As a kid I would play pétanque, a game of reflections, with hollow metal balls (or boules) with circular grooves carved to the side of the balls.
Each player had their own boules that could only be distinguished from each other by the number of adjacent circular grooves. There were at least one, two and three-circle boules, where the circle groups were replicated four times around four node-points inside the boule.
As it happens, a rather similar feature is also true for the unit spheres of reflection, as is illustrated in this rotating 3D model:
The only difference is the location of the nodes and the angle and number of the rings. But the general shape is definitely recognized as a pétanque boule. While it might not be obvious to you, dear reader, this new model of reflection means that the B-node in the picture is the CenterPoint of two grazing orthogonal grazing vectors. The image also means that what I have called grazing isn’t really grazing at all. Rather, there must be a distance between the two kaus flying past each other. So, perhaps I should change the term grazing to flyby.
I might not have emphasized this in my last post, but this new realization is quite a large break from the old model regarding its mathematics. This means that I need to redo the equations once again. This might be a quick task, or I might need to work on it for who knows how long. I’ve been so confident that the final solution is just around the corner for so long, that I won’t be making such promises anymore, even though I definitely feel like it.
P.S. The 3D model above is a ‘cheat’. I took the old model and just added a hinge angle without increasing the size of the unit sphere. This means that the model is only valid as an illustration.
Comentários