## Saturday, January 3, 2015

### Just 2 Squares: Geometry in Construction, c. 1917

This house, c. 1917, once sat on several wooded and landscaped acres. Today that land has become a modern subdivision.

The house's owner and I stood in the front yard last fall, considering repairs. He asked why his house looks and feels so much better than the new Neo-Colonials which surround it. He knew his house had presence the others lacked, but wondered exactly why.

We talked about  the obvious things: His house is sited to be seen as one comes to it, its porch inviting.  The new houses' front doors face the street; however often a visitor's introduction to a house is at its garage. Cars first, people later.

The new houses have doors and windows of varying sizes with skimpy casings. They have 3 or 4 different eave details.  Lots of things to look at but no unity or focus.

This house uses 3 window widths, all the same length with the same sash and panes framed by generous casings. The entrance sidelights match the windows in length. The porch and house share eave details.  The centered bay window, the double windows above, the triple windows below, the porch columns, even the minuscule, almost non-existent corner boards, all focus the viewer's eye on the front porch, the entrance.

I told the owner I'd try the geometry of his house to see if it contributed to the sense of wholeness and calm which his neighbors' houses lack.

I was not sure his house used geometry; I had not explored geometry on houses build after 1860.
However, I had measured much of it and - as is clear from the photograph - it was symmetrical.

The house uses a basic geometry: the square.

The front facade is 2 squares.
The sloped lines are the diagonals of the squares.

For clarity I have only laid out the geometry for the square on the right side.
The diagonals define the center of the square and simplify dividing the square into 4 equal smaller squares. The horizontal center line ( red dot and dash line) determines the height of  the porch roof.
The vertical center line may be one of the determining lines of the 3 mulled windows. The windows are also centered in the rooms; that center-line may have been more important to their placement.
And see my paragraph below*.

The porch's width and height come from the first squares. The square of the porch is directly related in placement and size to the double square of the house.

Divide the squares into even smaller squares and the center of one is the center of the sidelight.

In the triple sash on the left I have superimposed a square with the diagonal extended. It doesn't fit.

However, looking at the photograph of the house it is clear that it is the complete window with its casing that we see. When a similar square with extended diagonal is drawn over the casing of the window, it almost fits - within 1-2".

Hmmm, I could have missed part of an inch here or there... My work for this house doesn't require changing windows. I measured them from the inside to get a sense of the rhythm of the space. I probably wasn't accurate enough.

* 2 geometries which expand a square are
The Square Root of 2 - using the diagonal of the square as the length of the rectangle (red lines) and
The Golden Section - using the diagonal of half the square to find the length (green lines).
Beginning with the left hand square I have drawn and labeled both.  They mark the center and the width of the triple window.

A careful look at the photograph will show that the right hand triple window is a modern replacement that's not the right dimensions. This window will be restored to its original proportions.

Unknown said...
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Jane said...

I hope you see my post on the geometry of the Cobb-Hepburn House which lays out another way to design a house.

yuma said...

OMG! I am so exited that I got a reply for my comment :) . Thank you for taking time to reply. I am following your blog very closely...keep enlightening !!

Jane said...

I wrote the latest post on the Cobb-Hepburn House in part so that someone like you could follow it. Please try to draw the geometry. It will make more sense that way than just reading the words.

yuma said...

Hello ma'm,
Yeah, thats exactly I am doing! I had been working in my computer. Paper work only for conceps. But, After reading your post, I took my old drafting tools out, and started drafting your instructions to assimilate...your analysis.
Thank you,
Yuma.