Wednesday, March 31, 2010

regulating lines #2 - Dynamic Symmetry and the Golden Section

'Dynamic symmetry' is the name Jay Hambridge (1867-1924) applied to his study of the use by the Greeks of mathematical and natural growth forms of nature in their design. His book explains his theories and gives 'Lessons' for the reader. The figures are taken from the his introduction and Lesson 2. (In figure 4, the ratio between the square and the rectangle derived from the radius of the diagonal of half the square is the golden section.)

The ratio of the Fibonacci Series was known in the Renaissance as the Golden Section or Ratio now called 'phi' (the Greek letter) or 6.18... It "... cannot be worked out arithmetically; but it can easily be obtained with nothing more than a compass and a straightedge." Peter Tompkins, Secrets of the Great Pyramid, p.190.

Artists tend to know about these ideas:

*About 10 years ago an art teacher casually mentioned the golden section, telling me it is a common organizing tool for artists. I have now heard this several times.

*On a tour of the Saint Gaudens National Historic Site, Cornish, NH, a guide mentioned that Maxwell Parrish, who often painted there, used the golden section. I can find no references to verify that memory. (Maybe I need to lay out regulating lines on his paintings!)

*Karyl M. Knee wrote a phd.thesis in 1966 on Byzantine icons which examines the use and history of dynamic symmetry from its development by the Egyptians to its use in Russian iconography. The thesis is on line.

*Luca Pacioli, author of the first book on accounting, was a mathematician. He taught Leonardo da Vinci. In 15o9, da Vinci illustrated Pacioli's book, De Divina Proportione, describing the 'golden ratio'. Leonardo da Vinci's painting, The Last Supper, uses the golden ratio as its organizing principle.

* French historian Charles Funck-Hellet analyzed the golden section in Renaissance paintings, unfortunately for me, in French. I have not found a translation.

Sunday, March 28, 2010

Regulating lines #1 - Le Corbusier

This is a post on my knowledge about 'regulating lines'.

Le Corbusier (1887- 1965) was one of the best known 20th C. modern architects.
As an architectural student I was so aware of him that I remember where I was when he died.
He wrote a book, The Modular, about visual relationships - a study on where to put what and why. Among other things he postulated a series of interlocking dimensions based on human scale, the Fibonacci Series, and the Golden Section.

In the book Corbu mentioned an associate, Jerzy Soltan, who was in my time, Dean of the Harvard School of Design. With amazing bravery for me, I, a student at MIT, called Professor Soltan to ask for a private reading class. He agreed. The first book he assigned was Dynamic Symmetry, by Jay Hambridge, an investigation of the Golden Section.

That year at MIT we had a series of visiting professors. I asked each of them privately if they used the Golden Section. Although they told me they did, they never mentioned it in lectures. It was considered a kind of magic.

I have Corbu's numbers posted beside my drafting board. I use them. I also use the Golden Section. When a client asks for a wing on an old house, I explore the existing pattern of the house - using the square, the diagonal, the permutations of the Golden Section - to help me read the regulating lines of the house so my design can be sympathetic to what is already there.
A note on the Fibonacci Series: any 2 numbers if added to each other will, within 6 calculations, become the same ratio:
1+2= 3, 2+3= 5, 3+5=8, 5+8=13, 8+13 = 21, 13+21=34 21/34 =0.617
1234 + 789=2023, 789+2023=2812, 2023+2812=4835, 2812+4835=7647, 4835+7647= 12,482
7,647+12,482 = 20129 12,482/20,129 = 0.620

Try it yourself.

Saturday, March 20, 2010

carpenter squares

In 1815, Silas Hawes in S. Shaftsbury, VT, joined 2 legs of steel together to make a stable, true 90* angle carpenter square. Hawes patented his idea in 1819 and began manufacturing. (Iron squares did exist before this. Illustrations of them can be found in the pyramids and in medieval English carvings. There was one recorded in Plymouth in the 1620's, and another in New Haven, CT, before 1700.)

I became curious about these steel squares when I realized that there were several factories producing steel squares on Paran Creek, which runs from Shaftsbury, through N. Bennington to the Walloomsac River. Lots of factories because of lots of demand - one factory, swept away in a flood in 1852, was immediately rebuilt.

At the same time Asher Benjamin is publishing his pattern books.
And post and beam framing systems are evolving from scribe rule to square rule. This is a change from each tendon fitting only one mortise, to the parts being interchangeable. For example, a brace could fit between the post and beam (sill and stud in the illustration) at the front of a barn or at the back.

Do these facts have anything in common?

A joiner needs to know the angle he uses will be the same each time, dependable, before he can make the same part to be used many places. He needs to own a carpenter square even if it is expensive, and it was - at least a week's pay.

Does the manufacturer of many, many carpenter squares in Vermont a play a role in the evolution away from design using 'regulating lines'?

The Eagle Square sign comes from The Shires of Bennington, published by the Bennington Museum in 1975. The illustrations were drawn by Edwin Tunis for his book, Colonial Craftsmen, the World Publishing Company, 1965.

Thursday, March 11, 2010

glass for Show and Tell

These items were part of the 'Show and Tell' we assembled for the forum on windows at the Dorset Historical Society in February. Choosing the pieces made me look more carefully.

The first is the piece left over from blowing glass. Today we call it a bulls-eye. It can sometimes be seen in the transoms over front doors in old houses. In the center is the closed-in hole where the molten glass was attached to the pontil - the tube the glass maker blows through. The swirls were caused by twirling the soft glass to thin it out to a plate about 5 ft. across which could then be cut into window panes. This was how glass was made before 1800. This center part was basically waste that someone found a use for.

The second is a reproduction Sandwich glass tumbler c. 1830, made with a 3 piece mold. I tried to photograph it so the light would shine at one of the seams. The use of a bucket to pour the molten glass into a mold instead of blowing up the glass glob on the end of a tube was a major change. Flat glass techniques changed too so window panes could be bigger.

The later goblet - 1880's or so - has a 3 piece base holding a seamless bowl. Wow! Compare the technology involved to mass produce this - buckets that were filled, moved and tipped, molds that closed and opened, machinery that brought the two parts together while they were still mailable - to the simple tool used to blow the bull's eye, the way of making glass for that had been used for centuries.

I also had a piece of window glass, c. 1900, with some waves in it. Extruding glass with a smooth surface was not easily done until around 1940.

Finally, I brought a modern art glass tankard because it showed the molten qualities of glass so well.
And here I was surprised at my response. This is the mug I use at home. Now I saw the air bumbles that mean the glass wasn't as carefully blown as early window glass was. It had the pontil mark - the place where the molten glass was attached to the blowing tube, and I liked seeing how the mug was made. But the piece was heavy, not light and airy. The glass was thick, not clear and delicate. The light shone through the others 'better'. The handle was just a snake, a blob of glass, crude.

I know the glass blower probably chose to make it like this - the nature of molten glass right there to see. But right now, partly because I understand the skills required to create them, I much prefer the other pieces.