This class is an introduction to Non-Euclidean Geometry and builds on the content of a standard High School Geometry course. To my knowledge, the material in this course is not part of any curriculum on the secondary or post-secondary level. It is the byproduct of my graduate work in Geometric Group Theory and spending many years teaching high school students. 

Offering material that is intuitive and accessible to teens, but also is beautiful and has deep mathematical roots has been a calling for me. I believe Kieran Egan said this best: "We represent the world to children as mostly known and rather dull. The opposite is the case: we are surrounded by mystery, and what we know is fascinating."

Class meetings will start with a discussion of ideas and discoveries from the week. We will then establish a common vocabulary and I will identify and discuss a clear area of inquiry for the next week. After class, I will distribute a summary of new material from the day and guiding questions that will build on these topics and encourage students to explore the material. 

As a nonstandard class, the primary goal is to foster creativity and exploration while adhering to a mathematically rigorous framework. Following the students' lead, I will guide the group deeper into topics they find interesting. This creates a positive feedback loop that rewards curiosity in a collaborative and supportive way. 

For an example of how our first lesson will start, review the following PDF:
https://divmath.org/files/GeoAdv.pdf