Math 342
Modern Geometry II
Informal Assignment 1: 450 degree cone

Begin to develop the geometry of the 450 degree cone, by doing the following:  

  1. Give a workable definition of what it means for a line to be straight on any surface.
  2. Use your definition to explain which lines are straight on the surface of a 450 degree cone.
  3. Explain which of Euclid's five postulates are true on the 450 degree cone using the straight lines you identified in part 2.  Also evaluate Postulate 1': "Two points determine a unique straight line."  For each postulate, you should explain whether it is true or false, and justify your answer.