Tuesday, October 3, 2023

Teaching Practical Geometry

 Several educators, curious about Practical Geometry, have asked me how I would share this geometry in the classroom. This post is an introduction to how I would begin.

In September, 2023, I presented 3  workshops at IPTW, the International Preservation Trades Workshops.* The last day was open to the public. About 10 people, aged 10-70+, came to learn about Practical Geometry. Some had never held a compass.  

Here is what we did:

We drew circles with compasses. Then we divided the circumferences into 6 equal parts and connected the points to make rectangles and squares. We used no numbers. 


We  explored the  design and layout tools a carpenter would have had before the Industrial Revolution: the compass, a line and a scribe. We talked about how those tools were used and are still used. We compared cubits (the length from your elbow to your longest finger).  We set carpenter's dividers for a day's work by the radius or the diameter of a daisy wheel. One of the participants taught the others how to snap a chalk line.

I brought my daisy wheel with me. It was scribed into a 9 ft tall board which was once sheathing on Vermont barn, c.1780. The barn was deconstructed about 10 years ago. The deconstruction contractor gave me the board.



I showed them the floor plan of one of the early Virginia folk houses recorded by Henry Glassie,** which used the geometry we had drawn. 




I shared a few pictures including this house whose plan we had just laid out.  



That image introduced the class to the chimney wing. Its plan would have used the 3/4/5 rectangle to make sure the wing was parallel to the house so that all the roof framing could be cut the same length.  




I showed the group a Menagery, a retreat intended for an English gentleman's estate, designed by James Gibb's ***, c. 1720.  



 The wings are laid out in the same way, using the 3/4/5 rectangle. Here it is because the rough laid stone on the exterior would have made an accurate layout and construction difficult.


Then the class learned about the 'star', the Lines, in the center of the Menagery. Those are also the lines on our cellphones which help us edit images, known by artists as the Rule of Thirds.  

Here is the geometry: the diagonal of the square and the Lines from the ends of one side (the corners) to the middle of the opposite side. The  pattern is turned 4 times.



Where the lines cross are points. 2 points connected are a line. That line is always straight.

Here, the points divide the large square into 9 small squares - the diagram used on cellphones - or 3 equal rectangles.

There are also 4 squares within the large square. If their diagonals are drawn, the large square can be divided into 16 small squares or 4 equal rectangles.


The Lines on the elevation for this brick house tell the mason where the sides of the door and window openings are. On the plan the Lines show the fireplace edges and the placement of the interior walls. 

The drawing is Plate 56 in Owen Biddle's pattern book, The  Young Carpenter’s Assistant,  published in 1805, by Benjamin Johnson, Philadelphia.





 I ended with these Lines in Sebastiano Serlio's Book I, c. 1540. It explains where to place a door in a castle wall. He ends Book I: On Geometry, " However, honest reader, although the things resulting from the various intersections of lines is infinite, to avoid being long-winded I shall come to an end."


This was more than enough for one 75 minute session. 

Several shorter lessons would have been easier for everyone. There was very little time for questions, more examples, or in-depth understanding.  


For more information: In 2020,  I wrote 7 posts entitled 'Lessons' for students of all ages. https://www.jgrarchitect.com/2020/04/lessons.html .

*The 25th International Preservation Workshops were held this year in Frederick, MD, at the Hargett Farm which will become the Historic Preservation Trade Center for the National Park Service.          See the Preservation Trades Network website, ptn.org, for more information.

** Henry Glassie,. Folk Housing in Middle Virginia, U of Tennessee Press: Knoxville, 1979

*** James Gibbs,  Book on Architecture, London, 1728, Dover reprint

**** Sebastiano Serlio . On Architecture, Lyon, France 1530, translated in1611,  on-line and translated by Vaughan Hart and Peter Hicks, 1996, Yale University Press, New Haven

To read more about this diagram see https://www.jgrarchitect.com/2022/10/serlios-lines.html 


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