Dividing the numbers $0, 1, 3, 9$ by $3$ and taking square roots gives the values of—

Dividing $0,1,3,9$ by $3$ gives $0,\tfrac13,1,3$, and their square roots are $0,\tfrac{1}{\sqrt3},1,\sqrt3$ — exactly $\tan 0^\circ,\tan 30^\circ,\tan 45^\circ,\tan 60^\circ$. This is the standard memory device for the tangent values at the special angles.