**Design Secrets of the Greeks & the Shakers**

I know about as much about the Shakers as I do about the Greeks, which is to say almost nothing.

Sure, I have seen plenty of pictures of the Parthenon, and I stood for an hour in awe of the Winged Victory of Samothrace at the Louvre during my post-college hitch-hiking trip around Europe in 1969, which was possibly the last great year of European hitchhiking, and maybe the last year they actually let you touch the statues in the Louvre. I recently read a fascinating book of Greek history - Lords of the Sea - which more-or-less argues that Greek rowing led to the birth of democracy. I love that idea. And I loved the scene in one of the James Bond movies (I get them all mixed up) with the stone house on top of a precarious Greek cliff where the Roger-Moore-Bond ties his shoelaces into prusicks to ascend the vertical face and save the day, prior to ending up with the gorgeous Greek brunette in a fabulous yacht floating on an impossibly turquoise sea. That's about it on the Greek front.

As for the Shakers, I'm pretty sure they were a religious society along the lines of the Amish, that "Simple Gifts" is a Shaker song, and that they lived simply and made furniture. That's about it in the Shaker department.

I am about to learn a lot more about both, about the relationship of one to the other, plus dust off a few geometry concepts I haven't used much since high school math class.

Jim Tolpin enters the classroom on Tuesday morning, a lovely curved-handled wooden toolbox in hand and a long roll of paper and some thin sticks tucked under one arm. We gather around the large table at the back of the room. As he unrolls the paper and begins taping it to the table, I can't help but admire the toolbox. It is elegant, beautifully proportioned, exactly the right size for the few small tools it holds, and has three perfect dovetail joints at each corner. (The fact that I can now recognize, name and admire the execution of dovetail joints is a sign of progress, I think.) Jim removes a few items from the box: two large pairs of dividers, a circle-drawing compass with a point on one end and a pencil on the other, a small square, a pencil. He sets the sticks on the table, and I can now see that they are two pairs of two sticks joined at one end with a small hinge and marked off in equal-sized segments numbered from one to 13, one pair longer than the other.

As he is organizing these tools, Jim begins talking about our project for the week, which will be to collectively design and lay out a small side table or lamp table in the Shaker style, develop a cut list for materials, then choose and mill all the wood needed for the six identical tables our class will assemble next week. Given the fact that most of us are not even close to finishing the small benches and stools we have been working on for a couple of weeks now, and even though we will be working in teams of two and using power tools for dimensioning the wood, this seems a daunting task.

Jim says that Shaker design was a system of thinking that has been largely lost in today's furniture design. Though their pieces were built to exacting tolerances, there was very little measuring - rarely more than one parameter, such as the length of a tabletop to fit a certain space, would have been expressed in feet or inches. The rest was done with simple geometry and whole number proportions. A Shaker shop foreman might have said to a furniture maker something like: "Make a table 18 inches wide and a square and a half high." That would be all the information a skilled worker needed to create a perfectly fitted and proportioned piece, with no 13/16ths or 11/64ths involved. In fact, Jim said, most craftsmen would not have known much more math than simple arithmetic, did not have accurate measuring tools, and would not have been able to see them by candlelight anyway. Paper was expensive, if it existed at all, so designs would not have been drawn out, especially full-size. Rather, "Geometry was the language that artisans spoke in." He describes how he designed the pretty little tool box, starting with a segment of a circle for the curved handle and a length that was about right for the tools he intended to put in it. The complicated angles just fell into place.

"As far as we know," he continues, "the process has been used at least since the time of the Greeks. It is how the Parthenon was built, and the great cathedrals. " It is incredibly fast - all you need is a straightedge and a pair of dividers to draw out circles, squares and other geometric shapes that are accurately sized to the point of the dividers - perhaps a ten-thousandth of an inch. The proportions are those found in nature, those of the human body. They are Leonardo da Vinci's Vituvian Man. They are the golden rectangle and the Fibonacci sequence. When such proportions are used, things "look right," the way the Parthenon looks, or a Shaker table, or a frame of 35mm film.

So we start with the given parameter for this project: we will design a square-top table that is 18 inches wide and a square and a half high. Jim grabs a yard stick and quickly draws an 18-inch line at the top of the paper. He then uses the dividers first to estimate half this width, refining the distance by slight adjustments until he can rotate them from the middle precisely to each end of the line, and then steps off three times this distance, perpendicular to the line. This will be the height of our table - which turns out to be 27 inches, the standard height of a side table.

**Galileo's Sector**

Next we have to decide the thickness of the legs. Jim spreads one of the hinged-stick tools and says that it is called a sector and was invented by Galileo.

The sector is a short-cut tool for getting whole number proportions: the sides of the sector are spread apart until you can line up one of the pairs of markings at each end of a line and then the dividers are used to measure across at another pair of lines to get that proportion. For example, to make the legs 1:9 relative to the top, we line up the "9" marks on the sector with each end of the top, then measure with the dividers at the "1" mark. This makes the legs 2" thick, which looks more Stickley-like than Shaker. So we try 1:11, which makes the legs 1-5/8" and very Shaker-like. We use this same process for the other visible parts of the table - aprons and blades - quickly arriving at a design that is pleasingly proportioned and accurately drawn.

Using geometry in the ways Jim demonstrated is so magically simple and quick that I feel a bit lightheaded. Even though I was actually quite good at math in my youth and can still do basic arithmetic in my head faster than I can use a calculator, taking accurate measurements and working with many fractions can be a real pain. The older I get, the more I have to write down, which takes time and leaves plenty of room for error. Jim mentions an essay - A Mathematician's Lament - which I read as soon as I get home. It is worth perusing, especially if you are one who grits your teeth at the mere mention of math.

That the Parthenon, the great cathedrals, and Shaker tables were all designed pretty much the same way - the whole thing is a revelation to me. I will never again look at one without seeing the other. I expect we will be doing quite a bit more designing like this over the coming weeks. Jim mentions that, as far as he has been able to determine, no one else is teaching this method of furniture design (perhaps another Jim Tolpin book soon?) and I feel privileged to be in this class. Remember, you heard it here first!

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