This is a topic that definitely needs an Introductory section, Intermediate section, etc. Defining a circle from the get-go in terms of a locus on points is going to send many middle school (and even some high school) students running for the hills.--MCrawford 18:39, 19 June 2006 (EDT)

Planar is important, otherwise you're definiting a sphere. DPatrick 17:36, 30 June 2006 (EDT)