# Books on geometric transformations and/or analytic geometry?

I've been looking to expand my knowledge in geometry as it's not covered in my undergraduate curriculum.

For some reason I'm repelled by the classical approach (hopefully it will pass) as I feel it's not very connected to what we study but I could be wrong as I've only began recently.

Recently, in my "intro to proofs" course we studied plane isometries from a classical approach, and found it piqued my interest. I assume it has a modern treatment somewhere and generalizations?

Thus, I'm looking for literature involving:

• Analytic Geometry (formal treatment of $n=2$ and $n=3$ would suffice). Atleast containing derivations of conics, quadratic surfaces, vector treatment of plane/space geometry. (to my understanding it's sometimes studied in highschool, perhaps there's a treatment an undergrad would enjoy?).
• Transformations(*) and their derivations in euclidean space such as dilations, rotations, reflections, shear etc from coordinates point of view. Their derivations using matrices or complex numbers (as mentioned in wiki articles).

(*) Linear Algebra books which contains these applications in geometry are acceptable. I have browsed the table of contents of several reccomended introductory books on linear algebra but they don't seem to cover the geometric perspective. Correct me if I'm wrong.

Edit: One book is out of reach, the other seems above my current level, so I've changed the requested literature slightly.

• From your second bullet, it seems you should pick up any book on linear algebra. I'm pretty sure there are numerous lists of books on linear algebra on this site already. – rschwieb Jan 10 '14 at 15:32
• The transformations I'm refering to are not necessarily linear, and I haven't seen these subjects in the tables of contents of some LA books. could you be more specific? – user7610 Jan 10 '14 at 15:38
• OK, I understand :) But you do realize that dilations, rotations, reflections and shear are all linear transformations? Maybe you are more interested than you previously thought. – rschwieb Jan 10 '14 at 15:47
• I'm indeed interested, but to my knowledge (haven't took LA yet) T(0)=0 for all Linear transformations, which is not always true in the ones mentioned here. – user7610 Jan 10 '14 at 15:52
• OK, I take it you are defining them about arbitrary points in space. This means that they are the composition of a linear transformation and a translation, so while not strictly linear themselves they're still well within the realm of linear algebra. You might look up affine transformation article to see how matrices are used to encode these linear-plus-translation transformations. – rschwieb Jan 10 '14 at 15:57