I first wrote about the geometry of the Old First Church in Bennington, Vermont, in September, 2012, focusing on the 2nd floor windows with their round tops.
I will not repeat that post and the ones that followed - just expand upon it here.
As I studied how the church was designed I saw that the window design was the logical extension of the basic design.
The circle geometry which determined the curves in the half round top also determined the size of the window itself and muntin pattern in the lower section.
The completed circle of the top half intersects with the circle which begins in the lower sash. The circles divided in 4 determine the size
of the window panes.
The panes themselves are not quite square because of the thickness of the frame.
The pattern in the rounded top is made by 7 intersecting circles. The window itself is 2 intersecting circles.
I have called these 'rolling circles' because visually they seem able to roll one way or the other. Perhaps in a church the circles roll toward each other and meet..
It would be fitting symbolism for Old First Church whose covenant says the members hope to " ... become a people whom the Lord hath bound up together... "
Here is this geometry:
looking at the windows in the balcony in the church,
Here is the floor plan, measured and drawn in the 1930's by Denison Bingham Hull, the architect who supervised the church's restoration.
I superimposed a circle with its rectangle marked in red which matches the circles that define the east interior elevation and the exterior front elevation.
This is what I had not seen before - how the geometry of the floor layout uses the same forms as the windows. Both are 2 intersecting circles.
The rectangles laid out by the circles determine the size of the sanctuary. The diamond shape where the 2 circles cross, the center of the church, is the location of the dome -an acoustic device - a technological tour-de-force in 1805. The narthex fills and over flows the lower quarter of the circle. The depth and width of the front bay is determined by the arc of the circle's perimeter.
Expanding the circles in the way that the window design 'roll' I saw that Lavius Fillmore, the master builder, did not need divide his circles into daisy wheels to locate columns and determine proportions.
This relationship of one circle to another in a linear (up and down, side to side) pattern rather than relating one circle to the next by moving around the perimeter is seen in all the elevations and plans for the Old First Church.
In the drawing to the left I have added small circles at the intersections of the arcs which mark the lines of the columns, the corners of the front bay and intersect with the perimeters of the circles at the 4 major columns - the black squares - which run from piers in the basement through the sanctuary into the attic to anchor the trusses which carry the roof and the trusses from which the dome is suspended.
Fillmore need not have drawn a daisy wheel with its 6 petals to refine his design.
He might just have rolled his circles.
In many ways these different approaches to 'basic geometry' - as Asher Benjamin calls it - cross-reference each other. The daisy wheel and the rolling circles are variations of the same proportions.
My 'aha' moment is when I find for one way of working that is clean, simple and 'obvious'.
Here are the earlier posts about the church geometry. Each one was posted when I learned (taught myself) more about how circle geometry can be used for design. Part 1, therefore. is a preliminary understanding.
Part 3 http://www.jgrarchitect.com/2014/11/old-first-church-and-daisy-wheel-part-3.html
Part 2 http://www.jgrarchitect.com/2014/01/old-first-church-and-daisy-wheel-part-2.html
Part 1 http://www.jgrarchitect.com/2013/01/old-first-church-and-daisy-wheel.html