A classical problem in homogeneous Diophantine approximation can be modeled as follows: When a fixed length is repeatedly laid off on the circumference of a circle, which integer multiples of the length come close to the starting point? This is changed to an inhomogeneous problem by asking which integer multiples come close to a fixed generic point on the circumference (not the starting point). For many applications the techniques used to solve these problems are as important as the results themselves. Continued fractions have been successfully applied to homogeneous problems since the nineteenth century, and sixty years ago a promising algorithm for inhomogeneous problems was introduced. However, it was infeasible because of the amount of computation required. In ongoing collaboration with Richard Bumby (Rutgers), we use advances in both the homogeneous theory and symbolic computation to better understand and simplify this algorithm.