Draw a straight line through u and through the point on the sphere that represents | ↓ ↓ ⟩ . (Let (0,0,1) represent | ↑ ↑ ⟩ and (0,0,−1) represent | ↓ ↓ ⟩ .) This line intersects the sphere at another point besides | ↓ ↓ ⟩ . (The only exception is when u = ∞ ∞ , i.e., when α α = 0 and β β ≠ ≠ 0 .) Call this point P. Point u on the plane z = 0 is the stereographic projection of point P on the Bloch sphere. The vector with tail at the origin and tip at P is the direction in 3-D space corresponding to the spinor | ↗ ↗ ⟩ . The coordinates of P are