Center-to-Center Reflection

After the realization that for a fleeting instance during grazing, four elementary particles of energy (kaus/dots) lie on a common plane (in the Most Important Angle -post), I’ve been mulling over the exact geometry of the reflection based on this observation.

Once again, I’ve been looking at the basic shape and trying to find additional hints on its geometry. You see, the shape isn’t 100 % accurate. It has certain clear imperfections that relate to the guesses I’ve made on the rather complex shape that haven’t been perfect. But having a shape allows me to play with it.

So, what have I found now? I realized something so obvious that you’d be amazed that I hadn’t done it before. I realized that you could draw an orthogonal vector from the center of the (yellow) grazing vector to the center of the (imaginary) red vector ‘connecting’ two neighboring reflecting dots. As I’ve mentioned before, the two dots on either sides of this vector are separated by a gap, so this vector is just a geometric tool.

Here is what the (yellow) orthogonal vector looks like in a rotating 3D model:

If you look at the model closely, these vectors come in pairs, where one vector starts at the center of the one cross connecting four kaus and the other vector end in the center of the other cross. Both of these vectors mark the exact path of the center point of two neighboring kaus. This also means that of the four central vectors depicted in the model above, one pair is continuous (i.e. one vector being parallel to the one after it), whereas the other pair experiences reflection: that is the center point of the pair of dots is being reflected at the center of the central cross.

So, what does all this mean? I’m not that far, yet. In short, it means that I should be able to draw the accurate model of reflection (and define the accompanying equations) pretty soon. However, as you might see from the wonky nature of the model above, pretty soon isn’t the same as now.

While it seems I’m really close to the final solution, I’ve been saying the same thing for too long. Who knows: perhaps there’s all sorts of revelation left before I reach the final truth. But if I was a guessing man, I’d say there’s a good chance that I’ll be able to formulate the accurate equations for reflection within a week. I’m just hoping these aren’t one of those famous last words…