Math 300Third Hour 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 third hour exam for Math 300 will be held on Friday, April 27, and will cover chapter 3
(from the Saccheri-Legendre theorem) through chapters 5, 6, and 7 (through the
first few properties of the inverse of a point).
- Definitions:
- Be able to define the terms that appear (formal definitions). Be
able to describe (and use!) some of the features of hyperbolic geometry.
Be able also to describe some of the equivalents to Hilbert's parallel
postulate.
- Proofs
- Be able to construct proofs for fairly straightforward
statements. Be able to justify the steps
in a proof. A review of homework problems (including those done by your
colleagues in classroom presentations) would be the best
review for this part.
- Straight-edge and compass constructions: Be able to do the
constructions we did on Friday, April 13 (Klein and Poincaré
disk models). Please be sure to bring a straight-edge and compass
- Historical questions:
- Much of the material we have covered since the last exam has
been historical in nature. Please be prepared to discuss the
history of the parallel postulate and the discovery of non-Euclidean
geometry, including the various attempts and short biographies of
the notable figures in that history.
Please let me know if there are any questions. Many thanks!