UPDATE: I have more or less finished the first three parts now and the last part is well underway. I am trying my best to get it all finished by the end of this year. I may miss that target, but I don't think I will miss it by too much. Anyway, I am not sure it makes sense to offer these files on a lesson-by-lesson basis anymore-- there are just too many of them. It is probably more convenient to have it all available in larger batches. Here are the three parts done so far:
I. Neutral Geometry
II. Euclidean Geometry
III. Euclidean Transformations
This is my forever-in-progress geometry book. Eventually it will have four parts: neutral geometry, Euclidean geometry, Euclidean transformations and hyperbolic geometry. The first two parts are now done, and the third is in progress. Each of these large parts is divided into several more manageable lessons which are available below. I hope that the lessons have a light feel, so that they may be read in one sitting. To that end I have tried to keep the discourse casual (maybe too casual), and loaded nearly every page down with pictures that I hope (1) clearly illustrate the situation and (2) look cool, so that you will be enticed to keep on reading. At the same time, this is serious stuff-- I have tried to develop the subject systematically and thoroughly.
I am not sure if this will ever be published. At the least, I would like to get it out to e-reader devices at some point (they would have to be color of course), but right now mathematics is in a sorry state in the EPUB format. Looking at the similarly sorry state of math on the web does not give me much hope either. So for now all I can do is make the PDFs available right here:
The Lessons
I won't maintain these individual lessons anymore, but they have been up for a long time, so I am leaving them up for now.
0. Axioms and Models
1. Incidence and Order
2. Angles and Triangles
3. Congruence I
4. Congruence II
5. Congruence III
6. Shorter and Longer
7. Distance and Length
8. Angle Comparison
9. Angle Measure
10. Triangle Measurements
11. Polygons
12. Quadrilaterals
13. The Parallel Axiom
14. Parallel Projection
15. Similarity
16. Circles
17. Circumference
18. Constructions
19. Concurrence I
20. Concurrence II
21. Concurrence III
22. Trilinear Coordinates
23. Analytic Geometry
24. Isometries