Difference between revisions of "User:Tohline/2DStructure/ToroidalCoordinateIntegrationLimits"
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==Preamble== | ==Preamble== | ||
Some useful figures: | Some useful figures: | ||
* | * | ||
* [https://upload.wikimedia.org/wikipedia/commons/b/b2/Apollonian_circles.svg] | * [https://upload.wikimedia.org/wikipedia/commons/b/b2/Apollonian_circles.svg] | ||
<table border="1" cellpadding="8" align="center"> | <table border="1" cellpadding="8" align="center"> | ||
<tr> | <tr> | ||
<th align="center"><font size="+1">Apollonian Circles (schematic)</font><p></p> | |||
(see also [https://en.wikipedia.org/wiki/File:Apollonian_circles.svg Wikipedia's Apollonian Circles])</th> | |||
<th align="center"><font size="+1">Figure 2</font></th> | <th align="center"><font size="+1">Figure 2</font></th> | ||
<th align="center"><font size="+1">Figure 3</font></th> | <th align="center"><font size="+1">Figure 3</font></th> | ||
</tr> | </tr> | ||
<tr> | <tr> | ||
<td align="center"> | |||
[[File:Apollonian_myway4.png|300px|Apollonian Circles]] | |||
</td> | |||
<td align="center"> | <td align="center"> | ||
[[File:TCoordsE.gif|300px|Diagram of Torus and Toroidal Coordinates]] | [[File:TCoordsE.gif|300px|Diagram of Torus and Toroidal Coordinates]] | ||
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</tr> | </tr> | ||
</table> | </table> | ||
=See Also= | =See Also= | ||
Revision as of 01:39, 9 November 2015
Toroidal-Coordinate Integration Limits
In support of our accompanying discussion of the gravitational potential of a uniform-density circular torus, here we explain in detail what limits of integration must be specified in order to accurately determine the volume — and, hence also the total mass — of such a torus using toroidal coordinates.
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Preamble
Some useful figures:
| Apollonian Circles (schematic) (see also Wikipedia's Apollonian Circles) | Figure 2 | Figure 3 |
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![[1]](https://upload.wikimedia.org/wikipedia/commons/b/b2/Apollonian_circles.svg){kind=link}
See Also
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© 2014 - 2021 by Joel E. Tohline |