Great circles around a point
Creating bench points
If two electrons follow great circle paths, they must physically create points that each converges in more often than alternate points.
Just like a teenager converges again and again at certain places in the house (their bed, the fridge, the couch in front of the TV monitor, the bathroom) more often than in other places, our electron comes back to the same places.
As an example, look at the converging great circles in the diagram. As electrons travel along a great circle path, they converge at the poles of the sphere. There is a superimposition and clustering of points where multiple great circles meet.
This is a function of the rules that the electron must follow (see last article). Thus, an electron seems like a traveler resting on a bench for a bit before getting up to check alternate paths. This is why I call them electron bench points.
Tetrahedral bench points
Let's look at the great circles that form along a tetrahedron. As I noted in the table in the last article, there are 6 possible geodesic paths.
The great circle forms along each of the edges of the tetrahedron, such as that plane passes through the center of the sphere. In the attached diagram, we have shown only three of the great circles each encircling one edge (to simplify the diagram). One can see from the diagram that one of the vertices (the top right one) has a convergence of 3 arcs at that point.
If all 6 arcs were drawn, we can predict that each of the 4 vertices of the tetrahedron will have a convergence of three arcs (note that three edges come together at each of the 4 vertices).
great circles around tetrahedron
Favorable electron bench points
As electrons follow the rules outlined in the last article (far away from each other, equidistant, shortest distance path, and minimal number of paths), they create a physical reality of positions that they converge in.
However, this does not tell the whole story! While those electron bench points are frequented spots in an electron's travels, there is another wrinkle to bench points when two or more atoms come together.
Some bench points are more favorable than others. Not all electron bench points are created equal.
Picture credits:
- Karl Horton. Geomag tetrahedron inside cube; 3/4" balls for steric issues and little wafer thin magnets inserted into the tetrahedral sides to make everything line up, uploaded on April 27, 2007.
- Grafixo. Sketches of great circles, in a longitudanal direction, Uploaded Nov 2021.
- Grafixo. Three great circles around tetrahedron, uploaded Nov2021.