Cassels' theorem on small zeros of quadratic forms revisited

We give an overview of classical and recent results related to the famous statement by Cassels concerning small zeros of isotropic quadratic forms. In particular we discuss new theorems on intrinsic rational approximation on $n$-dimensional sphere by Kleinbock and Merrill and the generalizations by Fishman, Kleinbock, Merrill and Simmons. We will show that these results easily follows from Cassels' theorem.