One can choose an auxiliary circle formula_7 (the pink circle in the figure) such that each of the infinitely many circles decomposing the torus passes through a point of formula_7. This auxiliary circle is said to "parametrize" the circles of the decomposition, meaning there is a correspondence between them and points of formula_7. The circle formula_7 is more than just a list, however, because it also determines how these circles are arranged on the torus. This auxiliary space plays an important role in the SYZ conjecture.