Final Exam Review
Disclaimer: I have attempted to be comprehensive in the following, but important items may have been omitted by mistake. If you see such an omission, please let me know, but you are responsible for all of the lecture material to date.
The final exam for this class will be at 8:00 AM Monday, May 12. It will be a comprehensive, two hour in-class examination.
Please be sure to bring a straight-edge and a compass to the exam.
In your review you should examine
There will be at least one and probably at least two (including the recent worksession) ruler and compass constructions on the exam.
Since the last hour exam we have discovered more about hyperbolic geometry, including discussions on the varieties of parallel lines and of the three models for hyperbolic geometry. We will have explored the Poincaré model to the extent of verifying the axioms of hyperbolic geometry (including, of course, neutral geometry), including the definition and properties of Poincaré distance, copying angles, and looked (more briefly) at inversions of circles and the verification of congruence axiom 6 (we skimmed over the details of CA6). We have discussed the Metamathematical Theorem, its proof and consequences. We have also discussed some of the foundational implications of the discovery of hyperbolic geometry (notably the material in Chapter 8.
Please let me know if there are any questions. Many thanks!