************************************ The start of a day-by-day plan for the remaining 5  classes,  prefaced by suggested reading for that day. Nov 22: [OLD PLAN] read on CP^1 [complex projective line] under `incarnations of the sphere' in the `lectures'. Read on the three reflections theorem : see this topic in the index of Stillwell's `The Four Pillars...'  Inversion through unit circle = (Stereo)(Reflec about equator)Stereo^{-1}.  Projective line = `space of fractions' Complex and real:  RP^1 \subset CP^1.  Homogeneous parameterizations; relation to stereo projections. Parameterizing all Pythagorean triples.    HW St 1. Where the matrices come from in linear fractional (=Mobius); Eigenlines = fixed points... time permitting:  Three reflections theorem. Classification of isometries and Mob transformations in terms of  fixed points. HW R1-R3. ******************** [NEW PLAN!] Replacement lecture! Isometries of the upper half plane. Why z -> 2z is an isometry. Def. of distance. Of isometry, in terms of `infinitesimal distance' (element of arc length). Recall logarithmic distance scale along y-axis. Comparison of distances and isometries for three models. K =0, K < 0 (hyperbolic), K > 0 (spherical). The two models of the sphere. HW St 1. Time permitting: three reflections theorem discuss HW R1-R3. ***************** Nov 25.  Continue reading on  the sphere and on  the hyperbolic plane: in Reader and in Stillwell's `The Four Pillars..'  Distance formulae for  sphere; HW Sph 1-3;  for the hyperbolic plane. Gauss Bonnet. The angle deficit formulae for areas. topics not covered from NOV 22 lecture Time permitting: go to [OLD PLAN] of Nov 22 HW GB1-2 Nov 27: forget it. No one will be around.  Thanksgiving is the next day.   Dec 5 makeup. Dec 2.  Gauss-Bonnet ct'd.  Loose ends  on HW and on lecture. Dec 4.  HW8 due.  Where we go from here.  Some on final exam expectations.  Dec 5.  6pm planned `final review' Dec 6.  Last class.  Other surfaces.  Higher dimensions. Closure. Dec 9. Final 12 -3