Monday, April 9, 2018

Practical Geometry at MIT

This is the curtain wall of the Mass Ave entrance at MIT,  the Massachusetts Institute of Technology, Cambridge, Mass.
The picture arrived in my mail box last week.

Immediately I saw the geometry. I knew what geometry the designer used and how it was manipulated.

I was writing posts for this blog and my local blog. None quite came together. Each had parts which require more drawing, thinking, and better choice of words.
Frustrating.
Then the latest MIT mailing to alumni/ae showed up with this picture.
I laughed. I walked beneath that wall of glass and columns for 4 years. In that time I paid a lot of attention to how we used the space it sheltered, how the shape and size of that 'entrance' directed what we did. The curtain wall was not part of my thinking, although the light it allowed into the rotunda was.
The wall's pattern, rhythm, proportions - or even the idea that it was geometry - was not part of my analysis, nor was it ever alluded to by others.

Here is the pattern.
Upper left : A square and its diagonals.
Upper middle: The circle that comes from using the diagonal of the square as the circle's diameter.
Upper right: The square that fits around the circle.

How the pattern grows:
Top row: Overlap a circle of the same size, so that the perimeter of each circle touches the square inside the other.
Second row: This pattern can grow sideways as well as up and down.
4 squares on the right: Once established leave out the circle, continue the squares, add the diagonal, horizontal, and vertical lines.

The pattern could have started with the circle and the 2 squares fitted around it.
Using the circle as the unit  - the 'module' or 'diameter' in classical terms - is the traditional way to begin a design. (See Palladio through Asher Benjamin.)

From a photograph I cannot judge the diameter of the column.  Does it taper? have entasis? The pilaster in the corner on the right appears to be the same width as the unit I chose: the original square.
If instead the column is the unit, the module,  the circles of the curtain wall might be 3/4 or 2/3 of the module.

I have been told that the main buildings at MIT - dedicated in 1916, designed by William Wells Bosworth -  were designed using geometry. The drawings of those buildings would be well worth studying.

Practical Geometry has become an integral part of how I see buildings.  I was surprised to find that it has become a design tool for me as it was for those who used it for construction.

Meanwhile, this little bit of geometry was just plain fun.