The finding of accurate and useful approximations to implicitly defined surfaces has been a topic of study for many years. Within this topic, much work has been done on techniques which are numerical and which produce piecewise linear approximations (meshes). We give an overview of this history and present several new results. We present simple criteria for ensuring topological accuracy. We then describe an algorithm for finding such approximations which makes use of this criteria. This seems to be the first numeric algorithm developed without constraint on the number of dimensions.