with Drew Nucci
and Joey Reich
Week 2: (6/20 – 6/24)
Believe it or not . . . Geometry predates textbooks. In fact, one could argue that it predates numbers. Geometry is nothing less than the most essential manifestation of human reason. Kant wrote that our understanding of time and space is actually instinct!
Despite the fact that many associate geometry with something they learned from a textbook, geometry was originally written by the Great Minds, and we suggest that it is best learned from them.
In this course, we will dive in deeply to the writings and propositions of the following authors: Euclid, Lobachevsky, DesCartes, Apollonius, and Newton. We plan to spend a day on each, both reading and delving into their demonstrations and language. Not only is this mentally stimulating and challenging to us, it becomes a compelling teaching methodology as well. You’ll learn for yourself, but then also have a great deal to take back to your classroom.
You will not need to have read these works ahead of time, there will be plenty of time built in for reading in the beauty of Santa Fe and northern New Mexico. We also hope to do a few hikes like those at Kasha Katuwe and Ghost Ranch, and if we’re lucky, we may have a quantum physicist from Los Alamos National Labs join us as well to discuss geometry as an element of quantum physics. We hope you’ll come play!
Here are some things that 2015 participants had to say about the Great Books of Math course from which Advanced Geometry is derived:
- I have a long way to go; however, I feel that this course has given me the basis of beginning more in-depth study/work on Euclidean geometry.
- This course has changed my perspective on the basic foundations we teach. I want to change up Honors Geometry to truly make it a course where the focus is how to think logically rather than the coverage of content.
- I will definitely incorporate parts of these readings in my classes, especially the Euclid, and then seek other reading for myself and my students.