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Si-ci-spiral

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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.).

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)


Comments

References

[a1] M. Abramowitz, I.A. Stegun, "Handbook of mathematical functions" , Dover, reprint (1972)
How to Cite This Entry:
Si-ci-spiral. Encyclopedia of Mathematics. URL: http://www.encyclopediaofmath.org/index.php?title=Si-ci-spiral&oldid=32696
This article was adapted from an original article by D.D. Sokolov (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article