn parallel to the width of the drawer . Then you add this width to 1/2 the width of the original square and that total is the width of the next highest drawer. You repeat this- and the drawers get smaller,until you run out of drawer space or until infinity, when your drawers are verry thin.
This cqalculates the width of the drawer faces . The length youve already decided by design. If youve ever seen a QUeen ANne or a Federal Highboy chest of drawers, thats how they made the drawers smaller and smaller until the top drawers were very thin indeed.

I imagine that second floor windows of all old houses used the golden mean ratio to make sure their sizes were proportionately shorter than the first floor windows.

Caught a small halibut today.
set, thanks fer keeping me up dated on that other matter.

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I though I could take a shortcut there, but anyway, it's called the Hambridge Progression.

Well, it's always more satisfying to figure things out yourself, huh?

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FM, this is from the most current Science Content and Standards guide published by the Ohio Department of Education, Grades 9 & 10:

The Ohio Department of Education wrote:

A. Explain that cells are the basic unit of structure and function of living organisms, that once life originated all cells come from pre-existing cells,
and that there are a variety of cell types.

B. Explain the characteristics of life as indicated by cellular processes and describe the process of cell division and development.

C. Explain the genetic mechanisms and molecular basis of inheritance.

D. Explain the flow of energy and the cycling of matter through biological and ecological systems (cellular, organismal and ecological).

E. Explain how evolutionary relationships contribute to an understanding of the unity and diversity of life.

F. Explain the structure and function of ecosystems and relate how ecosystems change over time.

G. Describe how human activities can impact the status of natural systems.

H. Describe a foundation of biological evolution as the change in gene frequency of a population over time. Explain the historical and current scientific developments, mechanisms and processes of biological evolution. Describe how scientists continue to investigate and critically analyze aspects of evolutionary theory. (The intent of this benchmark does not mandate the teaching or testing of intelligent design.)

I. Explain how natural selection and other evolutionary mechanisms account for the unity and diversity of past and present life forms.

J. Summarize the historical development of scientific theories and ideas, and describe emerging issues in the study of life sciences.

Additionally, all the life sciences curricula standards beyond the third through sixth grade level require that students be able to give the summary described in J., above. The June review seems not to have changed anything here--basically, if a "science teacher" wants to pander to "intelligent design," they are free to do so. It is not required, and as it stands currently, cannot be required. (School districts must make a "good faith" effort to implement the state benchmark standards if they are to receive subsidies targeted for life sciences education--as is the case with each curriculum area.)

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wow, this is good news set. You can welcome OHIO into the new century. The past, more bogus standards had some wording that mentioned additional theories of origins
'Alternative theories to natural selection have been proposed by scientists. "... Something like that, this is happening all over , so fast now, that newspapers arent even reporting it anymore.

However,This is really good news. I havent seen any recent blurbs from the Assn of SCience Education about Ohios turnabout. Next is Virginia and, one other state.

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I always wondered about that near useless drawer on the top.

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While the math here makes sense; none of the actual design elements do.

The 'golden rectangle' is just that, a rectangle.

If you wish to use this theme for a chest, then decide on the height of the chest, or width, and whether it will be 'tall', or 'wide'; then calculate the alternate dimension.
e.g.: if the chest is to be wide, and 30" high, then the width must be 30x1.1618, or 34 15/16".
Now if each drawer is to be a "GR", then, again for example divide each dimension by two. and in the bottom half of the cabinet, place two drawers, side by side, measuring 15" h, by 17 13/32" wide. (round these off, no one will notice - box 30"x35"; drawer 15x17 1/2).
Now for the top provide six drawers, three top, and three below, all 7 1/2 " high, by 8 3/4" wide. (do not forget to allow for the 1/8" clearance between all edges!).

If you want a cabinet which has multiple variations on the "GR" theme, top to bottom, use a diagonal line to calculate the proportions, but it will be 'dimensional' hell, the cabinet will be borderline useless, and take forever to make, and it will probably look ridiculous as well, in spite of the 'theoretical'
beauty of its inspiration.

The golden rectangle is nothing more than a nice shape, (nothing magic, here!) and serves no greater purpose than allowing the unimaginative to think they are 'designing' something, when they are really just painting by number!

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BoGoWo wrote:

The golden rectangle is nothing more than a nice shape, (nothing magic, here!) and serves no greater purpose than allowing the unimaginative to think they are 'designing' something, when they are really just painting by number!

Either you are being cynical, or you entirely miss the significance of the mathmatical and geometric implications of what the Greeks named the "golden mean." The Greeks lacked any mathmatical notation system. Therefore, nearly all of their mathmatical endeavors which were not based on plane geometry were thought exercises, the greatest expressoin of which arose when Euclid combined those thought exercises with geometry, which by its graphic nature, allows for the testing of hypotheses.

Long before Fibonacci the Idiot came up with the numerical sequence which bears his name, and bears exactly that ration embodied in what the Greeks called the golden mean, those Greeks had made an observation about the proportion based on a graphic exercise. If one draws a rectangle in the appropriate proportions, squaring the end of the rectangle with the short line as the base, leaves a smaller rectangle of exactly the same proportions, which can also be demonstrated geometrically. One can also take a rectangle in such a proportion of the short line to the long, and, using the long side as a base, square that dimension, producing a larger rectangle who overall proportion is identical. For what it's worth, the ancient Greek mathmeticians, some of them at any event, did consider this "magical," and revered mathmatics and geometry as manifestations of the divine. Furthermore, they seem to have stumbled upon a proportion which is ubiquitous in nature. Using the method which i have clumsily described above, it is possible to draw a particular spiral. That spiral desribes the arc of the "arms" of spiral galaxies. It describes the spirals of the shell of a chambered nautilus. It describes the spirals of seeds of a sunflower. Not magical perhaps, and not mystical, but it ought to be easy to see why the ancient Greeks were impressed. They were so impressed that they made that proportion a basis for architecture. "Rediscovered" in what is called the Renaissance, that proportion, often somewhat prostituted, survives today in the preferred dimensions of door and window sashs. I'm sure it exists elsewhere, as well, but i can't think of any more examples off-hand.

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THOUGHTS FROM CAMP ABOUT THE GOLDEN RATIO,(PHI=1.618)

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