A closer look at the Schiefferstadt House practical geometry

Please see my update:  https://www.jgrarchitect.com/2024/09/from-circle-to-pythagorean-triangle-via.html
I am not deleting this post because of my last paragraphs: I find the ways the Lines and layouts in Practical Geometry overlap need more consideration.* 

The lay out of the Schiefferstadt House,* uses a geometric pattern that was well known at the 1750's: the rule for drawing a square starting with a radius and a circle.

The diagram begins with the daisy wheel, scribed by a compass or a divider.  The 'petals' created by the 6 arcs of the radius around the circle make 6 points on the circumference.

The length of the radius for the circle is the width of the house.

 

 

 

When those points of the daisy wheel are joined they create Lines - dashed lines in the diagram. (Basic Euclidean geometry : 2 points are required to create a Line.)  The arcs of the radii cross those Lines to lay out a square. **

When one point of the divider, still opened to the width of the radius of the circle, is set on each of the 2 upper corners of the square, and the arcs swung, the arcs cross the circumference at the top of the circle.  Stepping off the radius around the circumference, will locate 6 more points.  All 12 points are equidistant from each other; all can be used for layout and design.

There is also a short cut to those upper 2 points; the place where the arcs cross the daisy wheel petals are points. 2 points = a Line. That Line extended is the same Line shown in my next diagram.  

 

The carpenter of the Schiefferstadt House could have used this geometry to step off  a rectangle about 18 units wide x 26 units long.  If his compass was open to a 2 ft span, the floor plan would have been 36 ft.wide  x 52 ft long. He would have trued his rectangle by checking that his diagonals matched, just as builders do today.

*

However the carpenter could also have used the square and its diagonal to lay out the plan. Those arcs would cross the circumference at the same place (dashed line), but they would cross the vertical lines of the rectangle about one unit higher than if the 12 points had been used (see the points where the dashed and red lines cross the circumference).  

This would make the floor plan 36 ft wide x 54 ft long. That's not much longer,  probably of little consequence to the design. However if the mason and the the framer were not using the same geometric progression (both using the first diagram or both using the second) the stone foundation and the interior wood frame would not have fit together. 

 

The drawings made c. 1978 for the restoration of the Schiefferstadt House may give me more information. The Frederick County Landmarks Foundation is sending prints. 

I will be looking for the simplest and quickest layout. I find that a builder tends to use the same same geometric progression for his plans and elevations. The geometry is one of his tools. The repetition of one pattern and one unit of measurement would be efficient and leave fewer chances for mistakes.  

If another layout is introduced it is usually the work of a craftsman whose work comes later - the finish carpenter adding a mantle, or the mason building a firebox and flu. Each might prefer a different system.

* The Schiefferstadt House, Frederick, Maryland, built in 1755, owned by The Frederick County Landmarks Foundation.  See my previous post for the geometry of the floor plan: https://www.jgrarchitect.com/2024/07/the-geometry-of-schiefferstadt-house.html

 

**2  basic practical geometry diagrams:

The diagram laying out how the radius of a circle can become the side of a square.

 Audel's Carpenters and Builders Guides , published in 1923, shows this diagram.

100 years ago, this geometry was common and practical knowledge.