Geometry as Design

At the PTN Workshops last summer I tried to teach geometry in construction. I assumed most people had an understanding of geometry and facility with a compass. 
I was wrong.

This year I have been 'practice teaching' with students as my guides.



This year I taught children, teenagers and adults how to use a compass. 
How it opens, how it twirls, how to keep it steady.




Everyone needed these basic skills before I could begin to help them understand the science and art of geometry, never mind how it was used to frame a building.







I thought people knew this, like the ABC's. I thought it was taught in schools, but I had teachers practicing and asking for help along with the students.





Kids and adults responded in the same way, with awe and amazement, joy and laughter - with lots of  enthusiasm.








When the children realized they could make a star by connecting the 6 points on the perimeter of the circle, they had to show me how! tell me what I should connect next!


They had magnetic tessellation blocks for exploring.

With teenagers and adults real building elevations worked best. Most of my students know the Bennington Old First Church. Since good measured drawings of the church exist, I used those.



I began by asking the students to draw in the floor line, right at the bottom of the doors. This would have been where the framer began his layout, but I didn't tell them. I have found that interesting knowledge is - at this point - extraneous information.



  
I asked them to draw diagonals across the main body of the church - from the floor to the eaves. We noticed that the lines run up the sides of the roof over the main door and cross at its ridge. 


Then with a compass we found the radius and drew the circle.  This could take some time with people who were not familiar with compasses, radii, or circles. The discovery made the effort worthwhile.

I pointed out that if the roof lines extended through the steeple those lines would meet at the top of the circle  - the ridge of the roof.

 If time permitted we found the top and bottom points on the circle with the compass. We divided the circle beginning with a horizontal diameter to find  6 more points along the perimeter and saw how the facade of the church was laid out.
We added circles, as many as we had time for. Everyone kept their diagrams.





I am pleased with the interactions. All the students knew what they had drawn. Some could explore farther on their own. Even those who couldn't be rigorous had fun.

The adults had basic tools for real conversations about the use of geometry in design and construction.