As I often refer to it and use the diagrams when I lecture and teach, I copied it here for easy accessibility - with a few edits for clarity.
I invited myself to a Green Mountain Timber Frames barn dismantling in the fall of 2014. I wanted to watch it come down. I also wanted to investigate its geometry.
The three barns sat beside the road on the uphill slope of a valley, connected in an L shape.
None of them faced the road on their west and windy side. Instead they faced south and east, creating a protected barnyard, a sun pocket.
In the middle, protected from storms and wind, was the corn crib. Other farm buildings repeated the pattern, facing south, no doors on the west.
The main barn also had a door to the north, directly across from the one facing south. It fronted the farm road and looked at the house across the way. Two doors across from each other allowed for easy moving of machinery, ventilation and threshing. A north facing door was for bringing in hay and grain on the shady side of the barn in the summer.
After we had climbed up to and down from the rafters, Dan McKeen (who then owned Green Mountain Timber Frames) handed me prints o f the measured frame.
To have a sense of the building I checked some of the dimensions. The framers really did make his barn 30'-1" wide. He also made it 42'-6" long.
Why those dimensions? Laurie Smith, the English Geometer, suggested that a layout using the diagonal of the square was the reason.
The diagram shows how a framer would have used that set of proportions (which is the square root of 2) to layout the floor. This is easily drawn.
The rest of the barn frame comes directly from this diagram .
Both the extra inch and the square root are indications that the master carpenter for this barn used geometry to determine its size and framing. The ruler the carpenter used was not accurate by today's standards. Because he used Practical Geometry for his layout - proportions and relationships between parts, not fixed dimensions - it didn't matter.
The second diagram shows the floor plan of the barn.
The height of the new rectangle on the end of the square was a good height for the barn wall. So the framer drew a square in each corner. Using the diagonals for those squares he swung an arc on both sides. Where they met marked the ridge for the roof.
I have drawn the diagram as if the framer used the barn floor for his layout. Carpenters today use the floor of a house to layout the walls and the rafters for the roof above, so this is a reasonable assumption.
The measured drawings of the barn show how the diagrams were applied to frame the west end wall.
The red X on the right is the diagonals of the original square. The DASHED LINE is the arc of the diagonal locating the ridge.
The green DIAGONAL of the SQUARE on the left is cut by the green ARC of the length of the square. That intersection is the location of the left interior post.
The east end uses the same geometry as the west end.
Here is the diagram for he diagonal cut by the arc. It is easy to draw and based on dimensions already being used by the framer. Locating the posts is straight forward and simple, easy to do with a straight edge, some twine and a way to hold the twine taut.
The north and south walls also use matching diagrams.
Shown here is the north wall. The RIGHT SIDE matches the layout of left end of the west wall shown above: the divided by its DIAGONAL AND ARC INTERSECTION,.
Then comes the SQUARE door opening; its lintel determined by the INTERSECTION OF THE TWO ARCS of the square.
The left side was divided in half as shown by the DIAGONALS.
Note that the braces and the poles are also located using the same geometry: just turn the diagram above upside down. The diagram here shows all 4 arcs within the square.
Green Mountain Timber Frames website is https://www.greenmountaintimberframes.com/
The measured drawings used here were produced by James Plastteter in May 2014. Platteter is a master furniture maker. His website is down, but his fine work can be seen by searching by his name.