The book that we are mainly using for this class is not the best book in the world. It's fine if you were only interested in very basic geometry,
but we are going to try and cover a lot of material in this class: breadth instead of depth. You can follow up with whatever topics you find
relevant, and hopefully you are all using the presentation portion of this class to expand your knowledge.
To supplement the existing data, I have posted some notes that I have either stolen from the internet, or Xeroxed from other books about geometry.
Lemme know which of these you find useful, and which could be replaced. Some of these will be helpful/necessary for your homework assignment.
Spherical 1 - This set of notes covers polygons on the sphere pretty well. It also talks about Hilbert's
axioms, which we really haven't talked about, but I found these to be useful notes.
Hyperbolic 1 - Solid discussion of hyperbolic geometry, although it tosses some differential
stuff in there as well. A good read overall.
Hyperbolic 2 - A very thorough discussion of geometric constructs, including distance, which may be useful
for your 4th homework.
General Non-Euclidean - Very useful set of notes talking about spherical and hyperbolic
geometries and the associated properties.
Distance Function - This is a section of a book talking
about the existence of distance functions and how they play a role with the Ruler Postulate.
Hyperbolic Ruler Function - This briefly introduces
non-Euclidean geometries and describes an appropriate distance function to map hyperbolic lines
to a coordinate system and satisfy the ruler postulate.
Saccheri Quadrilaterals - A quick intro to Saccheri
quadrilaterals, some of their basic properties, and why they may be useful in some of our proofs,
including the discussion of area.
Area Derivation - This goes over finite dissection,
and describes how we define area in Euclidean and Hyperbolic space without integrals.