Difference between revisions of "Si-ci-spiral"
From Encyclopedia of Mathematics
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| − | A plane curve whose equation in rectangular Cartesian coordinates | + | {{TEX|done}} |
| + | A plane curve whose equation in rectangular Cartesian coordinates $(x,y)$ has the form | ||
| − | + | $$x=\operatorname{ci}(t),\quad y=\operatorname{si}(t),$$ | |
| − | where | + | where $\operatorname{ci}$ is the [[Integral cosine|integral cosine]], $\operatorname{si}$ is the [[Integral sine|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" /> | <img style="border:1px solid;" src="https://www.encyclopediaofmath.org/legacyimages/common_img/s084980a.gif" /> | ||
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Figure: s084980a | Figure: s084980a | ||
| − | The arc length from | + | 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==== | ====References==== | ||
| − | <table><TR><TD valign="top">[1]</TD> <TD valign="top"> E. Jahnke, F. Emde, F. Lösch, "Tafeln höheren Funktionen" , Teubner (1966)</TD></TR></table> | + | <table><TR><TD valign="top">[1]</TD> <TD valign="top"> E. Jahnke, F. Emde, F. Lösch, "Tafeln höheren Funktionen" , Teubner (1966)</TD></TR> |
| + | <TR><TD valign="top">[a1]</TD> <TD valign="top"> M. Abramowitz, I.A. Stegun, "Handbook of mathematical functions" , Dover, reprint (1972)</TD></TR></table> | ||
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Latest revision as of 19:17, 11 January 2024
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) |
| [a1] | M. Abramowitz, I.A. Stegun, "Handbook of mathematical functions" , Dover, reprint (1972) |
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How to Cite This Entry:
Si-ci-spiral. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Si-ci-spiral&oldid=14835
Si-ci-spiral. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Si-ci-spiral&oldid=14835
This article was adapted from an original article by D.D. Sokolov (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article