The geometry of can be described in terms of lines through the origin. Every line through the origin in formula_39 is the solution set of an equation formula_40. The solution set does not change when formula_41 is rescaled, so the line only depends on the equivalence class <math> That is, the lines through the origin are parametrized by formula_21. Furthermore, every point formula_43 in formula_39, except for formula_45, lies on a unique line through the origin, specifically, the line defined by formula_46. The point formula_47, however, lies on every line through the origin. For this point, the equation formula_48 degenerates to formula_49. This is always true, so every formula_50 is a solution. Consequently the set may be described as the disjoint union of the set of lines through the origin. This is the same as the union of the lines through the origin, except that it contains one copy of the origin for each line. These additional copies of the origin are a copy of formula_21 and constitute the center circle of the Möbius band. The lines themselves describe the ruling of the Möbius band. This point of view on exhibits it both as the total space of the tautological line bundle formula_52 on formula_21 as well as the blow-up of the origin in formula_39.