#12
One day, after a trip to the local vendor, the quantity of liquor bottles on my kitchen side table began to clearly exceed its given limits; the lady of the house suggested I build something capable of holding them on the wall. "I can build a shelf this very day", I says. And thus I took the opportunity to spend the rest of the week drinking said liquor and waxing (internally, mind you) on how modern design pedagogy had failed me as a woodworker. When a few kind folks in another thread mentioned interest in a drawing I posted of another project, I finally decided to design the shelf, build it, and post a little bit about the process as a basic introduction to the methods I've maladapted over the years. I've studied geometric ratio and proportion since graduate school, where I applied them to the music of Bach. It all carries through.

This design is unconventional because [it seems that] the rage these days is simple integer ratios. I don't like simple integer ratios. They're simple and boring. Paradoxically, I like simple furniture, and this is the simplest of shelves--an only once divided frame. Yet I've managed to design it completely out of those terrifyingly infinite decimal ratios known as the "incommensurable", and this is sure to raise the hackles of many.

Anyway, here's the drawing, with all the geometrical fluff left in:



Here's the short on the design process. I had 42" between the refrigerator and the end of the wall in which to put the shelf. This is the first constraint... thus, a circle with diameter 42. In my opinion, there are two major interesting three part divisions of a space: the square root of 5:1, that is, a square in a semi-circle... big in the middle; and the square root of 5+2:1, the division of line in the pentagram...skinny in the middle. (Both of these manifest the golden section). I opted for big in the middle, for reasons of capacity. Thus I draw a square in my semi-circle, and my overall width is ~18.78", or a hair fat 3/4.

From here I need to determine the overall height. What's in a good-looking rectangle? I know I've got two shelves on which bottles will sit. Tall on bottom, short on top. A bottle of Corralejos tequila is around 14", but I want a little headroom for appearance's sake. 15". A wine bottle averages 11.5" or so, so that's the max I need on top. 11.5"+15"+2.25" (for wood thickness) means I need at least 28.75", and preferably not more than 30, as we're pushing the height I want to ever reach from in front of the side table.

28.75/18.78 = ~1.531. Close to the golden section, but closer to the height of a pentagon (~1.5388:1), which I find to be the most handsome of the rectangles. So I draw a pentagon from the side of the square, and the height is 28.9", or a fat 7/8. Where do I put the middle shelf? Again, I need about 15" at the bottom. 15.75/18.78 = .839. Real close to the height of a triangle (.866). So I draw an equilateral triangle, and my height from the bottom is 16.27", or a fat quarter.

And thus I've determined the front elevation, and we have cycled through all the hated ratios of geometry, and all quite simply from a single width, determined in harmony with the space allotted. The side profile is easy: I want to slant the sides downward, so I need a couple of points from which to take the line. Minimum bottle depth capacity at the top should be about 3", for the aforementioned Pinot. But exactly 3" might be stuffy; at least an inch extra would look good. I eyeball and then arbitrarily divide the middle shelf in half from the center line (which is about 4.7 inches), and then eyeball how I want the slant to look. What I eyeball is almost exactly a tangent to the circle within the triangle. So I draw the circle (for thoroughness, at this point), and the side profile is determined.

The last element is a brace in the back through which I will screw the assembly to the wall. I divide the very top depth in half to echo the previous, and draw a circle with this radius. The width looks good, so I mark the line.

I build the shelf. Through dovetails and stopped dados in the cheapest conifer that grows, with a couple coats of blonde shellac. It looks like this:



Now the kitchen side table is covered in other junk.
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#13
Hah! nicely put, nicely done.
ken
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#14
Back when I was into working out and trying (and failing) to get ripped I was reading everything I could get my hands about sets, reps, rest periods, protein, creatine, and every other ine, and on and on.

One day somebody who I know who is quite fit put it like this. "Put weight on bar or machine. Lift weight."

The moral of the story is that then next time I want to build a shelf I'm just going to copy the final product from this post.
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When something has to be done, no one knows how to do it.  When they "pay" you to do it, they become "experts".
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#15
Axehandle said:


Back when I was into working out and trying (and failing) to get ripped I was reading everything I could get my hands about sets, reps, rest periods, protein, creatine, and every other ine, and on and on.

One day somebody who I know who is quite fit put it like this. "Put weight on bar or machine. Lift weight."

The moral of the story is that then next time I want to build a shelf I'm just going to copy the final product from this post.




My similar experience was "Find the heaviest object you can lift. Put it on the ground. Lift it above your head. Repeat." Of course, even this ended with Euclid.
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#16
Thanks,  Curt
-----------------
"Life can only be understood backwards; but it must be lived forwards."
      -- Soren Kierkegaard
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#17
One is tempted to mock a design narrative that one does not begin to understand. One could reply by describing an elaborate means for constructing a rhomboid using only a sundial and a pocket comb. But, not having consumed the spirit of the grape in at least six apparent half-lives one chooses to ask questions: What is the mystical meaning of the square root of 5 whether or not we add 2? Or "Why not just draw a shelf with pleasing dimensions?" Or, "WIBH are you talking about?"

Inquiring minds want to learn

Doug
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#18
Doug_H said:


One is tempted to mock a design narrative that one does not begin to understand. One could reply by describing an elaborate means for constructing a rhomboid using only a sundial and a pocket comb. But, not having consumed the spirit of the grape in at least six apparent half-lives one chooses to ask questions: What is the mystical meaning of the square root of 5 whether or not we add 2? Or "Why not just draw a shelf with pleasing dimensions?" Or, "WIBH are you talking about?"

Inquiring minds want to learn

Doug




There's no mystical meaning to the square root of five, at least, in the non-mathematical sense. It looks really good, first of all, but more importantly, it subsists in shapes that also naturally give rise to more good looking ratios and shapes. For instance, in a system of "modules", there's no real reason to choose any particular division other than what "looks" good. Why does it look good? Because it's a division of the module, of course! But in the system I use, what looks good also just happens to be the confluence of points and lines in a very regular geometric assemblage. I find it unlikely that any normal fudge could stand in front of a piece and say with any confidence "that second shelf is [insert any simple integer ratio] of the base". But if I told you to look at my piece and imagine a triangle from the bottom, you'd probably immediately recognize the height of the second shelf. And if I told you to imagine a circle between my fridge and the end of the wall and the top of the table, you'd see that the base of the cabinet (as I mounted it) sits on the diameter, and that a square in that half circle determined the width. And not only does this give the work some kind of "harmony"--where the whole thing is knitted from one thread--it more or less guarantees a cohesive (if not attractive) visual.

And why not just draw a shelf with pleasing dimensions? Because if anyone were to ever ask me how I determined the dimensions, I could never be satisfied responding with "Because it simply looked pleasing."
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#19
Good one Joel.
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#20
You need more booze
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#21
I'm not sure if I'm to take your post as tongue-in-cheek, or pray that you never need to remodel your kitchen. I like the result, though.
Still Learning,

Allan Hill
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The Simplest of Shelves; A Story in Unconventional Design.


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