Acknowledgements, and How to Read Analytic Euclidean Foundations

If you've already gone through the basics (lines/distance, angles, and perpendiculars)...

... then you may have noticed that a lot of the topic titles came with the caveat "Intuition". This is because we had to make a lot of assumptions along the way, to help you build as much geometric intuition as possible, without worrying too much about the details.

If you're interested in the foundations of geometry---the "how can we justify our intuition?"---then this section (Modern ($\mathbb{R}^2$) approach to foundations) is just for you. Our approach is largely inspired by Kiran Kedlaya's excellent open-source geometry textbook, Geometry Unbound.

If you haven't gone through the basics, and just want a rigorous introduction to geometry...

... this section (Modern ($\mathbb{R}^2$) approach to foundations) is also perfect for getting you started. The main question is, how much rigor do you want?

• If you read all of this section, then you'll be pretty much completely "set" for the basics, in the sense that you'll have most of the necessary coordinate-based definitions/technology (e.g. the definition of a point, line, and circle in terms of coordinates). Also, if you read this section, some things like the Pythagorean theorem will seem really obvious to you when you encounter them in the basics---read on to see why!

• ... the caveat is that this section is really difficult to read if you don't have the intuition for what a point, line, circle, angle, etc. is. So we still recommend at least a skim through the basics before you attempt to go through this section.

Either way...

Good luck, and have fun!