MATH32051HYPERBOLIC& Geometry20th& Jan& 20201.(I)& & Recall& That& A& Straight& Line& In& R2& & Is& Given& By& The& Equation& Ax+By& +C =& 0,& A,B,& C& ∈ R. & Show& That This& Equation& Can& Be& Written& In& The& Form. Βz + Βz +& &

MATH32051HYPERBOLIC Geometryjanuary 20221.(I) Letprove That Γ Is A Subgroup Of M¨Ob(H).(You May Use Facts From The Course About Composing M¨Obius Transformations And Matrices Without Proof, Provided That You State Them Clearly.)& & [10 Marks]2.(I) State, Without Proof, The Gauss-Bonnet Theorem