I was doing good at school in plane geometry and trigonometry - especially in geometric proofs like proving the equality of two line segments or two angles - more than I was doing in analytic geometry.
I am considering doing research in mathematics to be my career (and my life) someday. and I am wondering about the most interesting research area for me.
What I am asking about is :
Is there still open research fields in plane geometry or Euclidean geometry? Or this area is considered to be fundamentals that are already investigated enough?