Homogeneous Interpolation and Some Continued Fractions
  We prove: if $d/m < 2280/721$, there is no curve of degree $d$ passing through $n = 10$ general points with multiplicity $m$ in $\bf{P}^2$. Similar results are given for other special values of $n$. Our bounds can be naturally written as certain palindromic continued fractions. 
Ivan Petrakiev
math.AG