An atlas for all plane curves

This note deals with an application of Voronin's universality theorem for the Riemann zeta-function ζ .In particular, we show that every plane smooth curve appears, up to a small error, in the curve generated by the values ζ(σ + i t) for real t, where σ ∈ (1/2, 1) is fixed.In this sense, the values of the zeta-function on any such vertical line provide an atlas for plane curves. Curves generated by the Riemann zeta-functionCurves appear naturally in life, perhaps not as ideal objects, as Euclid defined a line as "a length without breadth" in his Elements, but as orbits of planets, trajectories in physics and technology, or drawings in art.Taking into account their variety, it might be surprising that one can find them all realized in a single curve.Following Tolkien, we may state this also as a "Lord of the Curves" poem: