Friday, April 18, 2014

Basic geometry - Sandown Meeting House revisited

I have just revised the post I wrote on the Sandown, NH, Meeting House.

I have learned a lot more about early New England geometry since I wrote about Sandown in February. I have been in the Sandown Meeting House, sat in the pews, climbed among the trusses, stood at the lectern in the pulpit. I have visited and explored the geometry of the Parson Capen House, 1683; and the Rockingham, VT, Meeting House, 1785-1800. I am reading Palladio's 4 Books.
I revisited the Sandown measured drawings, found simpler, cleaner geometries which could have been employed.
A new post would have let the old diagrams remain. They are better discarded. I really didn't want anyone to come across the old post through an internet search.  So I redrew and rewrote it.

People had looked at that post 84 times before I revised.
If you are one, please go back and read the new version.

Some of what I learned:

 - How to divide a square into halves; more importantly, why.
Follow the progression on the graph paper here: #1-#2-#3-#4 - counter-clockwise.
I saw how that geometry informed the Parson Capen House.

- What patterns happen when the square in question is divided both horizontally and vertically - see A, B, C, D, E.
- And all the diagonals added.
- And then, imagine 2 squares overlapping! Since this happens at all 3 of the meeting houses I've studied, I needed to think about it more carefully - see F, G.

- And if overlapping is reasonable, how about turning the square 45*, on its point?  See H. The circle surrounding the square is really unnecessary, and, I think, probably not used. Imagine G or H with all its diagonals as in F!
I presented some of that in my diagram for the doors of the Rockingham Meeting House.

Finally I have been trying to understand the influence of Palladio on American vernacular architecture before the 1820's in terms of geometry.
We seem to use squares as a base in New England, and daisy wheel circles in New York. We use 3-4-5 triangles, especially when building an addition. About 1800 the more urban builders seem to begin to explore the Golden Section and less traditional ways to use geometry.

Currently, I do not see builders north of Boston using circles before 1790.
And I will now be skeptical when I see what appears to be a Golden Section. The turned square - H above - uses diagonals just as does the Golden Section. But within the confines of the square, not as an extension.

1 comment:

Unknown said...

Jane, I enjoy your posts as I am a carpentry contractor and love geometry and proportions to be correct.

I noticed reading this one that you wrote "the square 45*" If you want the real degree mark like this 45° you need to use the ascii character #248. You can enter that by holding down the alt key and type 248 on the numeric keypad. It doesn't work if you use the numbers above qwerty keyboard.

You may also be interested in Alt+155 = ¢, 171 = ½, 172 = ¼, 227 = π, 232 = Φ, 237 = φ, 241 = ±, 242 = ≥, 243 = ≤, 246 = ÷, 251 = √.

Best regards,
Mike Rowan