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, May 2, and will cover chapter 3 (from the material on congruence) through chapters 5, and 6 (through Proposition 6.4).

• 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.
  • Be able to state the major theorems and axioms we have covered so far.  Notice that this includes
  • The axioms of continuity
  • Definitions of alternate interior angles and exterior angles
  • Saccheri and Lambert Quadrilaterals
  • Convex quadrilaterals
• 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.
  • Know the equivalents of the parallel postulate (and proofs which have been presented).
  • Know the other major theorems of these chapters, including the exterior angle theorem, the alternate interior angle theorem, the measurement theorem, the theorems relating angles to sides of triangles and Saccheri and Lambert quadrilaterals, and the Saccheri-Legendre theorem.
• 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.
  • n particular, know the efforts of Wallis, Saccheri, Clairaut, Proclus, Lambert, and Legendre. and be able to describe the roles of Bolyai, Lobachevsky, and Gauss in the development of non-Euclidean geometry.

Please let me know if there are any questions. Many thanks!