In this exposition, we will discuss the classical problem in number theory, which is diophantine approximations. To state simply, given an irrational number, we want to find the best and as many rational approximation to it. Initially studied but Dirichlet, Hurewicz, Roth et al, we will see how can basic hyperbolic geometric tools and interpreting concepts in the right way can lead to a more geometric interpretation of these results. There is also, an intricate relationship of diophantine approximations of irrational number with degenerate quadratic forms, which time permitted will also be discussed in brief. The whole talk will be based on a recent article by Boris Springborn.