Sometimes the difference between procrastination and deep thought can be wafer thin. In my last post I said I was procrastinating in forming spacetime projections and giving each element a latter. The reason for this is that I need to figure out the equations for each element in each of the three spatial coordinates (x, y and z) and the only way to keep track of my shape is to letter each of the components.
While I was doing this lettering, I realized that I needed to scrap the circles depicting the surface of the unit sphere of reflection in relation to the vectors. Once I did this, I realized some of the vectors were hidden behind the circles. But it wasn’t until I’d given each existing vector a letter that I realized that I had missed some crucial vectors. These are the folding vectors that are orthogonal to the two red diagonal vectors.
When they’re added to the projections, they look like this:
They’re the blue and yellow vectors that form sharp angles with the green connection vectors in the x-y and x-z projections (left and middle in the above image).
And this is how the vectors of the unit sphere look in 3D:
With this model, I should be able to formulate equations for each element. However, I might still need a bit of procrastination to make sure that I haven’t forgotten anything.
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