Michael N's Spiral Ribbon:

This space curve was produced using the following Maple commands:

> x:=rho*t*cos(t);
> y:=rho*t*sin(t);
> z:=2*t/Pi;
> rho:=2+sin(t^2);

                          x := rho t cos(t)


                          y := rho t sin(t)


                                     t
                             z := 2 ----
                                     Pi


                                          2
                          rho := 2 + sin(t )

> with(plots):
> spacecurve([x,y,z],t=0..5*Pi,numpoints=1000,
>  axes='NORMAL',orientation=[75,45],thickness=2);