Proves why the closed strand loops found in Celtic Art may be consistently interlaced, and explains how, by first making cuts in such strand configurations and then maneuvering and finally rejoining some or all of the strand ends, it is possible to produce all the forms of Celtic Interlaced Art. Consequently it gives both a formal mathematical basis for understanding the potential and limitations of the art form, and also a viewpoint from which to judge the relative merits of particular examples of the Art. -- AATA