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.

Apollonian Circles (schematic) (see also Wikipedia's Apollonian Circles)

Quantitative Illustration of Employed Toroidal Coordinate System

@@ Line 12: / Line 12: @@
 <table border="1" cellpadding="8" align="center">
 <tr>
-   <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>
-  <th align="center"><font size="+1">Figure 2</font></th>
-  <th align="center"><font size="+1">Figure 3</font></th>
 </tr>
 <tr>
@@ Line 21: / Line 19: @@
 [[File:Apollonian_myway4.png|300px|Apollonian Circles]]
 </td>
+<td align="center">
+[[File:Apollonian_myway5.png|300px|Apollonian Circles]]
+</td>
+</tr>
+<tr>
+  <th align="center" colspan="2"><font size="+1">Quantitative Illustration of Employed Toroidal Coordinate System</font></th>
+</tr>
+<tr>
 <td align="center">
 [[File:TCoordsE.gif|300px|Diagram of Torus and Toroidal Coordinates]]