Difference between revisions of "User:Tohline/2DStructure/ToroidalCoordinateIntegrationLimits"
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<table border="1" cellpadding="8" align="center"> | <table border="1" cellpadding="8" align="center"> | ||
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<th align="center"><font size="+1">Apollonian Circles (schematic)</font><p></p> | <th align="center" colspan="2"><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> | (see also [https://en.wikipedia.org/wiki/File:Apollonian_circles.svg Wikipedia's Apollonian Circles])</th> | ||
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[[File:Apollonian_myway4.png|300px|Apollonian Circles]] | [[File:Apollonian_myway4.png|300px|Apollonian Circles]] | ||
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[[File:Apollonian_myway5.png|300px|Apollonian Circles]] | |||
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<th align="center" colspan="2"><font size="+1">Quantitative Illustration of Employed Toroidal Coordinate System</font></th> | |||
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[[File:TCoordsE.gif|300px|Diagram of Torus and Toroidal Coordinates]] | [[File:TCoordsE.gif|300px|Diagram of Torus and Toroidal Coordinates]] | ||
Revision as of 23:39, 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
| Apollonian Circles (schematic) (see also Wikipedia's Apollonian Circles) | |
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| Quantitative Illustration of Employed Toroidal Coordinate System | |
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See Also
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© 2014 - 2021 by Joel E. Tohline |