Si-ci-spiral

A plane curve whose equation in rectangular Cartesian coordinates $(x,y)$ has the form

$$x=\operatorname{ci}(t),\quad y=\operatorname{si}(t),$$

where $\operatorname{ci}$ is the integral cosine, $\operatorname{si}$ is the integral sine and $t$ is a real parameter (see Fig.).

<img style="border:1px solid;" src="https://www.encyclopediaofmath.org/legacyimages/common_img/s084980a.gif" />

Figure: s084980a

The arc length from $t=0$ to $t=t_0$ is equal to $\log t_0$, and the curvature is equal to $\kappa=t_0$.

References

[1]	E. Jahnke, F. Emde, F. Lösch, "Tafeln höheren Funktionen" , Teubner (1966)
[a1]	M. Abramowitz, I.A. Stegun, "Handbook of mathematical functions" , Dover, reprint (1972)